论文检索

Bickel–Rosenblatt 拟合优度检验的功效与最优核AI 解读

Bickel and Rosenblatt proposed a procedure for testing the goodness of fit of a specified density to observed data. The test statistic is based on the distance between the kernel density estimate and the hypothesized density, and it depends on a kernel $K$, a bandwidth $b_n$ and an arbitrary weight function $a$. We study the behavior of the asymptotic power of the test and show that a uniform kernel maximizes the power when $a > 0$.

提前截停检验与一致最强序贯检验AI 解读

The final decision of a fixed-sample likelihood ratio test is often determined before the entire sample is taken. Such a test can be curtailed as soon as the final decision becomes obvious. The construction and properties of these curtailed tests are described. A particular class of such tests contains sequential tests which are uniformly most powerful. The asymptotic efficiency of this class is investigated.

二项分布参数若干近似置信区间的比较AI 解读

We consider two confidence intervals for the binomial parameter that are frequently recommended for large samples. We show that one of these, which is in fact less popular in the literature, enjoys certain advantages over the other one. The criteria used for comparison are the confidence coefficients, the lengths, and the Neyman shortness of the intervals.

估计理论中若干界的比较AI 解读

Conditions are given for the attainment of the Hammersley-Chapman-Robbins bound for the variance of an unbiased estimator, in both regular and nonregular cases. Comparisons are made between this bound and the Bhattacharyya system of bounds for a wide class of distributions and parametric functions. Sufficient conditions are provided to determine when one bound is sharper than the other one.

Behrens–Fisher 问题的两阶段程序AI 解读

We consider the problem of constructing a fixed-width confidence interval for the difference between the means of two normal populations with unknown variances. A Stein-type two-stage procedure is presented and some of its properties are investigated. It is shown that the procedure is generally more efficient than Chapman's [1] solution.

关于 Lehmann 方差齐性检验AI 解读

Summary For testing the equality of variances in k ≥ 2 normal populations Lehmann (1959) proposed a test procedure based on the logarithms of the sample variances. This paper investigates certain properties of that procedure, such as how to determine its critical region for small sample sizes, and whether or not the procedure is unbiased and robust. An asymptotic comparison is also made between Lehmann's test and the more well-known test due to Bartlett (1937).

序贯概率比检验所需样本量分布的矩AI 解读

Approximate expressions are given for the first four moments of the distribution of sample size required by a sequential probability ratio test. Some possible uses of these moments are also discussed.

摘要暂缺