Semiparametric inference on partially linear single-index model

ABSTRACT

We consider semiparametric inference on the partially linearsingle-index model (PLSIM). The generalized likelihood ratio (GLR) test is proposed to examine whether or not a family of new semiparametric models fits adequately our given data in the PLSIM. A new GLR statistic is established to deal with the testing of the index parameter α₀ in the PLSIM. The newly proposed statistic is shown to asymptotically follow a χ²-distribution with the scale constant and the degrees of freedom being independent of the nuisance parameters or function. Some finite sample simulations and a real example are used to illustrate our proposed methodology.     

PMSE performance of two different types of preliminary test estimators under a multivariate t error term

Abstract

In this paper, assuming that the error terms follow a multivariate t distribution, we derive the exact formula for the predictive mean squared error (PMSE) of two different types of pretest estimators. It is shown analytically that one of the pretest estimator dominates the SR estimator if a critical value of the pretest is chosen appropriately. Also, we compare the PMSE of the pretest estimators with the MMSE, AMMSE, SR and PSR estimators by numerical evaluations. Our results show that the pretest estimators dominate the OLS estimator for all combinations when the degrees of freedom is not more than 5.     

More on the Preliminary Test Estimator in Almost Unbiased Liu Regression

This article is concerned with the parameter estimation in linear regression model when it is suspected that the regression coefficients are the subspace of the equality restrictions. The objective of this article is to introduce the preliminary test almost unbiased Liu estimators (PTAULE) based on the Wald (W), the likelihood ratio (LR), and the Lagrangian multiplier (LM) tests and compare the proposed estimators in the sense of the quadratic bias and mean square error (MSE) criterion.     

Local Linear Estimation of Second-order Jump-diffusion Model

In this article, we propose the local linear estimators of the drift coefficient and diffusion coefficient in the second-order jump-diffusion model. We also show the consistency and asymptotic normality of these estimators under mild conditions.     

Complete convergence of the non-identically distributed pairwise NQD random sequences

ABSTRACT

In this article, we study complete convergence of the nonidentically distributed pairwise negatively quadrant dependent (NQD) random sequences by the moment inequality and terminating random variables,which extend and improve the previous relevant results.     

Concurrent Design for Process Quality,Statistical Tolerance,and SPC

The rapid response to the requirements of customers and markets promotes the concurrent engineering (CE) technique in product and process design. The decision making for process quality target, SPC method, sampling plan, and control chart parameter design can be done at the stage of process quality plan based on historical data and process knowledge database. Therefore, it is a reasonable trend to introduce the concepts and achievements on process quality evaluation and process capability analysis, CE, and SPC techniques into process plan and tolerance design. A new systematic method for concurrent design of process quality, statistical tolerance (ST), and control chart is presented based on a NSFC research program. A set of standardized process quality indices (PQIs) for variables is introduced for meeting the measurement and evaluation to process yield, process centering, and quality loss. This index system that has relatively strong compatibility and adaptability is based on raisonne grading by using the series of preferred numbers and arithmetical progression. The expected process quality based on this system can be assured by a standardized interface between PQIs and SPC, that is, quality-oriented statistical tolerance zone. A quality-oriented ST and SPC approach that quantitatively specifies what a desired process is and how to assure it will realize the optimal control for a process toward a predetermined quality target.     

Likelihood Ratio Order of m-Spacings in Multiple-Outlier Models

This article deals with the multiple-outlier exponential model. The likelihood ratio order between m-spacings of the combined sample is developed, some results extend the conclusions on simple spacings in Wen et al. (2007 Wen , S. , Lu , Q. , Hu , T. ( 2007 ). Likelihood ratio order of spacings of heterogeneous exponential random variables . J. Multivariate Anal. 98 : 743 – 756 .[Crossref], [Web of Science ®] , [Google Scholar]).     

Bayesian Approaches to Nonparametric Estimation of Densities on the Unit Interval

This paper investigates nonparametric estimation of density on [0, 1]. The kernel estimator of density on [0, 1] has been found to be sensitive to both bandwidth and kernel. This paper proposes a unified Bayesian framework for choosing both the bandwidth and kernel function. In a simulation study, the Bayesian bandwidth estimator performed better than others, and kernel estimators were sensitive to the choice of the kernel and the shapes of the population densities on [0, 1]. The simulation and empirical results demonstrate that the methods proposed in this paper can improve the way the probability densities on [0, 1] are presently estimated.     

Performance analysis of the retrial queues with finite number of sources and service interruptions

This paper aims at presenting an analytic approach for investigating a single-server retrial queue with finite population of customers where the server is subject to interruptions. A free source may generate a primary call to request service. If the server is free upon arrival, the call starts to be served and the service times are independent, generally distributed random variables. During the service time the source cannot generate a new primary call. After service the source moves into the free state and can generate a new primary call. There is no waiting space in front of the server, and a call who finds the server unavailable upon arrival joins an orbit of unsatisfied customers. The server is subject to interruptions during the service processes. When the server is interrupted, the call being served just before server interruption goes to the retrial orbit and will retry its luck after a random amount of time until it finds the server available. The recovery times of the interrupted server are assumed to be generally distributed. Our analysis extends previous work on this topic and includes the analysis of the arriving customer’s distribution, the busy period, and the waiting time process.     

On the sample breakdown robustness of some nonparametric tests

In this paper, relying on the sample breakdown points, we investigate the sample breakdown properties of some nonparametric tests. It is shown that the sample breakdown points of the sign test asymptotically dominate those of the Wilcoxon test for one–sided hypotheses, However, the different conclusion is derived in the case of testing some shrinking neighborhood hypotheses. The breakdown behaviors of the Kolmogorov test and X²–test are also explored. These studies unify or refine some existing breakdown analyses of tests.