Showing papers on "Coverage probability published in 2014"
TL;DR: In this article, the authors proposed a method to construct confidence intervals for individual coefficients and linear combinations of several of them in a linear regression model by turning the regression data into an approximate Gaussian sequence of point estimators of individual regression coefficients.
Abstract: Summary
The purpose of this paper is to propose methodologies for statistical inference of low dimensional parameters with high dimensional data. We focus on constructing confidence intervals for individual coefficients and linear combinations of several of them in a linear regression model, although our ideas are applicable in a much broader context. The theoretical results that are presented provide sufficient conditions for the asymptotic normality of the proposed estimators along with a consistent estimator for their finite dimensional covariance matrices. These sufficient conditions allow the number of variables to exceed the sample size and the presence of many small non-zero coefficients. Our methods and theory apply to interval estimation of a preconceived regression coefficient or contrast as well as simultaneous interval estimation of many regression coefficients. Moreover, the method proposed turns the regression data into an approximate Gaussian sequence of point estimators of individual regression coefficients, which can be used to select variables after proper thresholding. The simulation results that are presented demonstrate the accuracy of the coverage probability of the confidence intervals proposed as well as other desirable properties, strongly supporting the theoretical results.
892 citations
TL;DR: In this article, the authors proposed a hybrid intelligent algorithm approach to directly formulate optimal prediction intervals of wind power generation based on extreme learning machine and particle swarm optimization to estimate and quantify the potential impacts and risks facing system operation with wind penetration beforehand.
Abstract: Accurate and reliable wind power forecasting is essential to power system operation. Given significant uncertainties involved in wind generation, probabilistic interval forecasting provides a unique solution to estimate and quantify the potential impacts and risks facing system operation with wind penetration beforehand. This paper proposes a novel hybrid intelligent algorithm approach to directly formulate optimal prediction intervals of wind power generation based on extreme learning machine and particle swarm optimization. Prediction intervals with associated confidence levels are generated through direct optimization of both the coverage probability and sharpness to ensure the quality. The proposed method does not involve the statistical inference or distribution assumption of forecasting errors needed in most existing methods. Case studies using real wind farm data from Australia have been conducted. Comparing with benchmarks applied, experimental results demonstrate the high efficiency and reliability of the developed approach. It is therefore convinced that the proposed method provides a new generalized framework for probabilistic wind power forecasting with high reliability and flexibility and has a high potential of practical applications in power systems.
285 citations
TL;DR: This paper provides explicit finite-integral expressions for the coverage probability with ICIC and ICD, taking into account the temporal/spectral correlation of the signal and interference.
Abstract: Inter-cell interference coordination (ICIC) and intra-cell diversity (ICD) play important roles in improving cellular downlink coverage. By modeling cellular base stations (BSs) as a homogeneous Poisson point process (PPP), this paper provides explicit finite-integral expressions for the coverage probability with ICIC and ICD, taking into account the temporal/spectral correlation of the signal and interference. In addition, we show that, in the high-reliability regime, where the user outage probability goes to zero, ICIC and ICD affect the network coverage in drastically different ways: ICD can provide order gain, whereas ICIC only offers linear gain. In the high-spectral efficiency regime where the SIR threshold goes to infinity, the order difference in the coverage probability does not exist; however, a linear difference makes ICIC a better scheme than ICD for realistic path loss exponents. Consequently, depending on the SIR requirements, different combinations of ICIC and ICD optimize the coverage probability.
140 citations
TL;DR: New mathematical frameworks to the computation of coverage probability and average rate of cellular networks are introduced, by relying on a stochastic geometry abstraction modeling approach, and it is proved that coverage and rate can be compactly formulated as a twofold integral for arbitrary per-link power gains.
Abstract: In this letter, we introduce new mathematical frameworks to the computation of coverage probability and average rate of cellular networks, by relying on a stochastic geometry abstraction modeling approach. With the aid of the Gil-Pelaez inversion formula, we prove that coverage and rate can be compactly formulated as a twofold integral for arbitrary per-link power gains. In the interference-limited regime, single-integral expressions are obtained. As a case study, Gamma-distributed per-link power gains are investigated further, and approximated closed-form expressions for coverage and rate in the interference-limited regime are obtained, which shed light on the impact of channel parameters and physical-layer transmission schemes.
98 citations
TL;DR: In this article, it was shown that the confidence intervals for the regression coefficient have zero coverage probability asymptotically, and their predictive test statistic Q erroneously indicates predictability with probability approaching unity when the null of no predictability holds.
Abstract: Local to unity limit theory is used in applications to construct confidence intervals (CIs) for autoregressive roots through inversion of a unit root test (Stock (1991)). Such CIs are asymptotically valid when the true model has an autoregressive root that is local to unity (ρ = 1 + c/n), but are shown here to be invalid at the limits of the domain of definition of the localizing coefficient c because of a failure in tightness and the escape of probability mass. Failure at the boundary implies that these CIs have zero asymptotic coverage probability in the stationary case and vicinities of unity that are wider than O(n−1/3). The inversion methods of Hansen (1999) and Mikusheva (2007) are asymptotically valid in such cases. Implications of these results for predictive regression tests are explored. When the predictive regressor is stationary, the popular Campbell and Yogo (2006) CIs for the regression coefficient have zero coverage probability asymptotically, and their predictive test statistic Q erroneously indicates predictability with probability approaching unity when the null of no predictability holds. These results have obvious cautionary implications for the use of the procedures in empirical practice.
93 citations
TL;DR: This paper proposes a new method to construct approximate confidence intervals for the true prevalence when sensitivity and specificity are estimated from independent samples, and applies an adjustment similar to that described in Agresti and Coull (1998).
55 citations
TL;DR: The study gives insight into the conditions under which the statistical test can detect important inconsistency in a loop of evidence, and suggests that the test has low power for the ‘typical’ loop.
Abstract: The assumption of consistency, defined as agreement between direct and indirect sources of evidence, underlies the increasingly popular method of network meta-analysis. This assumption is often evaluated by statistically testing for a difference between direct and indirect estimates within each loop of evidence. However, the test is believed to be underpowered. We aim to evaluate its properties when applied to a loop typically found in published networks. In a simulation study we estimate type I error, power and coverage probability of the inconsistency test for dichotomous outcomes using realistic scenarios informed by previous empirical studies. We evaluate test properties in the presence or absence of heterogeneity, using different estimators of heterogeneity and by employing different methods for inference about pairwise summary effects (Knapp-Hartung and inverse variance methods). As expected, power is positively associated with sample size and frequency of the outcome and negatively associated with the presence of heterogeneity. Type I error converges to the nominal level as the total number of individuals in the loop increases. Coverage is close to the nominal level in most cases. Different estimation methods for heterogeneity do not greatly impact on test performance, but different methods to derive the variances of the direct estimates impact on inconsistency inference. The Knapp-Hartung method is more powerful, especially in the absence of heterogeneity, but exhibits larger type I error. The power for a ‘typical’ loop (comprising of 8 trials and about 2000 participants) to detect a 35% relative change between direct and indirect estimation of the odds ratio was 14% for inverse variance and 21% for Knapp-Hartung methods (with type I error 5% in the former and 11% in the latter). The study gives insight into the conditions under which the statistical test can detect important inconsistency in a loop of evidence. Although different methods to estimate the uncertainty of the mean effect may improve the test performance, this study suggests that the test has low power for the ‘typical’ loop. Investigators should interpret results very carefully and always consider the comparability of the studies in terms of potential effect modifiers.
54 citations
TL;DR: The main result is that the proposed modified Wald intervals maintain and exploit the type I error much better than the intervals of Agresti-Coull, Wilson, and Clopper-Pearson.
Abstract: The area under the receiver operating characteristic (ROC) curve, referred to as the AUC, is an appropriate measure for describing the overall accuracy of a diagnostic test or a biomarker in early phase trials without having to choose a threshold. There are many approaches for estimating the confidence interval for the AUC. However, all are relatively complicated to implement. Furthermore, many approaches perform poorly for large AUC values or small sample sizes. The AUC is actually a probability. So we propose a modified Wald interval for a single proportion, which can be calculated on a pocket calculator. We performed a simulation study to compare this modified Wald interval (without and with continuity correction) with other intervals regarding coverage probability and statistical power. The main result is that the proposed modified Wald intervals maintain and exploit the type I error much better than the intervals of Agresti-Coull, Wilson, and Clopper-Pearson. The interval suggested by Bamber, the Mann-Whitney interval without transformation and also the interval of the binormal AUC are very liberal. For small sample sizes the Wald interval with continuity has a comparable coverage probability as the LT interval and higher power. For large sample sizes the results of the LT interval and of the Wald interval without continuity correction are comparable. If individual patient data is not available, but only the estimated AUC and the total sample size, the modified Wald intervals can be recommended as confidence intervals for the AUC. For small sample sizes the continuity correction should be used.
54 citations
TL;DR: In this article, the authors compare several confidence intervals after model selection in the setting recently studied by Berk et al. [Ann. Statist. 41 (2013) 802-837], where the goal is to cover not the true parameter but a certain nonstandard quantity of interest that depends on the selected model.
Abstract: We compare several confidence intervals after model selection in the setting recently studied by Berk et al. [Ann. Statist. 41 (2013) 802-837], where the goal is to cover not the true parameter but a certain nonstandard quantity of interest that depends on the selected model. In particular, we compare the PoSI-intervals that are proposed in that reference with the "naive" confidence interval, which is constructed as if the selected model were correct and fixed a priori (thus ignoring the presence of model selection). Overall, we find that the actual coverage probabilities of all these intervals deviate only moderately from the desired nominal coverage probability. This finding is in stark contrast to several papers in the existing literature, where the goal is to cover the true parameter.
42 citations
TL;DR: The results of an extensive Monte Carlo simulation study demonstrate that the proposed kappa statistic provides consistent estimation and the proposed variance estimator behaves reasonably well for at least a moderately large number of clusters (e.g., K ≥50).
Abstract: Kappa statistic is widely used to assess the agreement between two procedures in the independent matched-pair data. For matched-pair data collected in clusters, on the basis of the delta method and sampling techniques, we propose a nonparametric variance estimator for the kappa statistic without within-cluster correlation structure or distributional assumptions. The results of an extensive Monte Carlo simulation study demonstrate that the proposed kappa statistic provides consistent estimation and the proposed variance estimator behaves reasonably well for at least a moderately large number of clusters (e.g., K ⩾50). Compared with the variance estimator ignoring dependence within a cluster, the proposed variance estimator performs better in maintaining the nominal coverage probability when the intra-cluster correlation is fair (ρ ⩾0.3), with more pronounced improvement when ρ is further increased. To illustrate the practical application of the proposed estimator, we analyze two real data examples of clustered matched-pair data. Copyright © 2014 John Wiley & Sons, Ltd.
41 citations
TL;DR: Two bias adjusted GEE estimators of the regression parameters in longitudinal data are obtained when the number of subjects is small, and both these methods show superior properties over the GEE estimates for small samples.
Abstract: Longitudinal (clustered) response data arise in many bio-statistical applications which, in general, cannot be assumed to be independent. Generalized estimating equation (GEE) is a widely used method to estimate marginal regression parameters for correlated responses. The advantage of the GEE is that the estimates of the regression parameters are asymptotically unbiased even if the correlation structure is misspecified, although their small sample properties are not known. In this paper, two bias adjusted GEE estimators of the regression parameters in longitudinal data are obtained when the number of subjects is small. One is based on a bias correction, and the other is based on a bias reduction. Simulations show that the performances of both the bias-corrected methods are similar in terms of bias, efficiency, coverage probability, average coverage length, impact of misspecification of correlation structure, and impact of cluster size on bias correction. Both these methods show superior properties over the GEE estimates for small samples. Further, analysis of data involving a small number of subjects also shows improvement in bias, MSE, standard error, and length of the confidence interval of the estimates by the two bias adjusted methods over the GEE estimates. For small to moderate sample sizes (N ≤50), either of the bias-corrected methods GEEBc and GEEBr can be used. However, the method GEEBc should be preferred over GEEBr, as the former is computationally easier. For large sample sizes, the GEE method can be used.
TL;DR: In this article, the authors considered interval estimation of the stress strength reliability in the two-parameter exponential distribution based on records and constructed Bayesian intervals, Bootstrap intervals and intervals using the generalized pivot variable.
Abstract: We consider interval estimation of the stress–strength reliability in the two-parameter exponential distribution based on records. We constructed Bayesian intervals, Bootstrap intervals and intervals using the generalized pivot variable. A simulation study is conducted to investigate and compare the performance of the intervals in terms of their coverage probability and expected length. An example is given.
TL;DR: In this article, the authors investigate the cost of using the exact one and two-sided Clopper-Pearson confidence intervals rather than shorter approximate intervals, first in terms of increased expected length and then the increase in sample size required to obtain a desired expected length.
Abstract: When computing a confidence interval for a binomial proportion $p$ one must choose between using an exact interval, which has a coverage probability of at least $1-\alpha$ for all values of $p$, and a shorter approximate interval, which may have lower coverage for some $p$ but that on average has coverage equal to $1-\alpha$. We investigate the cost of using the exact one and two-sided Clopper–Pearson confidence intervals rather than shorter approximate intervals, first in terms of increased expected length and then in terms of the increase in sample size required to obtain a desired expected length. Using asymptotic expansions, we also give a closed-form formula for determining the sample size for the exact Clopper–Pearson methods. For two-sided intervals, our investigation reveals an interesting connection between the frequentist Clopper–Pearson interval and Bayesian intervals based on noninformative priors.
TL;DR: A new formulation for the construction of adaptive confidence bands (CBs) in nonparametric function estimation problems, which have size that adapts to the smoothness of the function while guaranteeing that both the relative excess mass and the measure of the set of points where the function lies outside the band are small.
Abstract: This article proposes a new formulation for the construction of adaptive confidence bands (CBs) in nonparametric function estimation problems. CBs, which have size that adapts to the smoothness of the function while guaranteeing that both the relative excess mass of the function lying outside the band and the measure of the set of points where the function lies outside the band are small. It is shown that the bands adapt over a maximum range of Lipschitz classes. The adaptive CB can be easily implemented in standard statistical software with wavelet support. We investigate the numerical performance of the procedure using both simulated and real datasets. The numerical results agree well with the theoretical analysis. The procedure can be easily modified and used for other nonparametric function estimation models. Supplementary materials for this article are available online.
TL;DR: In this article, the authors evaluated the performance of the four most commonly used methods in practice, namely, complete case (CC), mean substitution (MS), last observation carried forward (LOCF), and multiple imputation (MI), and concluded that MI is more reliable and a better grounded statistical method to be used under MAR.
Abstract: Missing data can frequently occur in a longitudinal data analysis. In the literature, many methods have been proposed to handle such an issue. Complete case (CC), mean substitution (MS), last observation carried forward (LOCF), and multiple imputation (MI) are the four most frequently used methods in practice. In a real-world data analysis, the missing data can be MCAR, MAR, or MNAR depending on the reasons that lead to data missing. In this paper, simulations under various situations (including missing mechanisms, missing rates, and slope sizes) were conducted to evaluate the performance of the four methods considered using bias, RMSE, and 95% coverage probability as evaluation criteria. The results showed that LOCF has the largest bias and the poorest 95% coverage probability in most cases under both MAR and MCAR missing mechanisms. Hence, LOCF should not be used in a longitudinal data analysis. Under MCAR missing mechanism, CC and MI method are performed equally well. Under MAR missing mechanism, MI has the smallest bias, smallest RMSE, and best 95% coverage probability. Therefore, CC or MI method is the appropriate method to be used under MCAR while MI method is a more reliable and a better grounded statistical method to be used under MAR.
TL;DR: A fully Bayesian semiparametric method for the purpose of attenuating bias and increasing efficiency when jointly modeling time‐to‐event data from two possibly non‐exchangeable sources of information is proposed.
Abstract: Trial investigators often have a primary interest in the estimation of the survival curve in a population for which there exists acceptable historical information from which to borrow strength. However, borrowing strength from a historical trial that is non-exchangeable with the current trial can result in biased conclusions. In this paper we propose a fully Bayesian semiparametric method for the purpose of attenuating bias and increasing efficiency when jointly modeling time-to-event data from two possibly non-exchangeable sources of information. We illustrate the mechanics of our methods by applying them to a pair of post-market surveillance datasets regarding adverse events in persons on dialysis that had either a bare metal or drug-eluting stent implanted during a cardiac revascularization surgery. We finish with a discussion of the advantages and limitations of this approach to evidence synthesis, as well as directions for future work in this area. The paper’s Supplementary Materials offer simulations to show our procedure’s bias, mean squared error, and coverage probability properties in a variety of settings.
TL;DR: The Length/Coverage Optimal method as discussed by the authors is a variant of Sterne's procedure that minimizes average length while maximizing coverage among all length minimizing procedures, and it is superior in important ways to existing procedures.
Abstract: The problem of finding confidence intervals for the success parameter of a binomial experiment has a long history, and a myriad of procedures have been developed. Most exploit the duality between hypothesis testing and confidence regions and are typically based on large sample approximations. We instead employ a direct approach that attempts to determine the optimal coverage probability function a binomial confidence procedure can have from the exact underlying binomial distributions, which in turn defines the associated procedure. We show that a graphical perspective provides much insight into the problem. Both procedures whose coverage never falls below the declared confidence level and those that achieve that level only approximately are analyzed. We introduce the Length/Coverage Optimal method, a variant of Sterne's procedure that minimizes average length while maximizing coverage among all length minimizing procedures, and show that it is superior in important ways to existing procedures.
TL;DR: Bootstrap ensures an optimal coverage and should be preferred over parametric methods, and the stratification of "monolateral" prediction bands and intervals by age appears relevant for the correct classification of patients.
TL;DR: This paper presents a novel method for coverage hole detection with residual energy in randomly deployed wireless sensor networks by calculating the life expectancy of working nodes through residual energy and making a trade-off between network repair cost and energy waste.
Abstract: Coverage completeness is an important indicator for quality of service in wireless sensor networks (WSN). Due to limited energy and diverse working conditions, the sensor nodes have different lifetimes which often cause network holes. Most of the existing methods expose large limitation and one-sidedness because they generally consider only one aspect, either coverage rate or energy issue. This paper presents a novel method for coverage hole detection with residual energy in randomly deployed wireless sensor networks. By calculating the life expectancy of working nodes through residual energy, we make a trade-off between network repair cost and energy waste. The working nodes with short lifetime are screened out according to a proper ratio. After that, the locations of coverage holes can be determined by calculating the joint coverage probability and the evaluation criteria. Simulation result shows that compared to those traditional algorithms without consideration of energy problem, our method can effectively maintain the coverage quality of repaired WSN while enhancing the life span of WSN at the same time.
TL;DR: This paper uses a recursive method and the supplementary variable technique to develop the steady-state probabilities of down units at an arbitrary epoch, and an efficient algorithm is constructed to compute the Steady-state availability.
Proceedings Article•
29 May 2014TL;DR: In this article, the authors explore the degree to which this additional requirement of efficiency is satisfied in the case of Bayesian ridge regression; they find that asymptotically conformal prediction sets differ little from ridge regression prediction intervals when the standard Bayesian assumptions are satisfied.
Abstract: Conformal prediction is a method of producing prediction sets that can be applied on top of a wide range of prediction algorithms. The method has a guaranteed coverage probability under the standard IID assumption regardless of whether the assumptions (often considerably more restrictive) of the underlying algorithm are satisfied. However, for the method to be really useful it is desirable that in the case where the assumptions of the underlying algorithm are satisfied, the conformal predictor loses little in efficiency as compared with the underlying algorithm (whereas being a conformal predictor, it has the stronger guarantee of validity). In this paper we explore the degree to which this additional requirement of efficiency is satisfied in the case of Bayesian ridge regression; we find that asymptotically conformal prediction sets differ little from ridge regression prediction intervals when the standard Bayesian assumptions are satisfied.
Journal Article•
TL;DR: In this paper, the asymptotic distribution for the ratio of the sample correlations in two independent populations is established and the presented method can be used to derive the confidence interval and hypothesis testing for the ratios of population correlations.
Abstract: The asymptotic distribution for the ratio of the sample correlations in two independent populations is established. The presented method can be used to derive the asymptotic confidence interval and hypothesis testing for the ratio of population correlations. The performance of the new interval is comparable with similar method. Then the simulation study is provided to compare our confidence interval with Fisher Z-transform and Cauchy-transform methods. The proposed confidence set has a good coverage probability with a larger power.
TL;DR: In this paper, focused information criterion and frequentist model averaging are applied to post-model selection inference for weighted composite quantile regression (WCQR) in the context of the additive partial linear models.
Abstract: We study the focused information criterion and frequentist model averaging and their application to post-model-selection inference for weighted composite quantile regression (WCQR) in the context of the additive partial linear models. With the non-parametric functions approximated by polynomial splines, we show that, under certain conditions, the asymptotic distribution of the frequentist model averaging WCQR-estimator of a focused parameter is a non-linear mixture of normal distributions. This asymptotic distribution is used to construct confidence intervals that achieve the nominal coverage probability. With properly chosen weights, the focused information criterion based WCQR estimators are not only robust to outliers and non-normal residuals but also can achieve efficiency close to the maximum likelihood estimator, without assuming the true error distribution. Simulation studies and a real data analysis are used to illustrate the effectiveness of the proposed procedure.
TL;DR: In this article, a new sampling scheme for generating record-breaking data is introduced and called record ranked set sampling (RRSS), and a distribution-free two-sided prediction interval for future order statistics based on RRSS is derived.
Abstract: A new sampling scheme for generating record-breaking data is introduced and called record ranked set sampling (RRSS). A distribution-free two-sided prediction interval for future order statistics based on RRSS is derived. Numerical computations are obtained for comparing the results with the case based on ordinary records. Also, confidence intervals for quantiles of the parent distribution and prediction intervals for the ordinary records are given.
TL;DR: In this article, the authors revisited sequential estimation of the autoregressive parameter β in a first-order AR model and constructed a sequential confidence region for a parameter vector θ in a TAR(1) model.
Abstract: This article revisits sequential estimation of the autoregressive parameter β in a first-order autoregressive (AR(1)) model and construction of a sequential confidence region for a parameter vector θ in a first-order threshold autoregressive (TAR(1)) model. To resolve a theoretical conjecture raised in Sriram (1986), we provide a comprehensive numerical study that strongly suggests that the regret in using a sequential estimator of β can be significantly negative for many heavy-tailed error distributions and even for normal errors. Secondly, to investigate yet another conjecture about the limiting distribution of a sequential pivotal quantity for θ in a TAR(1) model, we conduct an extensive numerical study that strongly suggests that the sequential confidence region has much better coverage probability than that of a fixed sample counterpart, regardless of whether the θ values are inside or on or near the boundary of the ergodic region of the series. These highlight the usefulness of sequential s...
TL;DR: A novel hierarchical Bayesian method is developed to make statistical inference simultaneously on the threshold and the treatment effect restricted on the sensitive subset defined by the biomarker threshold, which provides better finite sample properties in terms of the coverage probability of a 95% credible interval.
TL;DR: In this article, an evaluation of the performance of several confidence interval estimators of the population coefficient of variation (τ) using ranked set sampling compared to simple random sampling is performed.
Abstract: In this paper, an evaluation of the performance of several confidence interval estimators of the population coefficient of variation (τ) using ranked set sampling compared to simple random sampling is performed. Two performance measures are used to assess the confidence intervals for τ, namely: width and coverage probabilities. Simulated data were generated from normal, log-normal, skew normal, Gamma, and Weibull distributions with specified population parameters so that the same values of τ are obtained for each distribution, with sample sizes n=15, 20, 25, 50, 100. A real data example representing birth weight of 189 newborns is used for illustration and performance comparison.
TL;DR: The proposed parametric bootstrap method is conceptually simpler than other proposed methods and consistently performs better than other methods: its coverage probability is close to the nominal confidence level and the resulting intervals are typically shorter than the intervals produced by other methods.
TL;DR: Alternative flexible models for the quantile function and methods for determining a quantiles function from a sample of values are proposed for meeting the above needs.
Abstract: The ?Guide to the Expression of Uncertainty in Measurement? (GUM) requires that the way a measurement uncertainty is expressed should be transferable. It should be possible to use directly the uncertainty evaluated for one measurement as a component in evaluating the uncertainty for another measurement that depends on the first. Although the method for uncertainty evaluation described in the GUM meets this requirement of transferability, it is less clear how this requirement is to be achieved when GUM Supplement 1 is applied. That Supplement uses a Monte Carlo method to provide a sample composed of many values drawn randomly from the probability distribution for the measurand. Such a sample does not constitute a convenient way of communicating knowledge about the measurand. In this paper consideration is given to obtaining a more compact summary of such a sample that preserves information about the measurand contained in the sample and can be used in a subsequent uncertainty evaluation. In particular, a coverage interval for the measurand that corresponds to a given coverage probability is often required. If the measurand is characterized by a probability distribution that is not close to being Gaussian, sufficient information has to be conveyed to enable such a coverage interval to be computed reliably.A quantile function in the form of an extended lambda distribution can provide adequate approximations in a number of cases. This distribution is defined by a fixed number of adjustable parameters determined, for example, by matching the moments of the distribution to those calculated in terms of the sample of values. In this paper, alternative flexible models for the quantile function and methods for determining a quantile function from a sample of values are proposed for meeting the above needs.
TL;DR: In this paper, the authors proposed a well-calibrated predictive distribution giving prediction intervals, and in particular prediction limits, with coverage probability equal or close to the target nominal value, based on the idea of calibrating prediction limits to control the associated coverage probability.
Abstract: This paper concerns prediction from the frequentist point of view. The aim is to define a well-calibrated predictive distribution giving prediction intervals, and in particular prediction limits, with coverage probability equal or close to the target nominal value. This predictive distribution can be considered in a number of situations, including discrete data and non-regular cases, and it is founded on the idea of calibrating prediction limits to control the associated coverage probability. Whenever the computation of the proposed distribution is not feasible, this can be approximated using a suitable bootstrap simulation procedure or by considering high-order asymptotic expansions, giving predictive distributions already known in the literature. Examples and applications of the results to different contexts show the wide applicability and the very good performance of the proposed predictive distribution.