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单纯形约束模型中遗传距离及其他量的估计偏差AI 解读

The genetic distance between two loci on a chromosome is defined as the mean number of crossovers between the loci. The parameters of the crossover distribution are constrained by the parameters of the distribution of chiasmata. Ott (1996) derived the maximum likelihood estimator (MLE) of the parameters of the crossover distribution and the MLE of the mean. We demonstrate that the MLE of the mean is pointwise less than or equal to the empirical mean number of crossovers. It…

假设检验中的合理性与无偏性AI 解读

The notion of a “rationality criterion” is defined. This criterion reflects a desirable property for statistical procedures that deal with censored data. In hypothesis testing situations, we show that when adapting this criterion to a uniformly most powerful unbiased (UMPU) test of comparing the scale parameters of two distributions, sometimes it is possible to determine a test so that it is unbiased and sometimes this is impossible. The question thus remains: What is more…

假设检验中的理性准则与无偏性AI 解读

The notion of a “rationality criterion” is defined. This criterion reflects a desirable property for statistical procedures that deal with censored data. In hypothesis testing situations, we show that when adapting this criterion to a uniformly most powerful unbiased (UMPU) test of comparing the scale parameters of two distributions, sometimes it is possible to determine a test so that it is unbiased and sometimes this is impossible. The question thus remains: What is more…

含无差别区间问题中 Student t 检验的替代方法AI 解读

Consider a sample from a normal population with mean, $\mu$, and variance unknown. Suppose it is desired to test $H_0:\mu \leq \mu_0$ versus $H_1:\mu \geq \mu_1$, with the region $H^I_1:\mu_0 < \mu < \mu_1$ being a (nonempty) indifference zone. It is shown that the usual Student's $t$-test is inadmissible for this problem. An alternative test is proposed. The two sided problem with indifference region is also discussed. By contrast with the above result, the usual Student's $t$…

被选中负指数分布总体的均值估计AI 解读

SUMMARY Let Xi be independent, negative exponentially distributed with unknown expectation λi, i = 1, …, k. Let J and M denote the (random) indices of the maximal and minimal observation, respectively. The paper considers estimation of the random quantities λJ and λM. The loss function is (a – λM)2/λ2 M for λM, and correspondingly for λJ. UMVUE and minimax estimators are shown to exist and are exhibited, and certain other reasonable estimators are discussed.