A comparison of mixed and minimax estimators of linear models

In this paper the stochastic properties of two estimators of linear models, mixed and minimax, based on different types of prior information, are compared using quadratic risk as the criterion for superiority. A necessary and sufficient condition for the minimax estimator to be superior to the comparable mixed estimator is derived as well as a simpler necessary but not sufficient condition.     

The generalized maximum Tsallis entropy estimators and applications to the Portland cement dataset

Tsallis entropy is a generalized form of entropy and tends to be Shannon entropy when q → 1. Using Tsallis entropy, an alternative estimation methodology (generalized maximum Tsallis entropy) is introduced and used to estimate the parameters in a linear regression model when the basic data are ill-conditioned. We describe the generalized maximum Tsallis entropy and for q = 2 we call that GMET2 estimator. We apply the GMET2 estimator for estimating the linear regression model Y = Xβ + e where the design matrix X is subject to severe multicollinearity. We compared the GMET2, generalized maximum entropy (GME), ordinary least-square (OLS), and inequality restricted least-square (IRLS) estimators on the analyzed dataset on Portland cement.     

A study of moments and likelihood estimators of the odd Weibull distribution

The odd Weibull distribution is a three-parameter generalization of the Weibull and the inverse Weibull distributions having rich density and hazard shapes for modeling lifetime data. This paper explored the odd Weibull parameter regions having finite moments and examined the relation to some well-known distributions based on skewness and kurtosis functions. The existence of maximum likelihood estimators have shown with complete data for any sample size. The proof for the uniqueness of these estimators is given only when the absolute value of the second shape parameter is between zero and one. Furthermore, elements of the Fisher information matrix are obtained based on complete data using a single integral representation which have shown to exist for any parameter values. The performance of the odd Weibull distribution over various density and hazard shapes is compared with generalized gamma distribution using two different test statistics. Finally, analysis of two data sets has been performed for illustrative purposes.     

A bayesian comparison of randomized and voluntary response sampling models

This paper is concerned with making a Bayesian comparison between the two types of survey sampling procedures where the individuals are asked sensitive questions. The randomized response procedure is designed to obtain information in such a way that the respondent is protected against revealing his/her status about the sensitive issue. In voluntary response model each individual chooses either to respond or not to respond. It is assumed that the respondents do not falsify their answers. The problem of interest is to estimate the proportion of the sampled population who belong to the sensitive group. A beta prior distribution is used for the proportion of interest. The loss function is taken to be the quadratic loss function.     

A general inverse sampling scheme and its application to adaptive cluster sampling

Not having a variance estimator is a seriously weak point of a sampling design from a practical perspective. This paper provides unbiased variance estimators for several sampling designs based on inverse sampling, both with and without an adaptive component. It proposes a new design, which is called the general inverse sampling design, that avoids sampling an infeasibly large number of units. The paper provide estimators for this design as well as its adaptive modification. A simple artificial example is used to demonstrate the computations. The adaptive and non‐adaptive designs are compared using simulations based on real data sets. The results indicate that, for appropriate populations, the adaptive version can have a substantial variance reduction compared with the non‐adaptive version. Also, adaptive general inverse sampling with a limitation on the initial sample size has a greater variance reduction than without the limitation.     

A new lower bound to A2-optimality measure for multi-level and mixed-level column balanced designs and its applications

In this paper, a new lower bound to A₂-optimality measure is derived and is applied to multi-level and mixed-level column balanced designs. A₂-optimal multi-level and mixed-level designs are obtained by the application of the new lower bound.