In this paper, we define two restricted estimators for the regression parameters in a multiple linear regression model with measurement errors when prior information for the parameters is available. We then construct two sets of improved estimators which include the preliminary test estimator, the Stein-type estimator and the positive rule Stein type estimator for both slope and intercept, and ...

‎Zero-inflated negative binomial model is an appropriate choice to count response variables with excessive zeros and over-dispersion simultaneously. ‎This paper addressed parameter estimation in the zero-inflated when there are many parameters, ‎so that some of them have not influence on variable. ‎We proposed based linear shrinkage, ‎pretest, ‎shrinkage pretest, ‎Stein-type, ‎and positive Stei...

Extended Abstract. In recent years, needs for small area estimations have been greatly increased for large surveys particularly household surveys in Sta­ tistical Centre of Iran (SCI), because of the costs and respondent burden. The lack of suitable auxiliary variables between two decennial housing and popula­ tion census is a challenge for SCI in using these methods. In general, the...

This paper addresses the problems of estimating the normal covariance and precision matrices. A commutator subgroup of lower triangular matrices is considered for deriving a class of invariant estimators. The class shows inadmissibility of the best invariant and minimax estimator of the covariance matrix relative to quadratic loss. Also, in estimation of the precision matrix, a dominance result...

The problem of estimating a covariance matrix in multivariate linear regression models is addressed in a decision-theoretic framework. Although a standard loss function is the Stein loss, it is not available in the case of a high dimension. In this paper, a new type of a quadratic loss function, called the intrinsic loss, is suggested, and unified dominance results are derived under the loss, i...

The simultaneous prediction of average and actual values of study variable in a linear regression model is considered in this paper. Generally, either of the ordinary least squares estimator or Stein-rule estimators are employed for the construction of predictors for the simultaneous prediction. A linear combination of ordinary least squares and Stein-rule predictors are utilized in this paper ...

In this paper we propose James–Stein type estimators for variances raised to a fixed power by shrinking individual variance estimators towards the arithmetic mean. We derive and estimate the optimal choices of shrinkage parameters under both the squared and the Stein loss functions. Asymptotic properties are investigated under two schemes when either the number of degrees of freedom of each ind...

The new century has brought us a new class of statistics problems, much bigger than their classical counterparts, and often involving thousands of parameters and millions of data points. Happily, it has also brought some powerful new statistical methodologies. The most prominent of these is Benjamini and Hochberg’s False Discovery Rate (FDR) procedure, extensively explored in this issue of Stat...