Variance Components Estimation in a K-way Nested Random Effect Models

This work aims to presented the k way nested random models (designs) and discuss the estimators for the variance components in this kind of models presented by Henderson (1953), proposing condition concern their existence, as well as its two proposed modifications presented by Khattree (1999). At the first proposal, where he choose to sacrifice the unbiasedness of the Henderson's one to preserve the nonnegativity of the variance, and after noting (through simulations) that his estimator has better performance than the Henderson's one except for the variance of the error term, which has less mean square error than the corresponding error term of the Khattree's estimator, Khattree (1999), on is proposed modification, replaced the error term by the error term of the Henderson's estimators. Using Henderson's estimators, method of determining hypothesis tests based on Satterwaite (1946) procedure are discussed as well.