Heteroscedasticity and/or Autocorrelation Checks in Longitudinal Nonlinear Models with Elliptical and AR(1) Errors

The aim of this paper is to study the tests for variance heterogeneity and/or autocorrelation in nonlinear regression models with elliptical and AR（1） errors. The elliptical class includes several symmetric multivariate distributions such as normal, Student-S, power exponential, among others. Several diagnostic tests using score statistics and their adjustment are constructed. The asymptotic properties, including asymptotic chi-squave and approximate powers under local alternatives of the score statistics, are studied. The properties of test statistics are investigated through Monte Carlo simulations. A data set previously analyzed under normal errors is reanalyzed under elliptical models to illustrate our test methods.

Matrix Image Method for Ranking Nonregular Fractional Factorial Designs

Nonregular fractional factorial designs such as Plackett-Burman designs and other orthogonal arrays are widely used in various screening experiments for their run size economy and flexibility. In this paper,we study matrix image theory and present a new method for distinguishing and assessing nonregular designs with complex alias structure, which works for all symmetrical and asymmetrical, regular and nonregular orthogonal arrays. Based on the matrix image theory, our proposed method captures orthogonality and projection properties. Empirical studies show that the proposed method has a more precise differentiation capacity when comparing with some other criteria.

Score Tests for Zero-inflated Double Poisson Regression Models

Count data with excess zeros encountered in many applications often exhibit extra variation. There- fore, zero-inflated Poisson （ZIP） model may fail to fit such data. In this paper, a zero-inflated double Poisson model （ZIDP）, which is generalization of the ZIP model, is studied and the score tests for the significance of dis- persion and zero-inflation in ZIDP model are developed. Meanwhile, this work also develops homogeneous tests for dispersion and/or zero-inflation parameter, and corresponding score test statistics are obtained. One numer- ical example is given to illustrate our methodology and the properties of score test statistics are investigated through Monte Carlo simulations.

On Moments of the Maximum of Partial Sums of Moving Average Processes under Dependence Assumptions

Let{Yi;-∞〈i〈∞}be a doubly infinite sequence of identically distributed φ-mixing random variables and let{ai;-∞〈i〈∞}be an absolutely summable sequence of real numbers. In this paper we study the moments of sup n〉1k=1-｜∞∑^n∑^∞aiYi＋k/n^1/r｜^p（1〈r〈2,P〉0）under the conditions of some moments.