Adjusted Likelihood Inference in an Elliptical Multivariate Errors-in-Variables Model

In this paper, we obtain an adjusted version of the likelihood ratio (LR) test for errors-in-variables multivariate linear regression models. The error terms are allowed to follow a multivariate distribution in the class of the elliptical distributions, which has the multivariate normal distribution as a special case. We derive a modified LR statistic that follows a chi-squared distribution with a high degree of accuracy. Our results generalize those in Melo and Ferrari (Advances in Statistical Analysis, 2010, 94, pp. 75–87) by allowing the parameter of interest to be vector-valued in the multivariate errors-in-variables model. We report a simulation study which shows that the proposed test displays superior finite sample behavior relative to the standard LR test.     

Testing the homogeneity of proportions for clustered binary data without knowing the correlation structure

A robust generalized score test for comparing groups of cluster binary data is proposed. This novel test is asymptotically valid for practically any underlying correlation configurations including the situation when correlation coefficients vary within or between clusters. This structure generally undermines the validity of the typical large sample properties of the method of maximum likelihood. Simulations and real data analysis are used to demonstrate the merit of this parametric robust method. Results show that our test is superior to two recently proposed test statistics advocated by other researchers.     

A pilot Monte Carlo study of two sequential estimation procedures based on generalized U-statistics

Recently two sequential estimation procedures based on generalized U-statistics have appeared in the statistical literature [Williams and Sen (1973, 1974)]. One of these procedures concerns the multi-sample problem of estimating a vector of parameters when the total sample size is fixed. The other procedure concerns the multi-sample problem of constructing a confidence ellipsoid of bounded maximum width for a vector of parameters. To supplement the asymptotic theory discussed in these earlier papers, a Monte Carlo study investigating the efficiency of these procedures for moderate sample sizes would be useful. This paper describes a preliminary Monte Carlo study utilizing a small number of replications and performed to provide information for the design of a more extensive study.     

Testing for bivariate normality using the empirical distribution function

The problem of testing for bivariate normality using the empirical distribution function is considered. A Cramér-von Mises type statistic is defined and asymptotic percentage points for this statistic given. This involves solving a two-dimensional homogeneous integral equation. Unfortunately the Cramér-von Mises statistic is not invariant under orthogonal transformations of the data so that an invariant statistic is developed. Approximations for the distribution of this statistic are found by Monte Carlo. Applications of the statistics are given. It is shown that the statistics are particularly sensitive to certain kinds of pattern in the data and they could be useful in data analysis apart from providing a formal test of bivariate normality     

On a geometrical derivation of the upper tail of the null distribution of w-exponential

Shapiro and Wilk (1972) proposed a goodness of fit test for the exponential distribution. Carrie (1980) obtained an explicit expression of the null distribution of their test statistic W (n) E in a neighbourhood of its upper tail. His derivation uses a certain transformation involving the order statistics from the standard exponential distribution. In this paper we present an alternative derivation of this distribution using an elementary geometrical argument.     

The exponentiated generalized gamma distribution with application to lifetime data

A four-parameter extension of the generalized gamma distribution capable of modelling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone and non-monotone failure rate functions, which are quite common in lifetime data analysis and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the exponentiated Weibull, exponentiated generalized half-normal, exponentiated gamma and generalized Rayleigh, among others. We derive two infinite sum representations for its moments. We calculate the density of the order statistics and two expansions for their moments. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is obtained. Finally, a real data set from the medical area is analysed.     

Robustness of three power transformation estimation procedures

Maximum likelihood, goodness-of-fit, and symmetric percentile estimators of the power transformation parameterp, are considered. The comparative robustness of each estimation procedure is evaluated when the transformed data can be made symmetric, but may not necessarily be normal. Seven types of symmetric distributions are considered as well as four contaminated normal distributions over a range of six p values for samples of size 25, 50, and 100. The results indicate that the maximum likelihood estimator was slightly better than the goodness-of-fit estimator, but both were greatly superior to the percentile estimator. In general, the procedures were robust to distributional symmetric departures from normality, but increasing kurtosis caused appreciable increases in variation for estimated p values. The variability of p was found to decrease more than exponentially with decreases in the underlying normal distribution coefficient of variation. The standard likelihood ratio confidence interval procedure was found not to be generally useful.     

A review of nonparametric ranked-set sampling methodology

Ranked-set sampling is an alternative to random sampling for settings in which measurements are difficult or costly. Ranked-set sampling utilizes information gained without measurement to structure the eventual measured sample. This additional information yields improved properties for ranked-set sample procedures relative to their simple random sample counterparts. We review the available nonparametric procedures for data from ranked-set samples. Estimation of the distribution function was the first nonparametric setting to which ranked-set sampling methodology was applied. Since the first paper on the ranked-set sample empirical distribution function, the two-sample location setting, the sign test, and the signed-rank test have all been examined for ranked-set samples. In addition, estimation of the distribution function has been considered in a more general setting. We discuss the similarities and differences in the properties of the ranked-set sample procedures for the various settings     

Asymptotic Distribution of the Estimated BDS Statistic from The Residuals of Location-Scale Type Processes

We introduce local asymptotic normality (LAN) for the log-likelihood ratio and the contiguity property of a class of location-scale processes in this paper. Using the contiguity property, we study the asymptotic distribution of the estimated Brock-Dechert-Scheinkman (BDS) statistic from the standardized residuals of fitting location-scale type processes.     

Testtesting for the equality of scale parameters of k(> 2) exponential populations based on complete and type ii censored samples

This paper is concerned with testing the equality of scale parameters of K(> 2) two-parameter exponential distributions in presence of unspecified location parameters based on complete and type II censored samples. We develop a marginal likelihood ratio statistic, a quadratic statistic (Qu) (Nelson, 1982) based on maximum marginal likelihood estimates of the scale parameters under the null and the alternative hypotheses, a C(a) statistic (CPL) (Neyman, 1959) based on the profile likelihood estimate of the scale parameter under the null hypothesis and an extremal scale parameter ratio statistic (ESP) (McCool, 1979). We show that the marginal likelihood ratio statistic is equivalent to the modified Bartlett test statistic. We use Bartlett's small sample correction to the marginal likelihood ratio statistic and call it the modified marginal likelihood ratio statistic (MLB). We then compare the four statistics, MLBi Qut CPL and ESP in terms of size and power by using Monte Carlo simulation experiments. For the variety of sample sizes and censoring combinations and nominal levels considered the statistic MLB holds nominal level most accurately and based on empirically calculated critical values, this statistic performs best or as good as others in most situations. Two examples are given.