Journal of the Korean Statistical Society最新文献

To capture the higher-order autocorrelation structure for finite-range integer-valued time series of counts, and to consider the interdependence between individuals, a pth-order generalized binomial autoregressive (GBAR(p)) process is proposed in this paper. The stationarity and ergodicity of the GBAR(p) model are proved, and the basic probabilistic and statistical properties of the model are discussed. The unknown parameters are estimated by the conditional least squares and conditional maximum likelihood methods. The performances of two kinds of estimators are studied via simulations, and the forecasting problem of this model is also considered in this paper. Finally, the model is applied to a real data set and compared with some existing models to investigate the rationality of the GBAR(p) model.

In this paper, we develop a nonparametric estimator of the regression function for a functional explanatory variable and a scalar response variable that is subject to left truncation and right censoring. The estimator is constructed by minimizing the mean squared relative error, which is a robust criterion that reduces the impact of outliers relatively to the Nadaraya Watson estimator. We prove the pointwise and uniform convergence of the estimator under some regular conditions and assess its performance by a numerical study. We also investigate the robustness of the estimator using the influence function as a measure of sensitivity to outliers and apply the estimator to a real dataset.

This paper considers modeling bounded multivariate time series of counts and the inferential procedures of this model. For modeling, we introduce a hybrid type model similar to the scheme of integer-valued autoregressive (INAR) and conditional autoregressive heteroscedastic (INARCH) models. To estimate the model parameters, we use the conditional least squares estimator (CLSE) and minimum density power divergence estimator (MDPDE). To evaluate the small sample performances of the proposed estimators, we conduct a Monte Carlo simulation study and demonstrate that the proposed methods work well. Real data analysis is also carried out using syphilis data in the U.S. for illustration.

The National Health and Nutrition Examination Survey (NHANES) is a major program of the National Center for Health Statistics, designed to assess the health and nutritional status of adults and children in the United States. The analysis of NHANES dental caries data faces several challenges, including (1) the data were collected using a complex, multistage, stratified, unequal-probability sampling design; (2) the sample size of some primary sampling units (PSU), e.g., counties, is very small; (3) the measures of dental caries have complicated structure and correlation, and (4) there is a substantial percentage of nonresponses, which are expected not to be missing at random or non-ignorable. We propose a Bayesian hierarchical spatial model to address these analysis challenges. We develop a two-level Potts model that closely resembles the caries evolution process, and captures complicated spatial correlations between teeth and surfaces of the teeth. By adding Bayesian hierarchies to the Potts model, we account for the multistage survey sampling design, while also enabling information borrowing across PSUs for small-area estimation. We incorporate sampling weights by including them as a covariate in the model and adopt flexible B-splines to achieve robust inference. We account for non-ignorable missing outcomes and covariates using the selection model. We use data augmentation coupled with the noisy Monte Carlo algorithm to overcome the numerical difficulty caused by doubly-intractable normalizing constants and sample posteriors. Our analysis results show strong spatial associations between teeth and tooth surfaces, including that dental hygienic factors, such as fluorosis and sealant, reduce dental disease risks.

For the analysis of square contingency tables with the same row and column ordinal classifications, this study proposes an index for measuring the degree of departure from the symmetry model using new cumulative probabilities. The proposed index is constructed based on the Cressie and Read’s power divergence, or the weighted average of the Patil and Taillie’s diversity index. This study derives a plug-in estimator of the proposed index and an approximate confidence interval for the proposed index. The estimator of the proposed index is expected to reduce the bias more than the estimator of the existing index, even when the sample size is not large. The proposed index is identical to the existing index under the conditional symmetry model. Therefore, assuming the probability structure in which the conditional symmetry model holds, the performances of plug-in estimators of the proposed and existing indexes can be simply compared. Through numerical examples and real data analysis, the usefulness of the proposed index compared to the existing index is demonstrated.

This study considers multiple values-inflated bivariate integer-valued autoregressive (MV-inflated BINAR) models. It develops the inferential procedures for parameter estimation on this model, which apply to constructing a change point test and outlier detection rule. We first introduce the MV-inflated BINAR model with one parameter exponential family and Poisson-Lindley innovations. Then, we propose a quasi-maximum likelihood estimator (QMLE) and divergence-based estimator featuring minimum density power divergence estimator (MDPDE) for robust estimation. To evaluate the performance of these estimators, we conduct Monte Carlo simulations and demonstrate the adequacy of MDPDE in zero–one inflated models. Real data analysis is also carried out using the number of monthly earthquake cases in the United States.

This paper is concerned with linear hypothesis testing problems in ultra high dimensional generalized linear mixed models where the response and the random effects are distribution-free. The constrained-partial-regularization based penalized quasi-likelihood method is proposed and the corresponding statistical properties are studied. To test linear hypotheses, we propose a partial penalized quasi-likelihood ratio test, a partial penalized quasi-score test, and a partial penalized Wald test. The theoretical properties of these three tests are established under both the null and the alternatives. The finite sample performance of the proposed tests has been shown by the simulation studies, and the forest health data is illustrated by our procedure.

Single-objective optimal designs might be criticized for not covering all aspects of the experiment when the experiment possesses multiple goals. In such a case, multi-objective optimal design is of interest. This paper adopts a sequential approach to obtain a multi-objective optimal design for Type-II progressive censoring with a dependent GLM-based random removal mechanism. Several simulation studies are conducted to evaluate and compare the performance of the proposed approach. A sensitivity analysis has been performed to investigate the effect of misspecification of design input parameters. Also, the sequential optimal design solution is used to construct the bounds in the (epsilon)-constraint optimal design. Finally, the usefulness of the proposed strategy is demonstrated through two real-life data analyses.

Expectile regression (ER) naturally extends the classical least squares to investigate heterogeneous effects of covariates on the distribution of the response variable. In this paper, we propose a penalized empirical likelihood (PEL) based ER estimator, which incorporates quadratic inference function and generalized estimating equation to construct the PEL procedure for longitudinal data. We investigate the asymptotic properties of the PEL estimator when the number of covariates is allowed to diverge as the sample size increases. The finite-sample performance of the proposed estimator is studied through simulations, and an application to yeast cell-cycle gene expression data is also presented.

In many block experiments where the treatments are applied to the experimental units sequentially over time or space, there may be a systematic trend effect that influences the observations in addition to the block and the treatment effects. In some previous literature, optimality of block designs under trend effects has been studied in the case of uncorrelated observations when the number of treatments is greater than the size of blocks. This article deals with the block model incorporating trend components when the observations are correlated under some correlation structures. We introduce methods for constructing trend-free optimal designs with every treatment number and block size.