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...

Let X,X1, X2, . . . , Xn be i.i.d. random variables distributed according to an exponential family with natural parameter θ ∈ Ω. A family of priors, not necessarily proper, given in Ghosh and Meeden (1977), Ralescu and Ralescu (l981), and Brown (1986), gives normal posterior distributions and generates linear generalized Bayes estimators for θ when Ω is the real line. Here, necessary and suffic...

     The quadratic loss function has been used by decision-theoretic statisticians and economists for many years.  In this paper  the estimation of scale parameter under a bounded loss function, which is adequate for assessing quality and quality improvement, is considered with restriction to the principles of invariance and risk unbiasedness. An implicit form of minimum risk scale equivariant ...

Summary We investigate estimation of a normal mean matrix under the quadratic loss. Improved loss implies improved any linear combination columns First, an unbiased estimate risk is derived and Efron–Morris estimator shown to be minimax. Next, notion superharmonicity for matrix-variate functions introduced have properties analogous those usual superharmonic functions, which may independent inte...

Charles Stein shocked the statistical world in 1955 with his proof that maximum likelihood estimation methods for Gaussian models, in common use for more than a century, were inadmissible beyond simple oneor twodimensional situations. These methods are still in use, for good reasons, but Stein-type estimators have pointed the way toward a radically different empirical Bayes approach to high-dim...

After performing a randomized experiment, researchers often use ordinary least-square (OLS) regression to adjust for baseline covariates when estimating the average treatment effect. It is widely known that resulting confidence interval valid even if linear model misspecified. In this article, we generalize conclusion covariate adjustment with nonlinear models. We introduce an intuitive way any...

SUMMARY Capture and recapture designs with only two occasions are still being used in a variety of situations especially in Epidemiological studies. Usually, the well-known Lincoln-Petersen (1896,1930) estimator is used to estimate the population size. Because only two occasions are being used some concern is devoted to the reliability of the final estimate. In this paper we will address the pr...