Decomposition of Variance for Spatial Cox Processes

Abstract. Spatial Cox point processes is a natural framework for quantifying the various sources of variation governing the spatial distribution of rain forest trees. We introduce a general criterion for variance decomposition for spatial Cox processes and apply it to specific Cox process models with additive or log linear random intensity functions. We moreover consider a new and flexible class of pair correlation function models given in terms of normal variance mixture covariance functions. The proposed methodology is applied to point pattern data sets of locations of tropical rain forest trees.     

Serials Clutter in Online Catalogs

Abstract

Finding and deciphering serials records in online catalogs is a challenge to many library users. To understand and analyze these challenges, the author conducted searches for scientific journal titles in the online catalogs of Committee on Institutional Cooperation (CIC) libraries. The first part of the study measures the difficulty of retrieving serial records from online catalogs comparing one-word versus multiple-word titles. The second part analyzes displays for complexity by measuring the length of the complete record and the length of the holdings statements. These data show the complexity of displays and indicate the potential confusion that these displays may induce in library users.     

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.     

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.     

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.     

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.     

The robust economic statistical design of the Hotelling's T2 chart

ABSTRACT

Economic statistical designs aim at minimizing the cost of process monitoring when a specific scenario or a set of estimated process and cost parameters is given. But, in practice the process may be affected by more than one scenario which may lead to severe cost penalties if the wrong design is used. Here, we investigate the robust economic statistical design (RESD) of the T² chart in an attempt to reduce these cost penalties when there are multiple scenarios. Our method is to employ the genetic algorithm (GA) optimization method to minimize the total expected monitoring cost across all distinct scenarios. We illustrate the effectiveness of the method using two numerical examples. Simulation studies indicate that robust economic statistical designs should be encouraged in practice.     

High dimensional asymptotics for the naive Hotelling T2 statistic in pattern recognition

Abstract

This paper examines the high dimensional asymptotics of the naive Hotelling T² statistic. Naive Bayes has been utilized in high dimensional pattern recognition as a method to avoid singularities in the estimated covariance matrix. The naive Hotelling T² statistic, which is equivalent to the estimator of the naive canonical correlation, is a statistically important quantity in naive Bayes and its high dimensional behavior has been studied under several conditions. In this paper, asymptotic normality of the naive Hotelling T² statistic under a high dimension low sample size setting is developed using the central limit theorem of a martingale difference sequence.     

A Unified Way to Represent and Compute the Cumulative Distribution Function for Noncentral t,F, and χ2

This short article shows an unified approach to representing and computing the cumulative distribution function for noncentral t, F, and χ². Unlike the existing algorithms, which involve different expansion and/or recurrence, the new approach consistently represents all the three noncentral cumulative distribution functions as the integral of the normal cumulative distribution function and χ² density function.     

Comparing several experimental groups with a control in the multivariate case

This paper presents a multivariate extension of Dunnett's test for comparing simultaneously k treatment group means with a single control group mean. A test based on Hotelling T²statistics is presented and approximate critical values are evaluated for the case of equal numbers of observations in each group, for the .05 and .01 levels of significance, for 1 to 5 variates, for 1 to 10 treatment groups, and for varying degrees of freedom. The accuracy of the procedure for generating approximate critical values is assessed via simulation studies conducted for selected cases and an example is presented using real data.