Approximation of Standard Errors of Estimates as a By-Product for MC EM REML Analysis

Abstract Text: We studied the possibility to utilize the Monte Carlo algorithm in estimation of standard errors for MC EM REML variance component estimates. Approach is based on the principle that the expected information matrix at the maximum likelihood estimate is equal to the variance of score function. While score functions include EM updates, the information matrix can be approximated as the variance of scaled EM updates over MC samples. Beef cattle data with birth weight and yearling weight observations was used to demonstrate the idea and to test the effectiveness of the method. The approximated standard errors agreed well with the asymptotic standard errors. Fairly large number of samples was needed to approximate variance of the (co)variance component estimates. The redeeming feature is that the approximated standard errors can be obtained as a by-product of variance component estimation.

Keywords:

Monte Carlo

standard error

variance component