Anoop Chaturvedi

The necessary and sufficient conditions for the uniform dominance of the two-stage stein estimators

Abstract The paper proves the necessary and sufficient conditions for the uniform dominance in quadratic loss of the c-class two-stage Stein estimators over the Stein estimator in the linear models.

Bayesian estimation for the Pareto income distribution

The Bayes estimators of the Gini index, the mean income and the proportion of the population living below a prescribed income level are obtained in this paper on the basis of censored income data from a pareto income distribution. The said estimators are obtained under the assumptions of a two-parameter exponential prior distribution and the usual squared error loss function. This work is also extended to the case when the income data are grouped and the exact incomes for the individuals in the population are not available. The method for the assessment of the hyperparameters is also outlined. Finally, the results are generalized for the doubly truncated gamma prior distribution.

Robust Bayesian analysis of the linear regression model

The robust Bayesian analysis of the linear regression model is presented under the assumption of a mixture of g-prior distributions for the parameters and ML-II posterior density for the coefficient vector is derived. Robustness properties of the ML-II posterior mean are studied. Utilizing the ML-II posterior density, robust Bayes predictors for the future values of the dependent variable are also obtained.

A necessary and sufficient condition for the dominance of an improved family of estimators in linear regression models

This article presents a necessary and sufficient condition for the dominance, with respect to the risk under a general quadratic loss function, of the double k-class estimators (characterized by non-stochastic scalars) over the least squares estimator of coefficients in linear regression models.

Operational Variants of the Minimum Mean Squared Error Estimator in Linear Regression Models with Non-Spherical Disturbances

There is a good deal of literature that investigates the properties of various operational variants of Theils (1971, Principles of Econometrics, Wiley, New York) minimum mean squared error estimator. It is interesting that virtually all of the existing analysis to date is based on the premise that the models disturbances are i.i.d., an assumption which is not satisfied in many practical situations. In this paper, we consider a model with non-spherical errors and derive the asymptotic distribution, bias and mean squared error of a general class of feasible minimum mean squared error estimators. A Monte-Carlo experiment is conducted to examine the performance of this class of estimators in finite samples.

Selecting a double k-class estimator for regression coefficients

This paper considers the choice of scalars characterizing the double k-class estimators of the coefficients in a linear regression model. We demonstrate the existence of a double k-class estimator that dominates the least squares and Stein-rule estimators and we give feasible values for the characterizing scalars which nearly minimize the risk of the estimator.

Stein rule prediction of the composite target function in a general linear regression model

This paper considers the problem of simultaneous prediction of the actual and average values of the dependent variable in a general linear regression model. Utilizing the philosophy of Stein rule procedure, a family of improved predictors for a linear function of the actual and expected value of the dependent variable for the forecast period has been proposed. An unbiased estimator for the mean squared error (MSE) matrix of the proposed family of predictors has been obtained and dominance of the family of Stein rule predictors over the best linear unbiased predictor (BLUP) has been established under a quadratic loss function.

STEIN-RULE RESTRICTED REGRESSION ESTIMATOR IN A LINEAR REGRESSION MODEL WITH NONSPHERICAL DISTURBANCES

In the present paper, we propose a Stein-rule estimator for the general linear regression model with nonspherical disturbances and a set of linear restrictions binding the regression coefficients. The asymptotic risk properties of the proposed estimator under a quadratic loss structure are derived, and a sufficient condition for the proposed estimator to dominate the feasible generalized restricted least squares estimator in large samples is presented. The small sample behavior of the proposed estimator is studied via a Monte-Carlo experiment.

Bayesian Estimation of Regression Coefficients Under Extended Balanced Loss Function

Appreciating the desirability of simultaneously using both the criteria of goodness of fitted model and clustering of estimates around true parameter values, an extended version of the balanced loss function is presented and the Bayesian estimation of regression coefficients is discussed. The thus obtained optimal estimator is then compared with the least squares estimator and posterior mean vector with respect to the criteria like posterior expected loss, Bayes risk, bias vector, mean squared error matrix and risk function.

Mining and gene ontology based annotation of SSR markers from expressed sequence tags of Humulus lupulus

Humulus lupulus is commonly known as hops, a member of the family moraceae. Currently many projects are underway leading to the accumulation of voluminous genomic and expressed sequence tag sequences in public databases. The genetically characterized domains in these databases are limited due to non-availability of reliable molecular markers. The large data of EST sequences are available in hops. The simple sequence repeat markers extracted from EST data are used as molecular markers for genetic characterization, in the present study. 25,495 EST sequences were examined and assembled to get full-length sequences. Maximum frequency distribution was shown by mononucleotide SSR motifs i.e. 60.44% in contig and 62.16% in singleton where as minimum frequency are observed for hexanucleotide SSR in contig (0.09%) and pentanucleotide SSR in singletons (0.12%). Maximum trinucleotide motifs code for Glutamic acid (GAA) while AT/TA were the most frequent repeat of dinucleotide SSRs. Flanking primer pairs were designed in-silico for the SSR containing sequences. Functional categorization of SSRs containing sequences was done through gene ontology terms like biological process, cellular component and molecular function.