IMPROVED ESTIMATORS OF VARIANCE-COMPONENTS WITH SMALLER PROBABILITY OF NEGATIVITY

• 成果类型: Article
• 署名作者: KELLY, RJ; MATHEW, T
• 署名单位: University System of Maryland; University of Maryland Baltimore County
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• 发表日期: 1993
• 页码: 897-911
• 关键词: model

摘要

A linear model with two variance components is considered, one variance component (say, sigma1(2) greater-than-or-equal-to 0) corresponding to a random effect, and a second variance component (say, sigma2 > 0) corresponding to the experimental errors. A class of invariant quadratic estimators (IQEs) is characterized, having uniformly smaller mean-squared error (MSE), and uniformly smaller probability of negativity, compared with the analysis-of-variance (ANOVA) estimator of sigma1(2). It turns out that for balanced models, among IQEs of sigma1(2) with uniformly smaller MSE than its ANOVA estimator, there exists an IQE with the smallest probability of being negative, uniformly in the parameters. The results are applied to the balanced one-way classification model. Numerical computations show that the MSE improvement achievable through the use of the proposed estimators is quite significant. It is noted that, for the non-negative estimation of sigma1(2), truncation of one of the proposed estimators at 0 provides a satisfactory solution. Extension of the results to the unbalanced case, and to the general mixed model with balanced data, is also indicated.