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数据分组导致的分布无关检验效率损失AI 解读

While distribution-free procedures are often appropriate when testing statistical hypotheses, they may become complicated or involve loss of power when the data are grouped. For rank tests the ties caused by grouping are generally broken either by using a randomization procedure or averaging the tied ranks. In this paper the power loss due to equi-spaced grouping (in terms of Pitman asymptotic relative efficiency) is investigated for some commonly used tests, for each method…

位置参数的渐近稳健估计量AI 解读

The robustness properties of four estimators of location are studied with respect to eight distribution types. For each type, the probability density function is symmetric about the median and the range of variate is infinite. For the entire class of distributions, the estimator with the highest guaranteed efficiency is the mean of the middle fifty percent of the sample. This study supplements the paper by Crow and Siddiqui (1967).

Wilcoxon 两样本检验的两种非参数竞争方法的渐近效率AI 解读

Wilcoxon's signed rank test and a test based on the uniform minimum variance unbiased estimator of P(X 1 + X 2 < Y 1 + Y 2) are considered as competitors of the Mann-Whitney-Wilcoxon (U) test. The criteria used to compare the tests are Bahadur and Pitman efficiency. For pure translation alternatives U is superior, but both tests compare favorably with respect to U for certain contamination alternatives.

生物测定中的随机游走设计AI 解读

Two estimators of the median based on sequentially obtained quantal response data are studied. The design is essentially the up-and-down method and consists of taking K observations per trial at sequentially determined levels until some fixed total sample size is obtained. The asymptotic distribution of the sample average, , of the levels is studied and an estimate of its variance is proposed. The bias and mean square error of , which have been numerically evaluated for the…

线性回归中更窄的置信带AI 解读

In many linear regression problems, the values of the independent variable or variables may be subject to certain constraints. For example, the independent variables may necessarily be positive; as another example, the variables may not only all be positive but are powers of a single variable (e.g., polynomial regression on time). Previous writers considering the problem of obtaining confidence bands on a regression function for all values of the independent variable have…

矩阵的分数次幂AI 解读

Statisticians occasionally need to compute a fractional power of a matrix. In certain practical cases a matrix A is given, and the statistician wants to compute the pth power of A, where p is a fractional or negative number; that is, a matrix R, such that R 1/p = A. He can often get a satisfactory approximation to Ap by using several leading terms of a power series. This procedure is similar to that of inverting certain matrices by power series.

有限总体均值的广义多元估计量AI 解读

Just as ratio estimators are often indicated when the variable y is positively correlated with an auxiliary variable x so product estimators are indicated when y is negatively correlated with x. The method of estimation suggested by Olkin [4] is extended to the case where some or all of the auxiliary variables are positively correlated and some or all are negatively correlated with y.

多类别比例的随机化回答模型AI 解读

In surveys of human populations respondents are not likely to participate or tell the truth when the reply may tend to stigmatize them in the eyes of the surveyor. Warner developed a technique for estimating the proportion of persons with such a sensitive characteristic in a binomial situation by having the respondent answer only “Yes” or “No” to one of two questions selected at random. This technique is hereby extended to the case where the population can be divided into t…

两样本 Kolmogorov–Smirnov 检验的渐近效率AI 解读

A simple derivation of asymptotic efficiency for the two sample Kolmogorov-Smirnov statistic is given and evaluated for normal location and normal scale alternatives. Using equal samples to simplify the derivation, the limiting efficiency is obtained by letting the type I error α go to zero while the type II error goes to β, 0 < β < 1. For unimodal symmetric location alternatives, the efficiency is the same as that obtained for the Mood and Brown median test. Limits of…

几何分布顺序统计量的精确矩及其与逆抽样和冗余系统可靠性的关系AI 解读

Formulae for the first two moments of the order statistics from a geometric distribution are presented in closed form. Brief illustrative tables of the first two moments of the order statistics from a geometric distribution are included and two related dice games are discussed. The distribution of the range of a set of independent observations from a geometric distribution is presented in closed form. A system of redundant components which performs a given task repetitively…

从使用者角度评估电子计算机的最小二乘程序AI 解读

Although there are many linear least squares programs available for use on the electronic computer, the algorithms specified in many of these programs are numerically more appropriate for the desk calculator than for the electronic computer. Routines which may be efficient for desk calculators may not be efficient for electronic computers. Since most computers carry about eight digits in the calculations, routines which do not take the problem of round-off errors and…

有限样本蒙特卡洛研究：一个自回归示例AI 解读

In this paper the problem of choosing among point estimators on the basis of their small sample properties is discussed from the sampling point of view. The indeterminacy of most Monte Carlo studies is analysed and resolved within the framework of statistical decision theory. A first order autoregressive model is worked through in detail both for its own sake and to illustrate how a complete Monte Carlo study might be done.

贝叶斯分析中先验分布的评估AI 解读

In the Bayesian framework, quantified judgments about uncertainty are an indispensable input to methods of statistical inference and decision. Ultimately, all components of the formal mathematical models underlying inferential procedures represent quantified judgments. In this study, the focus is on just one component, the prior distribution, and on some of the problems of assessment that arise when a person tries to express prior distributions in quantitative form. The…

信息性停止规则与总体规模推断AI 解读

It is a consequence of the likelihood principle that identical likelihood functions imply identical inferences. If the rule by which sample size is determined—the stopping rule—is reflected in the likelihood function, as it should be, apparently identical likelihood functions (without allowance for stopping rule) may in fact be different. This can happen if the stopping rules are informative. If the stopping rule is informative, the analysis must take the rule into account,…

摘要暂缺

摘要暂缺

心理学与教育学中的统计分析AI 解读

This is a main text for an upper-level undergraduate or graduate-level introductory statistics course in departments of psychology, educational psychology, education and related areas.

摘要暂缺

存在零差值时符号秩抽样分布的正态近似AI 解读

If, in using the Wilcoxon signed-rank test, the ranks corresponding to zero differences are deleted, the usual formula for the critical ratio used with the normal approximation must be modified. This note gives the required modification.

线性回归中更窄的置信带AI 解读

In many linear regression problems, the values of the independent variable or variables may be subject to certain constraints. For example, the independent variables may necessarily be positive; as another example, the variables may not only all be positive but are powers of a single variable (e.g., polynomial regression on time). Previous writers considering the problem of obtaining confidence bands on a regression function for all values of the independent variable have…

Wilcoxon 两样本检验的两种非参数替代方法的渐近效率AI 解读

Wilcoxon's signed rank test and a test based on the uniform minimum variance unbiased estimator of P(X 1 + X 2 < Y 1 + Y 2) are considered as competitors of the Mann-Whitney-Wilcoxon (U) test. The criteria used to compare the tests are Bahadur and Pitman efficiency. For pure translation alternatives U is superior, but both tests compare favorably with respect to U for certain contamination alternatives.

两样本 Kolmogorov–Smirnov 检验的渐近效率AI 解读

A simple derivation of asymptotic efficiency for the two sample Kolmogorov-Smirnov statistic is given and evaluated for normal location and normal scale alternatives. Using equal samples to simplify the derivation, the limiting efficiency is obtained by letting the type I error α go to zero while the type II error goes to β, 0 < β < 1. For unimodal symmetric location alternatives, the efficiency is the same as that obtained for the Mood and Brown median test. Limits of…

几何分布次序统计量的精确矩及其与逆抽样和冗余系统可靠性的联系AI 解读

Formulae for the first two moments of the order statistics from a geometric distribution are presented in closed form. Brief illustrative tables of the first two moments of the order statistics from a geometric distribution are included and two related dice games are discussed. The distribution of the range of a set of independent observations from a geometric distribution is presented in closed form. A system of redundant components which performs a given task repetitively…

有限样本Monte Carlo研究：自回归模型示例AI 解读

In this paper the problem of choosing among point estimators on the basis of their small sample properties is discussed from the sampling point of view. The indeterminacy of most Monte Carlo studies is analysed and resolved within the framework of statistical decision theory. A first order autoregressive model is worked through in detail both for its own sake and to illustrate how a complete Monte Carlo study might be done.