日期精度：到日 1 篇 · 到月 10 篇 · 到年 0 篇
若干非标准情形下似然比的渐近分布
In an earlier article [8] conditions were given under which maximum likelihood estimators are asymptotically normal and asymptotically efficient in certain nonstandard cases. Under these same conditions, the asymptotic distribution of the likelihood ratio is found. An easily computed asymptotic equivalent of the likelihood ratio is developed, and is applied to a problem of testing fit.
若干非标准情形下似然比的渐近分布
In an earlier article [8] conditions were given under which maximum likelihood estimators are asymptotically normal and asymptotically efficient in certain nonstandard cases. Under these same conditions, the asymptotic distribution of the likelihood ratio is found. An easily computed asymptotic equivalent of the likelihood ratio is developed, and is applied to a problem of testing fit.
拟合检验中少量次序统计量的渐近充分性
For each $n, X_n(1), \cdots, X_n(n)$ are independent and identically distributed continuous random variables over $(0, 1)$, with common density function equal to $1 + r(x)/n^{\frac{1}{2}}, r(x)$ unknown but satisfying certain regularity conditions. The problem is to test the hypothesis that $r(x) = 0$ for all $x$ in (0, 1). $Y_n(1) < \cdots < Y_n(n)$ are the ordered values of $X_n(1), \cdots, X_n(n). \delta$ is a fixed value in the open interval $(\frac{3}{4}, 1)$. It is…
若干非标准情形下最大似然估计量的渐近性质（二）
In an earlier article, asymptotic properties of maximum likelihood estimators were found in a class of nonstandard cases when three assumptions were satisfied. The third assumption was rather complicated. In this article it is shown that if we strengthen the second assumption slightly, we can dispense with the third assumption entirely.
若干非标准情形下最大似然估计量的渐近性质
Most results on the asymptotic properties of maximum likelihood estimators are for the standard cases where we observe independent and identically distributed random variables, whose distribution satisfies certain regularity conditions. In this article, similar properties are shown to hold for a class of cases where the observed random variables are not necessarily independent and identically distributed.
多项分布各类别概率相等的序贯检验
For testing the hypothesis that all the categories in a multinomial distribution are equally likely, a sequential test is proposed which at each stage of the sampling observes whether the observation falls in the set of categories containing the largest number of earlier observations. It rejects the hypothesis if at too many stages the observation does fall in that set of categories. The properties of the test are discussed.
多项分布各类别概率相等的序贯检验
For testing the hypothesis that all the categories in a multinomial distribution are equally likely, a sequential test is proposed which at each stage of the sampling observes whether the observation falls in the set of categories containing the largest number of earlier observations. It rejects the hypothesis if at too many stages the observation does fall in that set of categories. The properties of the test are discussed.