Empirical-likelihood-based Test for Partially Linear Single-index Models with Error-prone Linear Covariates

In this article, we consider whether the empirical likelihood ratio (ELR) test is applicable to testing for serial correlation in the partially linear single-index models (PLSIM) with error-prone linear covariates. It is shown that under the null hypothesis the proposed ELR statistic follows asymptotically a χ²-distribution with the scale constant and the degrees of freedom. A comparison between the ELR and the normal approximation method is also considered. Both simulated and real data examples are used to illustrate our proposed methodology.     

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.     

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.     

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.     

Four tests of fit for the beta-binomial distribution

Tests based on the Anderson–Darling statistic, a third moment statistic and the classical Pearson–Fisher X ² statistic, along with its third-order component, are considered. A small critical value and power study are given. Some examples illustrate important applications.     

Rank tests for the k-sample problem with restricted alternatives

An asymptotically maximin most powerful rank test among somewhere asymptotically most powerful linear rank tests with scores generating function cf> is derived for each of the simple order alternative, the simple loop alternative and the simple tree alternative in the k-sample problem. The comparisons of the tests obtained with the rank analogues of the Bartholomew's xv tests are made in terms of local asymptotic relative efficiency. It is found that our tests are better than the rank analogues of the xk tests. Furthermore, the asymptotic equivalence of the ranking by the pooled sample to the ranking in pairs are discuss¬ed and the tests which are asymptotically equivalent to ours are given.     

On optimal tests for general interval-hypotheses

Optimal statistical tests, using the normality assumptions for general interval hypotheses including equivalence testing and testing for nonzero difference (or for non-unit) are presented. These tests are based on the decision theory for Polya Type distributions and are compared with usual confidence tests and with ’two one-sided tests’- procedures. A formal relationship between some optimal tests and the Anderson and Hauck procedure as well as a procedure recommended by Patel and Gupta is given. A new procedure for a generalisation of Student's test as well as for equivalence testing for thet-statistics is shown.     

Estimation in noncentral distributions

This paper investigates alternatives to MIU estimators in noncentral X ² and F distributions. Two directions are pursued. In the first, a general approach for uniformly improving on MVU estimators is described and illustrated. In the second, Bayesian, procedures are characterized and illustrated as well. This effort extends earlier work of Perlman and Rasmussen and of Neff and Strawderman.     

C434. Local bounds on power of T2 in scale families

In this paper, we have developed a likelihood ratio factorization technique for variable selection for multiple observations model. The asymptotic distribution of the selection criterion is also given. This technique has been applied to a marketing data set for illustration of the technique developed.     

Some issues in logistic regression

Much research has been performed in the area of multiple linear regression, with the resuit that the field is well-developed. This is not true of logistic regression, however. The latter presents special problems because the response is not continuous. Some of these problems are: the difficulty of developing a suitable R² statistic, possibly poor results produced by the method of maximum likelihood, and the challenge to develop suitable graphical techniques. We describe recent work in some of these directions, and discuss the need for additional research.