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.     

Hayter and Tsui's test with double sampling for the vector mean of multivariate normal population

Abstract

In this paper, we introduce a version of Hayter and Tsui's statistical test with double sampling for the vector mean of a population under multivariate normal assumption. A study showed that this new test was more or as efficient than the well-known Hotelling's T² with double sampling. Some nice features of Hayter and Tsui's test are its simplicity of implementation and its capability of identifying the errant variables when the null hypothesis is rejected. Taking that into consideration, a new control chart called HTDS is also introduced as a tool to monitor multivariate process vector mean when using double sampling.     

Two-stage generalized moment method approach for bidimensional random coefficient autoregressive models

ABSTRACT

A two-dimensionally indexed random coefficients autoregressive models (2D ? RCAR) and the corresponding statistical inference are important tools for the analysis of spatial lattice data. The study of such models is motivated by their second-order properties that are similar to those of 2D ? (G)ARCH which play an important role in spatial econometrics. In this article, we study the asymptotic properties of two-stage generalized moment method (2S ? GMM) under general asymptotic framework for 2D ? RCA models. So, the efficiency, strong consistency, the asymptotic normality, and hypothesis tests of 2S ? GMM estimation are derived. A simulation experiment is presented to highlight the theoretical results.     

Some concepts of mult1variate dependence

Several types of positive dependence are shown to be equiv-alent to the concept of a distribution with a density which is TP₂ in pairs. Among these is the concept of m^?-positive depend-ence of Alam and Wallenius. Using this result, all relationships among many of the most important concepts of positive dependence are determined. Furthermore, an application of the equivalences of these types of positive dependence yields a results of Ahmed, Langberg, Leon and Proschan.     

A note on a parametric extension of rank tests to the analysis of multifactor experiments within blocks

A general rank test procedure based on an underlying multinomial distribution is suggested for randomized block experiments with multifactor treatment combinations within each block. The Wald statistic for the multinomial is used to test hypotheses about the within–block rankings. This statistic is shown to be related to the one–sample Hotellingt's T² statistic, suggesting a method for computing the test statistic using the standard statistical computer packages.     

A note on positive dependence im multivariate distributioms

I counterexample is presented to the result by Alam and Malleolus asserting that if Y is stochastically increasing in a random vector X, then Y is stochastically increasing in a subvector of X. Their result concerning m*-positive dependence, whose proof relies on the erroneous result, is still true.     

A test for variance-covarianch parameters in normal linear models

This paper derives a test statistic for the variance-covariance parameters which is a quadratic function of their MINQUE (Minimum Norm Quadratic Unbiased Estimation) estimates. The test is a Wald-type test, and its development closely parallels the theory used to derive a similar test for the coefficients in linear models. In fact, the derivation proceeds by first setting up the estimation problem in a derived linear model in which the dispersion parameters are the coefficients. The test statistic is shown to be the sum of the squares of independent standardized x² variables.     

On L 1-consistency of kernel-type density estimator for stationary markov processes

A convergence result for kernel type density estimators, proved by Devroye and Gyrofi (1985), is extended to stationary Markov processess satisfying (G ₂-condition introduced by Rosenblatt (1970).     

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.     

Diagnosis of Multivariate Control Chart Signal Based on Dummy Variable Regression Technique

Abstract

It is common to monitor several correlated quality characteristics using the Hotelling's T ² statistic. However, T ² confounds the location shift with scale shift and consequently it is often difficult to determine the factors responsible for out of control signal in terms of the process mean vector and/or process covariance matrix. In this paper, we propose a diagnostic procedure called ‘D-technique’ to detect the nature of shift. For this purpose, two sets of regression equations, each consisting of regression of a variable on the remaining variables, are used to characterize the ‘structure’ of the ‘in control’ process and that of ‘current’ process. To determine the sources responsible for an out of control state, it is shown that it is enough to compare these two structures using the dummy variable multiple regression equation. The proposed method is operationally simpler and computationally advantageous over existing diagnostic tools. The technique is illustrated with various examples.