Showing papers on "Coverage probability published in 1996"

A comparison of confidence interval methods for habitat use-availability studies

Abstract: Wildlife managers routinely compute sets of simultaneous confidence intervals to estimate the actual proportion of use of a set of k habitat types. Confidence intervals are determined by assuming that the counts of observed use are from k binomial populations. A set of k intervals is constructed from a large sample approximation for a confidence interval for a single binomial proportion. The simultaneous confidence level is controlled by use of the Bonferroni inequality. The coverage probability of these intervals can be less than the nominal (1 - a) 100% level. This paper presents results of a simulation study comparing the performance of these intervals with 3 alternatives; the usual method with a continuity correction factor, and 2 methods of computing confidence intervals for multinomial proportions. The 2 latter methods are superior and should be used in place of the binomial intervals. J. WILDL. MANAGE. 60(3):653-658

A Note on Bootstrapping Generalized Method of Moments Estimators

Abstract: Recently, Arcones and Gine (1992, pp. 13–47, in R. LePage & L. Billard [eds.], Exploring the Limits of Bootstrap, New York: Wiley) established that the bootstrap distribution of the M-estimator converges weakly to the limit distribution of the estimator in probability. In contrast, Brown and Newey (1992, Bootstrapping for GMM, Seminar note) discovered that the bootstrap distribution of the GMM overidentification test statistic does not converge weakly to the x2 distribution. In this paper, it is shown that the bootstrap distribution of the GMM estimator converges weakly to the limit distribution of the estimator in probability. Asymptotic coverage probabilities of the confidence intervals based on the bootstrap percentile method are thus equal to their nominal coverage probability.

Conservative confidence regions in multivariate calibration

Abstract: In the multivariate calibration problem using a multivariate linear model, some conservative confidence regions are constructed. The regions are nonempty and invariant under nonsingular transformations. Situations where the explanatory variable occurs nonlinearly in the model are also considered. Computational aspects of the confidence region and its practical implementation are discussed. The results are illustrated using two examples. The examples show that our confidence regions are much more satisfactory compared to those based on some of the existing procedures. Furthermore, simulation results for the examples reveal that the coverage probability of the conservative confidence regions are very close to the assumed confidence level.

On sequential fixed-width confidence intervals for the mean and second-order expansions of the associated coverage probabilities

Abstract: In order to construct fixed-width (2d) confidence intervals for the mean of an unknown distribution function F, a new purely sequential sam- pling strategy is proposed first. The approach is quite different from the more traditional methodology of Chow and Robbins (1965, Ann. Math. Statist., 36, 457-462). However, for this new procedure, the coverage probability is shown (Theorem 2.1) to be at least (1 - a) + Ad 2 + o(d 2) as d --* 0 where (1 - (~) is the preassigned level of confidence and A is an appropriate functional of F, un- der some regularity conditions on F. The rates of convergence of the coverage probability to (1 - a) obtained by Csenki (1980, Scand. Aetuar. J., 107-111) and Mukhopadhyay (1981, Comm. Statist. Theory Methods, 10, 2231-2244) were merely O(dl/~-q), with 0 < q < 1/2, under the Chow-Robbins stopping time T*. It is to be noted that such considerable sharpening of the rate of con- vergence of the coverage probability is achieved even though the new stopping variable is Op (T*). An accelerated version of the stopping rule is also provided together with the analogous second-order characteristics. In the end, an exam- ple is given for the mean estimation problem of an exponential distribution.

Asymptotically honest confidence sets for structural errors-in-variables models

Abstract: The problem of constructing confidence sets for the structural errors-in-variables model is considered under the assumption that the variance of the error associated with the covariate is known. Previously proposed confidence sets for this model suffer from the problem that they all have zero confidence levels for any sample size, where the confidence level of a confidence set is defined to be the infimum of coverage probability over the parameter space. In this paper we construct some asymptotically honest confidence sets; that is, the limiting values of their confidence levels are at least as large as the nominal probabilities when the sample size goes to $\infty$. A desirable property of the proposed confidence set for the slope is also established.

Inference on a Structural Parameter in Instrumental Variables Regression with Weak Instruments

Abstract: In this paper we consider the problem of making inference on a structural parameter in instrumental variables regression when the instruments are only weakly correlated with the explanatory endogenous variables. Adopting a local-to-zero assumption as in Staiger and Stock (1994) on the coefficients of the instruments in the first stage equation, the asymptotic distributions of various test statistics are derived under a limited infomation framework. We show that Wald-type test statistics are not asymptotically pivotal, thus (1 - a)*100% confidence intervals implied by those test statistics can have zero coverage probability if standard asymptotic distribution theory is used. In contrast, likelihood-type test statistics are asymptotically pivotal when the model is just identified thus providing valid confidence intervals. Even when the model is overidentified, we show that the distributions of the likelihood-type test statistics are asymptotically bounded from above by a chi- square distribution with degrees of freedom given by the number of instruments. Hence, we can always invert the likelihood-type statistics to obtain valid, although conservative, confidence intervals. The confidence intervals obtained by using this bounding distribution are compared with those obtained by using the standard chi-square 1 asymptotic distribution and an alternative bounding distribution, a transformation of the distribution of the Wilks statistic, suggested by Dufour (1994). Using Monte Carlo methods, confidence intervals based on our chi-square bounding distribution are shown to be tighter in finite samples than those based on the Wilks bounding distribution.

Families of smooth confidence bands for the survival function under the general random censorship model

Abstract: Randomly right censored data often arise in industrial life testing and clinical trials. Several authors have proposed asymptotic confidence bands for the survival function when data are randomly censored on the right. All of these bands are based on the empirical estimator of the survival function. In this paper, families of asymptotic (1-α)100% level confidence bands are developed from the smoothed estimate of the survival function under the general random censorship model. The new bands are compared to empirical bands, and it is shown that for small sample sizes, the smooth bands have a higher coverage probability than the empirical counterparts.

Accuracy of estimators, confidence intervals and tests

Abstract: To determine the accuracy of the estimates that we made in chapter 1, we demonstrate in this chapter how to calculate confidence intervals and how to perform tests. The specific concerns of each of our particular experiments are described below. We then introduce the methodology, first describing classical asymptotic procedures and two asymptotic tests, the Wald test and the likelihood ratio test, and then presenting procedures and tests based on a resampling method, the bootstrap. As before, we conclude the chapter by applying these methods to the examples.

On the asymptotic normality of multinomial population size estimators with application to backcalculation of AIDS epidemic

Abstract: SUMMARY Estimation of the unknown size of a multinomial distribution is required in some important applications. It has been previously shown that the maximum likelihood estimators of the size and other parameters in the multinomial distribution are asymptotically normal under suitable regularity conditions. Unfortunately, one of these conditions is difficult to verify in practice. Here we present an alternative regularity condition that is straightforwardly verifiable. An application to the backcalculation estimates of AIDS incidence is presented. Explicit formulae are given for the asymptotic variances and covariances of the backcalculation estimators. The associated confidence interval for the size of the HIV infected population is comparable to the likelihood-ratio-test-based interval given in Brookmeyer & Gail (1988). A simulation study shows that the asymptotic normal interval is highly accurate in terms of coverage probability.

Inferring coverage probabilities by optimum 3-stage sampling

Abstract: Reliability assessment is an important step in the development of fault-tolerant computing systems. Availability, MTTF, and, in general, any reliability measure is determined by the system ability to handle faults and errors and the rate of occurrence of these events. A special parameter, the coverage probability, provides information about the effectiveness of the fault tolerance mechanisms embedded into the system. Practically, physical or simulated fault injection experiments are conducted for evaluating the coverage. Unfortunately, the extremely large number of events which can perturb the operation of a computing system makes exhaustive testing intractable. As a consequence, statistical inference has been employed to derive meaningful results after performing a relatively small number of fault injection experiments. This paper presents a new method for inferring the coverage probability by means of optimum 3-stage sampling. A three-dimensional space of events is considered. It is represented by the cross product of system inputs, times of injection, and fault locations. The fault injection consists of a pilot experiment followed by the main injection experiment. The sample size of the main experiment is chosen to minimize the cost of the fault injection for a fixed value of the variance. This approach is used for estimating the coverage probability of a hypothetical fault-tolerant system. Based on our experiments, we conclude that the optimum 3-stage sampling method is especially useful when a low variance of the coverage probability is required.

On admissibility and optimality of treatment-control designs

Abstract: The relationship between admissible incomplete block designs for confidence intervals with maximal coverage probability for treatment-control contrasts and optimal designs for estimation is investigated. For certain types of designs, admissible designs are shown to be precisely those with the number of replications of the control less than or equal to that of an optimal design. Moreover, admissible designs are the Bayes optimal designs for a class of priors.

Bootstrap for finite populations

Abstract: The bootstrap method is compared with the classical (linearization) and jackknife procedures for estimating the mean square errors (MSEs) of the ratio estimator and the combined ratio estimator. The initial samples are considered to be selected without replacement, and different procedures for selecting the bootstrap samples with or without replacement from them are examined. The biases, stabilities, coverage probabilities and confidence widths of all the procedures are compared.

Nonparametric methods for 1-out-of-2: G repairable systems

Abstract: The steady state availability of 1-out-of-2 : G repairable system is obtained under the assumption that the life time of a component in standby position follows exponential distribution. It's nonparmetric estimator is proposed. The asymptotic properties of the estimator are used to provide the fixed width coinfience interval with specified coverage probability and testing of hypothesis problem using sequential procedure.

A Note on the Conservative Multivariate Tukey-Kramer Multiple Comparison Procedure

Abstract: SYNOPTIC ABSTRACTIn this article, the conservative simultaneous confidence intervals for pairwise multiple comparisons among correlated mean vectors including the case of unequal sample sizes are considered. One of the important problems is to evaluate the bound of simultaneous confidence levels for approximate multiple comparisons procedures. For all pairwise comparisons as a particular case, the multivariate Tukey-Kramer procedure proposed by Seo, Mano and Fujikoshi(1994) is discussed, and its bound for conservativeness is given by the reduction of the coverage probability. The numerical results by Monte Carlo simulations are presented for the selected parameters.

A symptotic robustness of sequential confidence intervals and the connection with influence functions

Abstract: The robustness of sequential confidence intervals is studied by considering contamination with probability e of the basic underlying distribution in a so-called gross errors model. Asymptotic theory is considered when d → 0, where the prescribed length of the interval is 2d, and simultaneously e ≏ e(d) → 0. A general theorem, in a distribution free setting, is given which provides expressions for the asymptotic coverage probability and the asymptotic distribution of the stopping variable. The results depend on the rate of e(d)/d as d → 0 and on the contaminating distribution. If the latter distribution is degenerate, it turns out that the influence functions of the above mentioned two estimators used in the construction of the procedure, appear in the expressions for the asymptotic coverage probability and the asymptotic distribution of the stopping variable respectively. This shows how the sequential procedure inherits the robustness properties of the estimators concerned and how this is quantified. The ...

Bootstrap Variable-Selection and Confidence Sets

Abstract: This paper analyzes estimation by bootstrap variable-selection in a simple Gaussian model where the dimension of the unknown parameter may exceed that of the data. A naive use of the bootstrap in this problem produces risk estimators for candidate variable-selections that have a strong upward bias. Resampling from a less overfitted model removes the bias and leads to bootstrap variable-selections that minimize risk asymptotically. A related bootstrap technique generates confidence sets that are centered at the best bootstrap variable-selection and have two further properties: the asymptotic coverage probability for the unknown parameter is as desired and the confidence set is geometrically smaller than a classical competitor. The results suggest a possible approach to confidence sets in other inverse problems where a regularization technique is used.

Estimation with prescribed proportional accuracy for a two-parameter exponential family of distributions

Abstract: We propose a sequential procedure for estimating with prescribed proportional accuracy one parameter in a class of two-parameter exponential family of distributions. We study the properties of the resulting stopping time and provide second-order analysis of the coverage probability associated with it by using Edgeworth expansion.

The neyman accuracy and the wolfowitz accuracy of the stein type confidence interval for the disturbance variance

Abstract: In this paper we consider the Neyman accuracy and the Wolfowitz accuracy of the Stein type improved confidence interval I∗S for the disturbance variance in a linear regression model. The Neyman accuracy is a measure related to the unbiasedness of a confidence interval, and the Wolfowitz accuracy is related to the closeness of the endpoints to the true parameter. We show that I∗S is not unbiased and give some numerical results for the Neyman accuracy. As for the Wolfowitz accuracy we derive the sufficient condition for I∗S to improve on the usual confidence interval under this criterion and show numerically that a large degree of improvement can be obtainted.

A note on bootstrapping generalized method of

Abstract: GMM overidentification test statistic does not converge weakly to the x2 distribution. In this paper, it is shown that the bootstrap distribution of the GMM estimator converges weakly to the limit distribution of the estimator in probability. Asymptotic coverage probabilities of the confidence intervals based on the bootstrap percentile method are thus equal to their nominal coverage probability.

Analysis of Extra-trinomial Data from Developmental Toxicity Experiments using Estimating Equations.

Abstract: For the analysis of data from developmental toxicity experiments that exhibits overdispersion, the beta-binomial model (Williams 1975) or the Dirichlet-multinomial model, an extension of the beta-binomial model, (Chen et al. 1991), is often used. However, investigations of these models suggest that when heterogeneous intra-litter correlations are incorrectly modeled as homogeneous the mean parameter estimates become biased (Kupper et al. 1986). Further even if the intra-litter correlation is correctly modeled, problems of bias of the parameter estimate and coverage probability of the parameter (e.g. coverage probability of 95 % confidence band) still exist (Liang and Hanfelt 1994). Liang and Hanfelt (1994) recommended the use of quasi-likelihood method for the inference instead of the beta-binomial maximum likelihood method. In this paper, two methods of analysis of extra-trinomial data using estimating equations are proposed. One is the quasi-likelihood/pseudolikelihood estimating equation method proposed by Carroll and Ruppert (1982) and Breslow (1989), which is also seen as a generalized estimating equations method, and the other is the quasi-likelihood/method of moments proposed by Williams (1982). From the results of White (1982), the parameter estimates are consistent when the mean model is correctly specified and the robust variance estimates of the parameter estimates can be calculated. An example of analysis using data from teratologica experiments is given.

Nonparametric conservative bands for the trend of Gaussian AR(p) models

Abstract: Conservative confidence bands for the trend function of a stationary Gaussian autoregressive model are proposed The case of an ARMA (1,1) model is also considered in brief Results are valid for finite sample sizes However, the bands are conservative in the sense that the true coverage probability is bounded below by the prefixed level

On the Robustness of Bayes Estimators of the Variance Ratio in Balanced One-Way ANOVA Models with Covariates

Abstract: This paper introduces some hierarchical Bayes (HB) estimators of the variance ratio in balanced one-way ANOVA models with covariates. Such estimators enjoy frequentist properties like consistency and asymptotic normality. Jackknifed estimators of the asymptotic variance of the HB estimators are found, and are used in the construction of asymptotic confidence intervals for the variance ratio. These intervals have larger coverage probability than similar intervals based on the maximum likelihood estimators, restricted maximum likelihood estimators, and estimators based on the Henderson-III method. The HB intervals are also much more robust than the competing intervals when the underlying distributions are double exponential or uniform.

Versorgungsaspekte bei der digitalen terrestrischen Ton- und Fernsehrundfunkübertragung

Abstract: For terrestrial broadcast services the reception situation at the border of the coverage area on principle is a problem which affects different coverage aspects. It is reasonable to have a graceful degradation for mobile reception of digital audio services at the edge of the coverage area, but for stationary reception it is only interesting whether a digital service can be received error-free or not at all. Furthermore, there is a big difference in the reception probability between portable receivers and receivers with directional roof-top antennas. This implies difficulties for the definition of a coverage area. The present contribution deals with coverage aspects of digital terrestrial audio and television broadcasting in general. Especially, it emphasises the possibility of the new specification for digital terrestrial video broadcasting (DVB-T) to increase the coverage probability for portable reception on the base of a hierarchical modulation. The coverage probability is determined for a regular single frequency network (SFN) on the basis of 'Monte Carlo' simulations.