统计科学研究所.pdf

統計科學研究所 壹．八十八年度研究工作重要成果 一?數理統計部分 1. Empirical Bayes procedures for selecting the best population with multiple criteria. 2. 擴展了古典的擇優理論，把古典的擇優程序擴展到很一般化的一種隨機函數不等式。探討了諸常態母體下（不同 均值，不同變異數），各取樣數不同下的廣義擇優，定義新的效度並作了比較。 3. 用Residual lifetime的觀念來特徵化分佈函數，修正了Chong (1977, JASA) 有關指數分佈函數的結果。 4. 修正文獻中有關L-class分佈函數族之特徵化結果，並探討在此分佈函數族中，指數分佈函數的特徵化性質。 5. 研究在一分佈函數族內，兩分佈函數相等的充要條件。 6. 得出 中iid 隨機向量(分量獨立、連續分布)之極大數目之漸近公式並指出在算法分析及凸殼方面之應用。 7. 得出n個隨機矩形(其對角於 獨立均勻分布)併集期望面積之漸近公式。 8. 對於iid幾何分布隨機變數列之空前大值之個數，得到漸近正態性，對於空前小值之個數，得出大偏差，局部極限 及漸近定理。 9. 獲得一個關於常態分佈之新不等式。 10. 修正最小二乘估計，使得其多項次係數估計的極限分佈均是常態，擺脫長相關非線性過程時非常態極限分佈的束 縛。 11. Let X be a random variable distributed according to an exponential family with parameter , the natural parameter space, and assume that have a nondegenerated prior distribution. If and , we find some necessary conditions on the coefficients, a,b, , and . Moreover we characterize the distribution of X and the prior distribution of through the linear and quadratic properties of the above posterior expectations. 12. For the problem of estimating the means of p independent normal random variables under the sum of squared error loss, we prove that the saving risk of the Hudson estimator over the usual MLE is consistent for any in the class , c any given constant, . We find that the Hudson estimator is “significant” for an infinite measure set of , while the Jame-Stien estimator is not. A necessary and sufficient condition for the domination of the Hudson estimator over the Jame-Stien estimator, and a criterion for choosing a proper estimator. 13. For a group with objects of type 1, …, type p, a sampling with quota fulfillment, QF(r) r= nonnegative integer, is defined in the following. Objects are sampled with replacement until at least of type i,have been abserved, i=1, …, p. Assume a population is consisted of K nonoverlapping subpopulations of the unknow size . For the problem of estimating , the sampling design with quota fulfill