Mixed Graphical Model Selection Using Holm's Procedure

The problem of selecting a graphical model is considered as a performing simultaneously multiple tests. The control of the overall Type I error on the selected graph is done using the so famous Holm's procedure. We prove that when we use a consistent edge exclusion test the selected graph is asymptotically equal to the true graph with probability at least equal to a fixed level 1 ? α. This method is then used for the selection of mixed concentration graph models by performing the χ²-edge exclusion test. We also apply the method to two classical examples and to simulated data. We compare the overall error of the selected model with the one obtained using the stepwise method. We establish that the control is better when we use the Holm's procedure.     

Detection and Interpretation of a Multivariate Signal Using Combined Charts

A control procedure is presented in this article that is based on jointly using two separate control statistics in the detection and interpretation of signals in a multivariate normal process. The procedure detects the following three situations: (i) a mean vector shift without a shift in the covariance matrix; (ii) a shift in process variation (covariance matrix) without a mean vector shift; and (iii) both a simultaneous shift in the mean vector and covariance matrix as the result of a change in the parameters of some key process variables. It is shown that, following the occurrence of a signal on either of the separate control charts, the values from both of the corresponding signaling statistics can be decomposed into interpretable elements. Viewing the two decompositions together helps one to specifically identify the individual components and associated variables that are being affected. These components may include individual means or variances of the process variables as well as the correlations between or among variables. An industrial data set is used to illustrate the procedure.     

On Two Types of Breakdown Points of Weighted L 2-median

Zuo (2004) investigated the simplified replacement finite sample breakdown point of weighted L ^p -depth and L ^p -median for some appropriate weight functions. The addition breakdown point of weighted L ^p -depth functions is studied firstly in this article. In addition, for some other weight functions different from those in Zuo (2004 Zuo , Y. ( 2004 ). Robustness of weighted L ^p -depth and L ^p -median . Allgemeines Statistics Archiv. 88 : 215 – 234 . [Google Scholar]), we establish the lower bounds of these two types of breakdown point of weighted L ²-median.     

Generalized Analysis-of-variance-type Test for the Single-index Quantile Model

In this paper, we are concerned with a test for the index parameter and index function in the single-index model. Based on the estimates obtained by the quantile regression, we extend the generalized analysis-of-variance-type test to the single-index model. We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null distribution follows an asymptotically χ²-distribution. The simulation studies and real data applications are conducted to illustrate the finite sample performance of the proposed methods.     

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.