ASSESSMENT OF PRECISION WITH AVERSITY TO OVERSTATEMENT

摘要

The sampling variance and standard error of an estimator are usually estimated with small or no bias. An argument is put forward that they should be overestimated, to reflect our aversity to overstating the precision (understating the variance or standard deviation). Such aversity is characterized by an asymmetric loss function. The minimum-expected-loss estimators of the sampling variances and standard errors of parameters in ordinary regression are derived for several classes of loss functions: piecewise quadratic, linear, multiplicative and reciprocal, and LINEX.