A NOTE ON ESTIMATION UNDER THE QUADRATIC LOSS IN MULTIVARIATE CALIBRATION

A Note on Estimation under the Quadratic Loss in Multivariate Calibration

The problem of estimation in multivariate linear calibration with multivariate response and explanatory variables is considered. In this calibration problem two estimators are well-known; one is the classical estimator and the other is the inverse estimator. In this paper we show that the inverse estimator is a proper Bayes estimator under the quadratic loss with respect to a prior distribution...

Estimation of the Multivariate Normal Mean under the Extended Reflected Normal Loss Function

Estimation with Quadratic Loss

It has long been customary to measure the adequacy of an estimator by the smallness of its mean squared error. The least squares estimators were studied by Gauss and by other authors later in the nineteenth century. A proof that the best unbiased estimator of a linear function of the means of a set of observed random variables is the least squares estimator was given by Markov [12], a modified ...

Appoximation-assisted estimation of eigenvectors under quadratic loss

Improved estimation of eigen vector of covariance matrix is considered under uncertain prior information (UPI) regarding the parameter vector. Like statistical models underlying the statistical inferences to be made, the prior information will be susceptible to uncertainty and the practitioners may be reluctant to impose the additional information regarding parameters in the estimation process....

Minimax estimation of multivariate normalmean under balanced loss function 1

This paper considers simultaneous estimation of multivariate normal mean vector using Zellner's(1994) balanced loss function when 2 is known and unknown. We show that the usual estimator X is minimax and obtain a class of minimax estimators which have uniformly smaller risk than the usual estimator X. Also, we obtain the proper Bayes estimator relative to balanced loss function and nd the minim...