Renyi Entropy Properties of Order Statistics

In this article, we discuss some properties of Renyi entropy and Renyi information of order statistics. Some bounds for Renyi entropy of order statistics are obtained. Also, we relate Renyi entropy ordering of order statistics to Renyi entropy ordering and other well known orderings of parent random variables. Then it is proved that the Renyi information between order statistics and parent random variable is distribution free, and it is shown, as expected, the distance is minimum for the median.     

On the Use of Superpopulation Model in Estimation of Population Mean in Two-Occasion Rotation Patterns

The present work is an attempt to study the estimation of the population mean on the current occasion in two-occasion successive (rotation) sampling under a superpopulation model. Six different estimators are proposed for estimating the current population mean in two-occasion successive (rotation) sampling. Optimum replacement policies and performances of the proposed estimators have been discussed. Results are interpreted via empirical studies.     

Effective Rotation Patterns Under Non Response in Two-Occasion Successive Sampling

This article intends to develop some effective rotation patterns with the aid of attractive imputation methods when the problems of non response occur in two-occasion successive sampling. Utilizing the information on p (p ??1) auxiliary variables regression methods of imputation have been considered and subsequently multiple linear regression type estimators are proposed to estimate the current population mean in two-occasion successive sampling. Proposed estimators are compared with the estimator for same situations but in the absence of non-response. Optimum replacement strategies of the respective estimators have been discussed and results are interpreted with the help of empirical studies. Conclusions and suitable recommendations are made.     

Maximal Invariant and Weakly Equivariant Estimators

Equivariant functions can be useful for constructing of maximal invariant statistic. In this article, we discuss construction of maximal invariants based on a given weakly equivariant function under some additional conditions. The theory easily extends to the case of two or more weakly equivariant functions. Also, we derive a maximal invariant statistic when the group contains a sharply transitive and a characteristic subgroup. Finally, we consider the independence of invariant and weakly equivariant functions under some special conditions.     

The Generalized Pascal Triangle and the Matrix Variate Jensen-Logistic Distribution

This article defines the so called Generalized Matrix Variate Jensen-Logistic distribution. The relevant applications of this class of distributions in Configuration Shape Theory consist of a more efficient computation, supported by the corresponding inference. This demands the solution of two important problems: (1) the development of analytical and efficient formulae for their k-th derivatives and (2) the use of the derivatives to transform the configuration density into a polynomial density under some special matrix Kummer relation, indexed in this case by the Jensen-Logistic kernel. In this article, we solve these problems by deriving a simple formula for the k-th derivative of the density function, avoiding the usual partition theory framework and using a generalization of Pascal triangles. Then we apply the results by obtaining the associated Jensen-Logistic Kummer relations and the configuration polynomial density in the setting of Statistical Shape Theory.     

Bootstrap test of hypothesis for the multi-state models in survival analysis

Abstract

In the present paper we develop bootstrap tests of hypothesis, based on simulation, for the transition probability matrix arising in the context of a multi-state model. The bootstrap test statistic is based on the paper of Tattar and Vaman (2008 Tattar, P. N., Vaman, H. J. (2008). Testing transition probability matrix of a multi-state model with censored data. Lifetime Data Anal. 14(2):216–230.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), which develops a statistic for the testing problems concerning the transition probability matrix of the non homogeneous Markov process.     

Some estimation procedures using a linear model in successive sampling

ABSTRACT

In successive sampling some recent works depict the use of super-population models where information on stable auxiliary variable over occasions has been utilized. Stability character of auxiliary variable may not sustain, if the duration between occasions is large. To cope with such situations, the present work is an attempt to develop some estimation procedures by utilizing the information on two independent auxiliary variables through a linear super-population model. Some estimators are proposed to estimate the current population mean in two occasions successive (rotation) sampling. Optimum replacement strategies are formulated and performances of the proposed estimators have been discussed. Results are interpreted through empirical studies.