Misspecified T2 tests. i. location and scale

Properties of Hotelling's (1931) T ² are studied under model misspecification in the model for a multivariate experiment. Stochastic bounds on T ² and further properties of the T ² test are studied under misspecified location and scale. The bounds are evaluated numerically in selected cases.     

Simultaneous Confidence Intervals for the Mean of Multivariate Poisson Distribution: A Comparison

Haibing (2009) proposed a procedure for successive comparisons between ordered treatment effects in one-way layout and showed that the proposed procedure has greater power than the procedure proposed by Lee and Spurrier (1995). Critical constants required for the proposed procedure were estimated using Monte Carlo simulation and few values of the constants were tabulated which limit the applications of the proposed procedure. In this article, a numerical method, using recursive integration methodology, is discussed to compute the critical constants which work efficiently for a large number of treatments and extensive values of critical constants are tabulated for the use of practitioners. Power comparisons of Haibing's and Lee and Spurrier's procedure is also discussed.     

Efficient Likelihood Estimators

If X ₁, …, X _n are identically and independently distributed, then as n ? ∞, there exists under suitable regularity conditions a sequence of solutions of the likelihood equation that is consistent and asymptotically efficient. However, this consistent solution is not necessarily the maximum likelihood estimate. Likelihood estimation should therefore emphasize the determination of a consistent sequence of solutions of the likelihood equations rather than maximizing the likelihood. The issues are illustrated on some examples.     

A Note on the Calculation of Pr{X 1 < X 2 < ··· < Xk }

Suppose that X_i are independent random variables, and that X_i has cdf F_i (x), 1 ≤ i ≤ k. Many statistical problems involve the probability Pr{X ₁ < X ₂ < ··· < X_k }. In this note a numerical method is proposed for computing this probability.     

CUSUM Chart with Transformed Exponential Data

Time Between Events (TBE) charts were proposed to monitor the time between events occur based on exponential distribution, and have been shown to be more effective than monitoring the fraction non conforming directly. In this article, we consider monitoring the TBE data with CUSUM scheme by transformation. The idea behind it is to transform the TBE data to normal, and then apply the CUSUM scheme for the approximate normal data. Several simple transformation methods are examined. The calculation of Average Run Length (ARL) with Markov chain approach is described. Comparative studies on the ARL performance show that the transformed CUSUM is superior to the X-MR (Moving Range) chart with transformation, the Cumulative Quantity Control (CQC) chart, and have comparable performance with exponential CUSUM charts. The design procedures of optimal CUSUM chart are also presented. This study provides another possible alternative for monitoring TBE data with easy design procedures and relatively good performance.     

On a Generalization of the Classical Random Sampling Scheme and Unbiased Estimation

A generalization of the classical random sampling scheme is suggested. Based on the proposed generalization one can derive many new minimum variance unbiased estimators for probabilities, as well as for other functions of unknown parameters, for the multivariate Pólya, the multivariate negative Pólya, the multinomial, the multivariate hypergeometric, the multivariate Poisson, and the Wishart probability distributions.     

On the Admissibility of Linear Estimators in a Multivariate Normal Distribution Under LINEX Loss Function

Consider an estimation problem of a linear combination of population means in a multivariate normal distribution under LINEX loss function. Necessary and sufficient conditions for linear estimators to be admissible are given. Further, it is shown that the result is an extension of the quadratic loss case as well as the univariate normal case.     

Asymptotic Properties of Generalized Multivariate Rank Statistics

This article discusses generalization of the well-known multivariate rank statistics under right-censored data case. Empirical process representation used to get the generalization. The marginal distribution functions are estimated by Kaplan–Meier estimators. Sufficient conditions for asymptotic normality of the generalized multivariate rank statistics under independently right censored data are specified. Several auxiliary results on sup-norm convergence of Kaplan–Meier estimators in randomly exhausting regions are given too.     

Modelling asymmetric volatility dynamics by multivariate BL-GARCH models

The class of Multivariate BiLinear GARCH (MBL-GARCH) models is proposed and its statistical properties are investigated. The model can be regarded as a generalization to a multivariate setting of the univariate BL-GARCH model proposed by Storti and Vitale (Stat Methods Appl 12:19–40, 2003a; Comput Stat 18:387–400, 2003b). It is shown how MBL-GARCH models allow to account for asymmetric effects in both conditional variances and correlations. An EM algorithm for the maximum likelihood estimation of the model parameters is derived. Furthermore, in order to test for the appropriateness of the conditional variance and covariance specifications, a set of robust conditional moments test statistics are defined. Finally, the effectiveness of MBL-GARCH models in a risk management setting is assessed by means of an application to the estimation of the optimal hedge ratio in futures hedging.     

Semiparametric estimation of multivariate partially linear models

Inspired by a primary hypertension study was conducted by Chinese government in the Inner Mongolia Autonomous Region, we introduce partially linear models with multivariate responses to evaluate the simultaneous effects of modifiable risk factors on both the systolic and the diastolic blood pressures. We propose a class of weighted profile least-squares approaches to estimate both the parametric and the nonparametric components of the multivariate partially linear models. We also investigate how the weight matrix affects the resultant estimation efficiency. We illustrate our proposals through simulations and an analysis of the primary hypertension data. Our analysis provides strong evidence that the obesity is indeed an important risk factor predisposing to primary hypertension even after adjusting for the ageing effect.