Variance Components, Their Estimation and Hypotheses Testing Based on Breeding Experiments : I. Approximate Distributions of the Linear Function of Independently Distributed Mean Squares

Abstract

Three formulas for transforming a linear function of mean squares into a variate approximately distributed as a normal or a chi-square distribution are given, which enable us to go on some significant tests on the statistic estimated by the linear function. Since nuisance parameters in the formulas have to be replaced by the corresponding estimates, the appropriateness of the approximations is discussed with Monte Carlo simulation.