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截断分布平移参数的最大似然估计AI 解读

$f(x)$ is a uniformly continuous density which equals zero for negative values of $x$, has a right-hand derivative equal to $\alpha$ at $x = 0$, where $0 < \alpha < \infty$, and satisfies certain regularity conditions. $X_1,\cdots, X_n$ are independent random variables with the common density $f(x - \theta), \theta$ an unknown parameter. Let $\hat{\theta}_n$ denote the maximum likelihood estimator of $\theta$, and define $\alpha_n$ by the equation $2\alpha_n^2 = \alpha n \log n$…

与t检验对应的渐近有效序贯检验AI 解读

Summary Let X1, X2, …, be independent, normally distributed chance variables, each with mean μ and variance σ2, both unknown to the statistician. Let it be required to test sequentially the hypothesis that (make a decision between) μ = μ1 against the alternative μ = μ2, μ1 < μ2. When the sample size is fixed the Student t-test is usually used for this purpose. In the present paper we give a sequential procedure for performing this test which is consistent and asymptotically…