论文检索

无矩条件下停止时间指数有界的一般定理及应用AI 解读

The stopping time $N$ of a sequential test based on an i.i.d. sequence $X, X_1, X_2, \cdots$ with common distribution $P$ is defined as the first integer $n \geqq 1$ such that $l_1 < L_n < l_2$ is violated, where $L_n$ is a statistic depending only on $X_1, \cdots, X_n$. If for all $l_1, l_2$ there exist constants $c > 0, \rho < 1$ such that $P(N > n) < c\rho^n, n = 1, 2, \cdots,$ then $N$ is called exponentially bounded under $P$. In the contrary case $P$ is termed…

序贯 t 检验停止时间的指数界AI 解读

Let N be the stopping time of the sequential t-test, based on the i.i.d. sequence $Z_1,Z_2,...$, for testing that the ratio of mean to standard deviation in a normal population equals $\gamma_1$ agaist the alternative that it equals $\gamma_2$. Let P be the actual distribution of the $Z_i$ (not necessarily normal). It is proved that if $\gamma_1^2\neq\gamma_2^2$ and P is an arbitrary unbounded distribution, then there exist constants c > 0 and $\rho<1$ such that $P(N > n) < c\rho^n, n =1,2,\cdots$…

关于达到 Cramér–Rao 下界AI 解读

A rigorous proof is given of the often stated fact that if the variance of an unbiased estimator of a function of a real parameter attains the Cramer-Rao lower bound then the family of distributions must be a one-parameter exponential family.