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效率稳健的两样本秩检验AI 解读

In the classical two sample problem, the null hypothesis of identical distribution functions is tested. Rank testing procedures have the property that they are valid (have Type I error identically equal to α) for any absolutely continuous distribution function. Choices among rank tests are usually based upon local power calculations for a given specified null distribution against specific parametric alternatives. A rank test is said to be efficiency robust when no other has…

双向布局中的若干最优非参数程序AI 解读

Some optimum nonparametric procedures for estimating and testing contrasts in two-way layouts are proposed and studied. These procedures are based on the Chernoff-Savage [4] type of rank order statistics which include the Wilcoxon and normal scores statistics among others. In the first three sections, the properties of the proposed point estimators of contrasts, such as symmetry, invariance and asymptotic normality, are studied and their asymptotic relative efficiencies with…

不平衡单向随机分类中随机效应与观测数量的统计依赖AI 解读

This paper deals with certain aspects of variance component estimation for the unbalanced one-way random classification where the number (Ni ) of observations in the ith class is treated as a random variable not necessarily independent of the class effect (Ai ). It is assumed that in general P(Ni = 0) > 0. The conditional expectations (given the number of observations in each class) of all estimators of the between variance component (σ2 a ) belonging to a certain class of…

效率稳健的两样本秩检验AI 解读

In the classical two sample problem, the null hypothesis of identical distribution functions is tested. Rank testing procedures have the property that they are valid (have Type I error identically equal to α) for any absolutely continuous distribution function. Choices among rank tests are usually based upon local power calculations for a given specified null distribution against specific parametric alternatives. A rank test is said to be efficiency robust when no other has…

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随机变量乘积的分布AI 解读

Summary The problem of finding the probability density function of the product of n identically distributed independent normal variables was solved by Springer and Thompson (1966). Their formulae for n ≤ 7 are simplified in this paper and generalized to an arbitrary number of factors. Similar formulae for the corresponding probability distribution functions are derived. The applicability of these results to the cases of the negative exponential, Weibull and gamma…

回归参数与均值向量的固定宽度置信界AI 解读

Summary In this paper Chow and Robbins's (1965) sequential theory has been extended to construct a confidence region with prescribed maximum width and prescribed coverage probability for (i) the linear regression parameters, and (ii) the mean vector of a multivariate population. Except for the finiteness of the unknown variance and covariances in the respective two cases, no assumption regarding the form of their distribution functions is made. This result was announced in…

经验贝叶斯方法：估计先验分布AI 解读

There is a random variable A distributed according to a specific but unknown prior distribution G from an appropriate class GP. The random variable Λ = λ is unobrvable but another random variable X = x, distributed with known conditional distribution function F(x∣λ), is observable. We construct estimators Gn(λ) of G(λ) such that lim E[{Gn(λ) − G(λ)}2]=0 and we use Gn(λ) to estimate the posterior distribution G(λ∣x) and hence to construct consistent estimators of posterior…

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两个随机序变量分布的最大似然估计AI 解读

The maximum likelihood estimates and Ĝ of two distribution functions F and G are found, subject to the restrictions that for all x and that and Ĝ are of the discrete type. Random samples x 1, ···, x m and y 1, ···, y n are taken from the respective distributions and these m+n values are ordered according to magnitude, with x's before y's in cases of equality. These n+m values are divided into a number of “strings” as follows. The first string ends after the y value that is…

分位数估计的若干问题AI 解读

Summary The problem of estimating quantiles in the context where restriction to particular parametric families is inappropriate is considered, for simple random sampling and stratified sampling. For the former type of sampling the distribution-free procedures are obtained and the admissible estimators identified, and certain other questions are dealt with. In the stratified sampling situation similar problems are considered, less successfully.

若干圆形误差分位数估计量的渐近性质AI 解读

Quantiles of circular error, of which the CPE (circular probable error) is a special case, are of importance in the evaluation of ballistic missile systems. In these applications, a quantile of circular error is the radius, R, of a circle centered at (0, 0) above which lies a specified proportion, P, of the bivariate normal probability distribution. For this distribution, R may be estimated by substituting estimates for parameters in the integral equation defining R and…

若干圆形误差分位数估计量的渐近性质AI 解读

Quantiles of circular error, of which the CPE (circular probable error) is a special case, are of importance in the evaluation of ballistic missile systems. In these applications, a quantile of circular error is the radius, R, of a circle centered at (0, 0) above which lies a specified proportion, P, of the bivariate normal probability distribution. For this distribution, R may be estimated by substituting estimates for parameters in the integral equation defining R and…

排序与滑移问题的若干渐近有效序贯程序AI 解读

Summary In this paper Chow and Robbins's (1965) sequential theory has been applied to ranking and slippage problems (including a multivariate slippage problem) and a class of asymptotically efficient sequential procedures is given for each problem. Except for the finiteness of the variance, no assumption regarding the form of the distribution function is made.

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Logistic 分布参数的估计AI 解读

Three different methods of estimation are studied for estimating the parameters of the logistic distribution. The best linear unbiased estimators based on sample quantiles proposed by Ogawa (1951) are obtained and the determination of the optimum spacing of the sample quantiles is discussed. Estimators proposed by Blom (1958) and Jung (1955), which are linear functions of order statistics, are discussed together with the relative efficiencies of them estimators with respect…

Wilks 似然比准则的精确分布AI 解读

The null distributions of Wilks's likelihood ratio criterion Λ are derived, and it is shown that the density and distribution functions of Λ have exact closed form representations when p, the number of variates, or q, the hypothesis degrees of freedom. are even. Tables of correction factors for converting chi-square percentiles to exact percentiles of a logarithmic function of Λ are provided in the appendix for twenty-two (p, q) paris. Tables for an additional nineteen pairs…

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针对标量备择的拟合优度检验渐近相对效率AI 解读

This paper deals with the asymptotic relative efficiency (A.R.E.) and the asymptotic power of certain tests. These tests are distribution-free goodness-of-fit tests based on the empirical distribution function. They are the one and two sided Kolmogorov-Smirnov tests and a new one based on the absolute values of the order statistics. The method of obtaining the A.R.E. is due to Quade [5] and is outlined in Section 1. In this paper we are concerned with the case of scalar…

针对标量备择的拟合优度检验渐近相对效率AI 解读

This paper deals with the asymptotic relative efficiency (A.R.E.) and the asymptotic power of certain tests. These tests are distribution-free goodness-of-fit tests based on the empirical distribution function. They are the one and two sided Kolmogorov-Smirnov tests and a new one based on the absolute values of the order statistics. The method of obtaining the A.R.E. is due to Quade [5] and is outlined in Section 1. In this paper we are concerned with the case of scalar…

用于空间遥测数据压缩的次序统计量AI 解读

The need for data compression, a consequence of the demands made on the telemetry system of a space vehicle, prompts consideration of the use of sample quantiles in estimating population parameters and obtaining tests of goodness of fit for large samples. In this paper optimal unbiased estimators of the mean and standard deviation are given using up to twenty quantiles when the parent population is normal. Moreover, the estimators are relatively insensitive to deviations…

投票定理在物理学与次序统计中的应用AI 解读

Summary The author finds the distribution of the number of gas molecules ionized by an electron passing through an electron tube, and the distribution of the deviation of empirical and theoretical distribution functions, when the sample size is a random variable having a Poisson distribution.

适用于千例以内样本的符号检验与中位数分布无关置信区间表AI 解读

In 1946 Dixon and Mood published a table of critical values for the sign test with the sample size n, the sum of the two binomial numbers, in the stub and running consecutively from 1 to 100. In 1959 the present writer also published a sign-test table, replacing n by d, the difference between the two binomial numbers, and extending the range of sample sizes to 1,000. However, this second table introduced complicated rules of use and did not facilitate determination of…

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