Simple Method to Compute Biases and Mean Squared Errors of Linear Estimators and Predictors in a Selection Model Assuming Multivariate Normality

Abstract

Evaluation of biases and mean squared errors of predictors by analytical methods is difficult when selection has occurred. Traditional simulation methods are very costly because of many possible incidence matrices, parameter values, and methods of prediction. Assuming multivariate normality and the Pearson model for selection, numerical solutions to evaluation of biases and mean squared errors can be obtained by use of distributions that are conditional on selection. A linear predictor and estimator is tested for bias by computing with conditional y and then comparing the solution to /3 and u with true /3 and conditional u. Mean squared errors are computed by adding to the conditional variance a quadratic in the bias evaluated for the estimation and prediction method that was examined. A numerical example involving cow culling is used to illustrate the methods.