Consider a normal model with unknown mean bounded by a known constant. This paper deals with minimax estimation of the squared mean. We establish an expression for the asymptotic minimax risk. This result is applied in nonparametric estimation of quadratic functionals.

The article considers a new approach for small area estimation based on a joint modelling of mean and variances. Model parameters are estimated via expectation–maximization algorithm. The conditional mean squared error is used to evaluate the prediction error. Analytical expressions are obtained for the conditional mean squared error and its estimator. Our approximations are second-order correc...

In dynamic regression models conditional maximum likelihood (least-squares) coeffi cient and variance estimators are biased. From expansions of the coeffi cient variance and its estimator we obtain an approximation to the bias in variance estimation and a bias corrected variance estimator, for both the standard and a bias corrected coeffi cient estimator. These enable a comparison of their mean...

Policy analysis often demands quantitative prediction-especially cost-benefit analysis, which requires the comprehensive quantification and monetization of all valued impacts. Using parameter estimates and their precisions, analysts can apply Monte Carlo simulation to create distributions of net benefits that convey the levels of certainty about the fundamental question of interest: Will net be...

The term “empirical predictor” refers to a two-stage predictor of a linear combination of fixed and random effects. In the first stage, a predictor is obtained but it involves unknown parameters; thus, in the second stage, the unknown parameters are replaced by their estimators. In this paper, we consider mean squared errors (MSE) of empirical predictors under a general setup, where ML or REML ...

In fields such as climate science, it is common to compile an ensemble of different simulators for the same underlying process. It is a striking observation that the ensemble mean often out-performs at least half of the ensemble members in mean squared error (measured with respect to observations). In fact, as demonstrated in the most recent IPCC report, the ensemble mean often out-performs all...

This paper develops and explores applications of a linear shaping transformation that minimizes the mean squared error (MSE) between the original and shaped data, i.e., that results in an output vector with the desired covariance that is as close as possible to the input, in an MSE sense. Three applications of minimum MSE shaping are considered, specifically matched filter detection, multiuser ...