On the total sojourn time of particles in semi-markov compartmental system with branching particles

We consider a semi-Markov compartroental system with branching particles, Me study the total sojourn time of all the particles and obtain the asymptotic behaviour of its mean. We also discuss some special systems.     

Nonparametric prediction analysis for binary data

A nonparametric inference algorithm developed by Davis and Geman (1983) is extended problem. The algorithm and applied to a medical prediction employs an estimation procedure for acquiring pairwise statistics among variables of a binary data set, allows for the data-driven creation of interaction terms among the variables, and employs a decision rule which asymptotically gives the minimum expected error. The inference procedure was designed for large data sets but has been extended via the method of cross-validation to encompass smaller data sets.     

On the asymptotic efficiency of moment and maximum likelihood estimators in the three-parameter inverse gaussian distribution

The asymptotic distribution of estimators generated by the methods of moments and maximum likelihood are considered. Simple formulae are provided which enable comparisons of asymptotic relative efficiency to be effected.     

Nonparametric estimation of the survival distribution in censored data

Two nonparametric estimators o f the survival distributionare discussed. The estimators were proposed by Kaplan and Meier (1958) and Breslow (1972) and are applicable when dealing with censored data. It is known that they are asymptotically unbiased and uniformly strongly consistent, and when properly normalized that they converge weakly to the same Gaussian process. In this paper, the properties of the estimators are carefully inspected in small or moderate samples. The Breslow estimator, a shrinkage version of the Kaplan-Meier, nearly always has the smaller mean square error (MSE) whenever the truesurvival probabilityis at least 0.20, but has considerably larger MSE than the Kaplan-Meier estimator when the survivalprobability is near zero.     

The pitman nearness criterion and its determination

A general method for determining Pitman Nearness is given In the case of univariate estimators. This method is then applied to some estimation problems. The concept of Pitman Nearness is also generalized to the multivariate case. The James-Stein estimators are used to illustrate the multivariate comparison.     

Bayesian outlier testing using the predictive distribution for a linear model op constant intraclass form

The problem of testing suspected outliers from a linear model with constant intraclass correlation is considered from a Bayesian viewpoint. The main objective of this paper is to develop an outlier test procedure based on the predictive distribution of suspected outlier observations given a set of existing inlier observations. The test procedure is easily performed with the usual F and t distributions.     

A cell means analysis of mixed linear models

The purpose of this paper is to describe a simple procedure for the estima-tion of parameters in the unbalanced mixed linear model. There are implications for hypothesis testing and interval estimation, A feature of these estimators is that they are expressed in terms of simple formulas. This has obvious advantages for computations and small sample analysis. In addition, the formulas suggest useful diagnostic procedures for assessing the quality of the data as well as possible defects in the model assumptions. The concepts are illustrated with several examples. Evidence is presented to indicate that, in cases of modest imbalance, these estimators are highly efficient and dominate AOV estimates over most of the parameter space. In cases of more extreme imbalance, the results are qualitatively the same but the estimators are less efficient than the AOV estimators for small values of the parameters. The extension of this method to factorial models with missing cells is not complete.     

Infiuence functions for certain parameters in discriminant analysis when a single discriminant function is not adequate

The influence function introduced by Hampel (1968, 1973, 1974) i s a tool that can be used for outlier detection. Campbell (1978) has derived influence function for ~ahalanobis's distance between two populations which can be used for detecting outliers i n discriminant analysis. Radhakrishnan and Kshirsagar (1981) have obtained influence functions for a variety of parametric functions i n multivariate analysis. Radhakrishnan (1983) obtained influence functions for parameters corresponding to "residual" wilks's A and i t s "direction" and "collinearity" factors i n discriminant analysis when a single discriminant function is ade- quate while discriminating among several groups. In this paper influence functions for parameters that correspond to "residual" wilks's A and its "direction" and "coplanarity" factors used to test the goodness of f i t of s (s>l) assigned discriminant func- tions for discriminating among several groups are obtained. These influence functions can be used for outlier detection i n m u l t i -variate data when a single discriminant function is not adequate.