Maximum Value of Hotelling's T 2 Statistics Based on the Successive Differences Covariance Matrix Estimator

In statistical process control applications, the multivariate T ² control chart based on Hotelling's T ² statistic is useful for detecting the presence of special causes of variation. In particular, use of the T ² statistic based on the successive differences covariance matrix estimator has been shown to be very effective in detecting the presence of a sustained step or ramp shift in the mean vector. However, the exact distribution of this statistic is unknown. In this article, we derive the maximum value of the T ² statistic based on the successive differences covariance matrix estimator. This distributional property is crucial for calculating an approximate upper control limit of a T ² control chart based on successive differences, as described in Williams et al. (2006 Williams , J. D. , Woodall , W. H. , Birch , J. B. , Sullivan , J. H. ( 2006 ). On the distribution of T ² statistics based on successive differences . J. Qual. Technol. 38 : 217 – 229 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]).     

Unit Roots: Bayesian Significance Test

The unit root problem plays a central role in empirical applications in the time series econometric literature. However, significance tests developed under the frequentist tradition present various conceptual problems that jeopardize the power of these tests, especially for small samples. Bayesian alternatives, although having interesting interpretations and being precisely defined, experience problems due to the fact that that the hypothesis of interest in this case is sharp or precise. The Bayesian significance test used in this article, for the unit root hypothesis, is based solely on the posterior density function, without the need of imposing positive probabilities to sets of zero Lebesgue measure. Furthermore, it is conducted under strict observance of the likelihood principle. It was designed mainly for testing sharp null hypotheses and it is called FBST for Full Bayesian Significance Test.     

Influential observation in complex normal data for problems in allometry

Abstract

The aim of this paper is to investigate how some results related to the complex normal distribution are relevant in size and shape analysis. Our main focus is on the derivation of influential measures. In particular, Cook and Kullback–Leibler distances are combined with their respective asymptotic results as well as to an alternative process of defining cut-off points. Some numerical examples illustrate how these measures are used in practice. We perform an application to simulated and actual data. Results provide evidence that the methodology based on Kullback–Leibler distance outperforms one in terms of the Cook classic distance.     

A variance shift model for detection of outliers in the linear mixed measurement error models

ABSTRACT

In this paper, we extend a variance shift model, previously considered in the linear mixed models, to the linear mixed measurement error models using the corrected likelihood of Nakamura (1990 Nakamura, T. (1990). Corrected score function for errors in variables models: methodology and application to generalized linear models. Biometrika 77:127–137.[Crossref], [Web of Science ®] , [Google Scholar]). This model assumes that a single outlier arises from an observation with inflated variance. We derive the score test and the analogue of the likelihood ratio test, to assess whether the ith observation has inflated variance. A parametric bootstrap procedure is implemented to obtain empirical distributions of the test statistics. Finally, results of a simulation study and an example of real data are presented to illustrate the performance of proposed tests.     

Asymptotic non-null distribution of a test connected with exponential populations

In this paper asymptotic expansions of the non-null distribution of the likelihood ratio criterion for testing the equality of several one parameter exponential distributions are obtained under local alternatives. These expansions are in terms of Chi-square distributions.     

Estimation in a Multivariable Two-Phase Regression

A likelihood approach is considered for the problems of estimating the changepoint and other parameters in a multivariable two-phase regression.Methods for finding the maximum likelihood estimates are given for the cases when the covariance matrix is known, and unknown.The distribution of the usual likelihood ratio test statistic is Investigated using simulations, and a Monte-Carlo aporoach is suggested for testing for the existence of a change-point.Numerical1 Illistrute aie provided.     

Tests for the two-sample problem based on empirical probability measures

Tests are proposed for the equality of two unknown distributions. For empirical probability measures that are defined for samples from the two distributions, the proposed tests are based on the supremum of the absolute differences between the corresponding empirical probabilities, the supremum being taken over all possible events (Borel sets). In contrast, competing EDF tests compare only empirical probabilities of a subclass of Borel sets. The proposed tests are compared for simulated samples to the Kolmogorov-Smirnov, Cramér-von Mises, Kuiper, and Mann-Whitney-Wilcoxon tests