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.
불균형 일원 변량모형에서 AOV추정량과 사전값이 0, 1, ${\infty}$인 MINQUE에 국한하여 정규분포를 가정할 때 분산성분의 추정량이 음이 될 이론적 확률을 구하고, 비정규분포에 대해서는 모의실험을 통해 추정량이 음이 될 확률을 구하였다. 이 때 정차분포에서의 이론적 확률과 모의실험에 의해 계산된 확률간에 유의한 차이가 없고 표본수, 수준수 그리고 ${\rho}$가 커지면 각 추정량은 음이 될 확률이 작아지며, 고려된 추정량 중에서 AOV추정량이 대부분의 경우에 음이 될 확률이 가장 작게 나타났다.
