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序贯检验维纳过程漂移符号的贝叶斯风险界AI 解读

Let $x(t)$ be a Wiener process with drift $\mu$ and variance 1 per unit time. The following problem is treated; test $H:\mu \leq 0$ vs. $A:\mu > 0$ with the loss function $|\mu|$ if the wrong decision is made and 0 otherwise, and with $c =$ cost of observation per unit time, where $\mu$ has a prior distribution which is normal with mean 0 and variance $\sigma^2_0$. An idea of Bickel and Yahav is followed to obtain a lower bound for the Bayes risk which is strict as $\sigma_0 \rightarrow \infty$…

若干序贯程序停止时间的渐近正态性AI 解读

Two problems of sequential estimation, viz. the estimation of the mean of a normal distribution with unknown variance and the estimation of a binomial proportion are studied as the cost per observation tends to 0. For the first problem the asymptotic distribution of the stopping time of a procedure due to Robbins (1959) is shown to be normal. For the second problem the stopping time of a modification of Wald's (1951) procedure is asymptotically normal when the parameter is…