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     

A new rank test for the K-Sample problem

The treatment sum of squares in the one-way analysis of variance can be expressed in two different ways: as a sum of comparisons between each treatment and the remaining treatments combined, or as a sum of comparisons between the treatments two at a time. When comparisons between treatments are made with the Wilcoxon rank sum statistic, these two expressions lead to two different tests; namely, that of Kruskal and Wallis and one which is essentially the same as that proposed by Crouse (1961,1966). The latter statistic is known to be asymptotically distributed as a chi-squared variable when the numbers of replicates are large. Here it is shown to be asymptotically normal when the replicates are few but the number of treatments is large. For all combinations of numbers of replicates and treatments its empirical distribution is well approximated by a beta distribution     

Infrence for non-negative autoregressive schemes

The object of this paper is the statistical analysis of Several Closely related models arising in water quality analysis. In particular, concern is with the autoregressive scheme X_r = ρX_r?1 + Y_r where 0 < ρ < 1 and Y's are i.i.d, and non-negative. The estimation and testing problem is considered for three parametric models - Gaussian, uniform and exponential - as well as for the nonparametric case where it is assumed that the Y's have a positive continuous distribution.     

On the distributions of the estimated process capability indices

The exact distributions of the estimated process capability indices are presented and their means, variances, and mean-squared errors are given. The basic assumption is that the process measurements are taken from a normal distribution. Theresults in this article are useful in evaluating process capability.     

Second order efficiency of the ban-estimators for the multinomial family

Rao (1961, 1963) introduced a measure of second order efficiency (s.o.e.) of a best asymptotically normal (BAN) estimator and obtained the s.o.e's of some well known estimators of the parameter of the multinomial family. Koorts (1985) dealt with a calss of BAN estimators and derived the s.o.e, of the estimator belonging to this class. In this paper we derive a general expressiion for the s.o.e. of a BAN estiimator based on its estimating equation.     

Testing for the mean of the inverse gaussian distribution and adaptive estimation of parameters

This paper provides the modified likelihood ratio criterion for testing whether the mean of the inverse Gaussian distribution can be set to unity giving rise to Standard form of the Wald distribution. Estimates of probability of correct selection has been obtained on the basis of a Monte Carlo study of 1,000 samples. Finally a set of adaptive estimators for the parameters are proposed and studied on the basis of data generated from the two distributions.     

Testing a main effect in a three factor mixed model

In the present paper, the author has considered and compared the power of three test procedures, based on two preliminary tests of significance (PTS), for testing a main effect in a three factor factorial experiment. Davenport and Webster (1973) type test statistics are used in the final test. Recommendation for a suitable size of PTS has been made so that the power of a test procedure is adequately high.