Showing papers in "Journal of The Korean Statistical Society in 2010"
TL;DR: The Forward Search as discussed by the authors is a powerful general method, incorporating flexible data-driven trimming, for the detection of outliers and unsuspected structure in data and so for building robust models, starting from small subsets of data, observations that are close to the fitted model are added to the observations used in parameter estimation.
Abstract: The Forward Search is a powerful general method, incorporating flexible data-driven trimming, for the detection of outliers and unsuspected structure in data and so for building robust models. Starting from small subsets of data, observations that are close to the fitted model are added to the observations used in parameter estimation. As this subset grows we monitor parameter estimates, test statistics and measures of fit such as residuals. The paper surveys theoretical development in work on the Forward Search over the last decade. The main illustration is a regression example with 330 observations and 9 potential explanatory variables. Mention is also made of procedures for multivariate data, including clustering, time series analysis and fraud detection.
88 citations
TL;DR: In this paper, weakly asymptotic formulas of the tail probability of randomly weighted sums ∑ i = 1 n Θ i X i and their maxima were obtained for the consistent variation class.
Abstract: This paper achieves some weakly asymptotic formulas of the tail probability of randomly weighted sums ∑ i = 1 n Θ i X i and their maxima, where { X i , i ≥ 1 } are bivariate upper tail independent random variables with common distribution F belonging to the dominant variation class, and { Θ i , i ≥ 1 } are other nonnegative random variables and independent of { X i , i ≥ 1 } . Particularly, when F belongs to the consistent variation class, some asymptotic formulas are established. An application to risk theory is proposed. The obtained results extend and improve the existing results of Zhang, Shen, and Weng (2009) .
49 citations
TL;DR: In this article, a wavelet block thresholding based adaptive estimator for density estimation from i.i.d. biased observations is proposed, where the bias function is assumed to be bounded from above and below.
Abstract: We consider the density estimation problem from i.i.d. biased observations. The bias function is assumed to be bounded from above and below. A new adaptive estimator based on wavelet block thresholding is constructed. We evaluate these theoretical performances via the minimax approach under the L p risk with p ≥ 1 (not only for p = 2 ) over a wide range of function classes: the Besov classes, B π , r s (with no particular restriction on the parameters π and r ). Under this general framework, we prove that it attains near optimal rates of convergence. The theory is illustrated by a numerical example.
39 citations
TL;DR: In this paper, the authors define a new smooth kernel estimator θ ˆ n (x ) of θ ( x ) and establish its almost sure convergence and asymptotic normality.
Abstract: Let ( T i ) 1 ≤ i ≤ n be a sample of independent and identically distributed (iid) random variables (rv) of interest and ( X i ) 1 ≤ i ≤ n be a corresponding sample of covariates. In censorship models the rv T is subject to random censoring by another rv C . Let θ ( x ) be the conditional mode function of the density of T given X = x . In this work we define a new smooth kernel estimator θ ˆ n ( x ) of θ ( x ) and establish its almost sure convergence and asymptotic normality. An application to prediction and confidence bands is also given. Simulations are drawn to lend further support to our theoretical results for finite sample sizes.
29 citations
SIDI1
TL;DR: In this article, a family of robust nonparametric estimators for a regression function based on the kernel method is proposed and established the asymptotic normality of the estimator under the concentration property on small balls probability measure of the functional explanatory variable when the observations exhibit some kind of dependence.
Abstract: We propose a family of robust nonparametric estimators for a regression function based on the kernel method. We establish the asymptotic normality of the estimator under the concentration property on small balls probability measure of the functional explanatory variable when the observations exhibit some kind of dependence. This approach can be applied in time series analysis to make prediction and build confidence bands. We illustrate our methodology on the US electricity consumption data.
27 citations
TL;DR: In this paper, one-parameter classes of imputation techniques have been suggested and their corresponding point estimators have been proposed to deal with the problems of non-response, and a design based approach is used to compare the proposed strategy with the existing strategies.
Abstract: To deal with the problems of non-response, one-parameter classes of imputation techniques have been suggested and their corresponding point estimators have been proposed. The proposed classes of estimators include several other estimators as a particular case for different values of the parameter. A design based approach is used to compare the proposed strategy with the existing strategies. Theoretical results have been verified through simulation studies handling real data examples.
23 citations
TL;DR: In this article, the authors used the empirical likelihood method to study the confidence regions construction for the parameters of interest in a semiparametric model with linear process errors under martingale difference.
Abstract: The purpose of this article is to use the empirical likelihood method to study the confidence regions construction for the parameters of interest in semiparametric model with linear process errors under martingale difference. It is shown that the adjusted empirical log-likelihood ratio at the true parameters is asymptotically chi-squared. A simulation study indicates that the adjusted empirical likelihood works better than a normal approximation-based approach.
21 citations
TL;DR: In this paper, the convergence properties of partial sums 1 a n ∑ k = 1 n X n k are investigated and some new results are obtained, extending and improving the corresponding theorems of rowwise independent random variable arrays.
Abstract: Let { X n k , 1 ≤ k ≤ n , n ≥ 1 } be an array of rowwise negatively orthant dependent random variables and let { a n , n ≥ 1 } be a sequence of positive real numbers with a n ↑ ∞ . The convergence properties of partial sums 1 a n ∑ k = 1 n X n k are investigated and some new results are obtained. The results extend and improve the corresponding theorems of rowwise independent random variable arrays by Hu and Taylor [Hu, T. C., Taylor R. L. (1997). On the strong law for arrays and for the bootstrap mean and variance. International Journal of Mathematics and Mathematical Sciences, 20(2), 375–382].
20 citations
TL;DR: In this paper, the authors considered the validity of the JB test for GARCH (generalized autoregressive conditional heteroscedastic) models and showed that the asymptotic behavior of the original form of JB is identical to that of the test statistic based on true errors.
Abstract: In this paper, we consider the validity of the Jarque–Bera normality test whose construction is based on the residuals, for the innovations of GARCH (generalized autoregressive conditional heteroscedastic) models. It is shown that the asymptotic behavior of the original form of the JB test adopted in this paper is identical to that of the test statistic based on true errors. The simulation study also confirms the validity of the original form since it outperforms other available normality tests.
17 citations
TL;DR: In this article, it was shown that the law of the iterated logarithm holds for sequences of identically distributed random variables with the underlying distribution in the domain of attraction of the normal distribution.
Abstract: Consider a sequence of NA identically distributed random variables with the underlying distribution in the domain of attraction of the normal distribution. This paper proves that law of the iterated logarithm holds for sequences of NA random variables.
17 citations
TL;DR: In this paper, some exponential inequalities for a linearly negative quadrant dependent sequence are obtained and the complete convergence and almost sure convergence of such a sequence are given. And the asymptotic behavior of the probabilities for the partial sums of such sequences is studied.
Abstract: Some exponential inequalities for a linearly negative quadrant dependent sequence are obtained. By using the exponential inequalities, we give the complete convergence and almost sure convergence for a linearly negative quadrant dependent sequence. In addition, the asymptotic behavior of the probabilities for the partial sums of a linearly negative quadrant dependent sequence is studied.
TL;DR: In this article, the authors study the D -optimal design problem for the common weighted univariate polynomial regression model with efficiency function λ and derive a differential equation for the efficiency function, such that an explicit solution of the optimal design problem is possible.
Abstract: We study the D -optimal design problem for the common weighted univariate polynomial regression model with efficiency function λ . We characterize the efficiency functions for which an explicit solution of the D -optimal design problem is available based on a differential equation for the logarithmic derivative of the efficiency function. In contrast to the common approach which starts with a given efficiency function and derives a differential equation for the supporting polynomial of the D -optimal design, we derive a differential equation for the efficiency function, such that an explicit solution of the D -optimal design problem is possible. The approach is illustrated for various convex design spaces and is depicted in several new examples. Also, this concept incorporates all classical efficiency functions discussed in the literature so far.
TL;DR: In this paper, an almost sure version of the maximum limit theorem for stationary Gaussian random fields under some covariance conditions was obtained, and a weak convergence of the stationary Gaussian random field maximum was obtained.
Abstract: We obtain an almost sure version of a maximum limit theorem for stationary Gaussian random fields under some covariance conditions. As a by-product, we also obtain a weak convergence of the stationary Gaussian random field maximum, which is interesting independently.
TL;DR: In this paper, the authors considered a system consisting of one operating unit, n − 1 spares and r repair facilities, and obtained the instantaneous availability function of such a system, when both life and repair times are exponentially distributed with possibly different scale parameters.
Abstract: We consider a system consisting of one operating unit, n − 1 spares and r repair facilities As soon as the operating unit fails, one of the spares, if available, takes over the operation The failed unit joins the repair queue and is serviced as soon as one of the repair facilities becomes free After a perfect repair the unit becomes a viable spare and remains on cold stand-by The system fails when the operating unit fails and there is no viable spare We obtain the instantaneous availability function of such a system, when both life and repair times are exponentially distributed with possibly different scale parameters
TL;DR: In this article, a cluster-based SIR is proposed to cluster the predictor space so that the linearity condition approximately holds in the different partitions, and then SIR in each cluster and finally estimate the dimension reduction subspace by combining these individual estimates.
Abstract: In the theory of sufficient dimension reduction, Sliced Inverse Regression (SIR) is a famous technique that enables us to reduce the dimensionality of regression problems. This semiparametric regression method aims at determining linear combinations of a p -dimensional explanatory variable x related to a response variable y . However it is based on a crucial condition on the marginal distribution of the predictor x , often called the linearity condition. From a theoretical and practical point of view, this condition appears to be a limitation. Using an idea of Li, Cook, and Nachtsheim (2004) in the Ordinary Least Squares framework, we propose in this article to cluster the predictor space so that the linearity condition approximately holds in the different partitions. Then we apply SIR in each cluster and finally estimate the dimension reduction subspace by combining these individual estimates. We give asymptotic properties of the corresponding estimator. We show with a simulation study that the proposed approach, referred as cluster-based SIR, improves the estimation of the e.d.r. basis. We also propose an iterative implementation of cluster-based SIR and show in simulations that it increases the quality of the estimator. Finally the methodology is applied on the horse mussel data and the comparison of the prediction reached on test samples shows the superiority of cluster-based SIR over SIR.
Abstract: A local linear estimator of the conditional hazard function in censored data is proposed. The estimator suggested in this paper is motivated by the ideas of Fan, Yao, and Tong (1996) and Kim, Bae, Choi, and Park (2005). The asymptotic distribution of the proposed estimator is derived, and some numerical results are also provided.
TL;DR: In this article, the authors deal with robust inference in heteroscedastic measurement error models and postulate a Student t distribution for the observed variables, rather than the normal distribution.
Abstract: In this paper we deal with robust inference in heteroscedastic measurement error models. Rather than the normal distribution, we postulate a Student t distribution for the observed variables. Maximum likelihood estimates are computed numerically. Consistent estimation of the asymptotic covariance matrices of the maximum likelihood and generalized least squares estimators is also discussed. Three test statistics are proposed for testing hypotheses of interest with the asymptotic chi-square distribution which guarantees correct asymptotic significance levels. Results of simulations and an application to a real data set are also reported.
TL;DR: The authors modify the tests of Dickey, Hasza, and Fuller (1984) to investigate results for less typical, long period cases such as 1440 min per day, 52 weeks per year, 365 days per year and so forth, getting some nice properties including a surprising effect of deterministic terms in the models.
Abstract: Seasonal differencing is often applied when reporting, for example, monthly sales. New car sales are often reported to be up or down from the same period last year. Tests for the need to seasonally difference data are seasonal unit root tests. We modify the tests of Dickey, Hasza, and Fuller (1984) to investigate results for less typical, long period cases such as 1440 min per day, 52 weeks per year, 365 days per year and so forth, getting some nice properties including a surprising effect of deterministic terms in the models.
TL;DR: In this paper, the authors studied the efficiency of generalized additive models for the exponential family and presented an asymptotically efficient estimation procedure based on the generalized profile likelihood approach.
Abstract: In this paper we study semiparametric generalized additive models in which some part of the additive function is linear. We study the semiparametric efficiency under this regression model for the exponential family. We also present an asymptotically efficient estimation procedure based on the generalized profile likelihood approach.
TL;DR: In this paper, an integrated process control (IPC) procedure is proposed, which combines the engineering process control and the statistical process control procedures for the process where the noise and a special cause are present.
Abstract: An integrated process control (IPC) procedure is a scheme which combines the engineering process control (EPC) and the statistical process control (SPC) procedures for the process where the noise and a special cause are present. The most efficient way of reducing the effect of the noise is to adjust the process by its forecast, which is done by the EPC procedure. The special cause, which produces significant deviations of the process level from the target, can be detected by the monitoring scheme, which is done by the SPC procedure. The effects of special causes can be eliminated by a rectifying action. The performance of the IPC procedure is evaluated in terms of the average run length (ARL) or the expected cost per unit time (ECU). In designing the IPC procedure for practical use, it is essential to derive its properties constituting the ARL or ECU based on the proposed process model. The process is usually assumed as it starts only with noise, and special causes occur at random times afterwards. The special cause is assumed to change the mean as well as all the parameters of the in-control model. The linear filter models for the process level as well as the controller and the observed deviations for the IPC procedure are developed here.
TL;DR: In this article, the authors obtain an asymptotically corrected empirical Bayes confidence interval in a nested error regression model with unbalanced sample sizes and unknown components of variance, and apply it to the posted land price data in Tokyo and the neighboring prefecture, showing that the corrected confidence interval is superior to the conventional confidence interval based on the sample mean in terms of the coverage probability and the expected width of the interval.
Abstract: In the small area estimation, the empirical best linear unbiased predictor (EBLUP) or the empirical Bayes estimator (EB) in the linear mixed model is recognized to be useful because it gives a stable and reliable estimate for a mean of a small area. In practical situations where EBLUP is applied to real data, it is important to evaluate how much EBLUP is reliable. One method for the purpose is to construct a confidence interval based on EBLUP. In this paper, we obtain an asymptotically corrected empirical Bayes confidence interval in a nested error regression model with unbalanced sample sizes and unknown components of variance. The coverage probability is shown to satisfy the confidence level in the second-order asymptotics. It is numerically revealed that the corrected confidence interval is superior to the conventional confidence interval based on the sample mean in terms of the coverage probability and the expected width of the interval. Finally, it is applied to the posted land price data in Tokyo and the neighboring prefecture.
TL;DR: In this paper, a general stochastic model for the spread of an epidemic developing in a closed population is introduced, where each model consisting of a discrete-time Markov chain involves a deterministic counterpart represented by an ordinary differential equation.
Abstract: A general stochastic model for the spread of an epidemic developing in a closed population is introduced. Each model consisting of a discrete-time Markov chain involves a deterministic counterpart represented by an ordinary differential equation. Our framework involves various epidemic models such as a stochastic version of the Kermack and McKendrick model and the SIS epidemic model. We prove the asymptotic consistency of the stochastic model regarding a deterministic model; this means that for a large population both modelings are similar. Moreover, a Central Limit Theorem for the fluctuations of the stochastic modeling regarding the deterministic model is also proved.
TL;DR: In this article, the authors consider the problem of determining optimal burn-in times and optimal maintenance policy for a component which fails at age t. But they assume that the cost of a minimal repair to the component that fails is a continuous non-decreasing function of t.
Abstract: Burn-in is a method used to eliminate early failures of components before they are put into field operation. Maintenance policy, such as block replacement policy with minimal repair at failure, is often used in field operation. In this paper burn-in and maintenance policy are taken into consideration at the same time. It is assumed that the cost of a minimal repair to the component which fails at age t is a continuous non-decreasing function of t . We consider the problems of determining optimal burn-in times and optimal maintenance policy.
TL;DR: In this paper, an adjusted empirical log-likelihood ratio for the index parameters, which are of primary interest, is proposed using a synthetic data approach, and the adjusted empirical likelihood is shown to have a standard chi-squared limiting distribution.
Abstract: This paper is concerned with an estimation procedure of a class of single-index varying-coefficient models with right-censored data. An adjusted empirical log-likelihood ratio for the index parameters, which are of primary interest, is proposed using a synthetic data approach. The adjusted empirical likelihood is shown to have a standard chi-squared limiting distribution. Furthermore, we increase the accuracy of the proposed confidence regions by using the constraint that the index is of norm 1. Simulation studies are carried out to highlight the performance of the proposed method compared with the traditional normal approximation method.
TL;DR: In this article, the scale mixture of matricvariate and matrix variate Kotz-type distributions and the inverse generalised gamma distribution were derived and the generalized Wishart and inverse-Wishart distributions were derived.
Abstract: We have derived the generalised Wishart and inverse-Wishart distributions based on the matrix variate and matricvariate Kotz-type distributions. The scale mixture of matricvariate and matrix variate Kotz-type distributions and the inverse generalised gamma distribution are then proposed. It is shown that the class of distributions termed the family of t -type distributions proposed by Arslan [Arslan, O. (2005). A new class of multivariate distributions: Scale mixture of Kotz-type distributions. Statistics and Probability Letters , 76 , 18–28] is obtained as particular cases of the result given here. We have also derived the compound matricvariate and matrix variate Kotz-type distributions and the inverse generalised Wishart based on the matrix variate and matricvariate Kotz-type distributions. These latter results lead us to propose a different matricvariate version of the family of t -type distributions and others cited in the above-mentioned reference.
TL;DR: In this article, a monitoring procedure for an early detection of parameter changes in random coefficient autoregressive models is developed, and the stopping rule signaling a parameter change satisfies the desired asymptotic property as seen in Lee, Lee, and Na.
Abstract: In this paper, we develop a monitoring procedure for an early detection of parameter changes in random coefficient autoregressive models. It is shown that the stopping rule signaling a parameter change satisfies the desired asymptotic property as seen in Lee, Lee, and Na (submitted for publication). Simulation results are provided for illustration.
TL;DR: In this paper, a classical continuous time surplus process is modified by adding two actions: if the level of the surplus goes below τ ≥ 0, the level is increased up to initial level u > τ by injecting capital to the surplus.
Abstract: A classical continuous time surplus process is modified by adding two actions. If the level of the surplus goes below τ ≥ 0 , we increase the level of the surplus up to initial level u > τ by injecting capital to the surplus. Meanwhile, the excess amount of the surplus over V > u is invested continuously to other business. After assigning several costs related to managing the surplus, we obtain the long-run average cost per unit time and illustrate a numerical example to show how to find an optimal investment policy minimizing the cost.
TL;DR: In this article, the spline empirical log-likelihood ratio (SLR) was used to test serial correlation in partially nonlinear models, and the proposed SLR converges to the standard chi-square distribution under the null hypothesis of no serial correlation.
Abstract: Partially nonlinear models, as extensions of partially linear models are extensively used in statistical modeling. This paper considers the spline empirical log-likelihood ratio for testing serial correlation in partially nonlinear models. It is shown that the proposed empirical log-likelihood ratio converges to the standard chi-square distribution under the null hypothesis of no serial correlation. Some simulations are conducted to estimate the rejection probabilities under the null hypothesis and serial correlation. An example of application is also illustrated.