불균형(不均衡) 일원(一元) 변량모형(變量模型)에서 추정방법(推定方法)에 따른 분산성분(分散成分)의 추정량(推定量)이 음(陰)이 될 확률(確率)의 계산(計算) = On the Probability of the Estimate of Variance Components that is Negative in Unbalanced One-Way Random Model

다국어 초록 (Multilingual Abstract)

For the One-way random effects model with unbalanced data, the AOV and MINQUE estimates of variance components are frequently found to be negative. The primary objective of present study is placed on the computation of the probability of the main effect variance component, being negative. The probability of negative estimators from AOV and MINQUE can be obtained by theoretical computation under the normality assumption. It is, however, difficult to compute the probability of negative estimates for these estimators under arbitrary distributions, and hence their probabilities of being negative were computed by simulation experiment in this study. It was shown that there was no significant difference between the theoretical probability under normality and calculated probability by simulation experiment, and that probability of negative estimates decreases as sample size, number of levels and the value of increase.