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次序统计量矩的界与近似AI 解读

In this paper methods for obtaining approximations and bounds for the moments of order statistics from a continuous parent distribution are discussed. These bounds and approximations depend on the distribution function only through certain moments of order statistics in small samples. It is shown that for the Cauchy distribution bounds and approximations of all finite moments can be obtained. Some numerical calculations for normal and Cauchy distributions are also given.

多元回归中的缺失观测：一阶方法的效率AI 解读

Abstract It is shown that the information contained in the incomplete portion of the sample that is relevant in the estimation of the regression parameters is in the form of a linear restriction. Although the parameters of this restriction are generally unknown they can be estimated in terms of the complete portion of the sample. It is then shown that regression parameter estimates based on first order methods, say, Ĉ, differ from the ordinary least squares estimates based…

指数分布参数的一类序贯检验AI 解读

Weiss [5] and Freeman and Weiss [2] have shown how to construct sampling plans which at least approximately minimize the maximum expected sample size in the case of Bernoulli and Normal populations. In this paper we construct sequential procedures of this type for the testing of an exponential parameter. An invariance property of the stopping region is presented which simplifies the construction of the Bayes regions. Several sampling plans are given and some of their…

国内迁移研究中净迁移率估计的误差AI 解读

The effect of relaxing the conditions regarding the equality of the mortality rates and of the errors of enumeration between the states and the nation, on the error in the estimation of the net migration rate by the census survival ratio method, is examined and it is shown that, when the national population is closed, the necessary and sufficient condition for this error to become zero is that the relative degree of enumeration for any age x of a given sex in the ith state…

高效率估计量在二元极值理论中的应用AI 解读

This paper uses a family of bivariate extreme-value distributions to estimate the probability of a large exceedance of a random variable given that a certain other random variable not independent of the first has exceeded a certain value. A simple method of reasonably good efficiency is given for estimating a bivariate extreme-value distribution from independent bivariate samples. The method is used to analyze the performance of a spacecraft command receiver which has an…

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图书使用的统计模型及其在图书存储问题中的应用AI 解读

A statistical model is presented for describing the distribution of book uses in a research library. This model is used to attack the problem of book storage in a research library. A rule which says that a book goes to the storage collection if it is not used for k consecutive years after its acquisition in the library is studied. A similar rule for transferring active books from the storage to the active collection is also examined. Examples are provided to illustrate some…

以随机场为解释变量的回归AI 解读

The use of observations of a random function in space (random field) as independent variables in regression is considered including the numerical aspects. Details are presented for obtaining a numerical approximation to a Karhunen-Loève expansion when the random function is observed at a large number of points. The procedure involves a two stage modified principal component analysis. The dependent variable is then regressed on the principal components. An example from…

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关于双样本检验的一则札记AI 解读

A double sample test for a hypothesis concerning the mean μ of a normal random variable with unknown variance σ2 is presented in this note. This test is an alternative to the usual single sample t test and is made by taking samples at two stages. After the first sample has been observed the hypothesis is rejected, accepted or a second sample is taken. This double sample test is a modification of a double sample test suggested by D. Owen. However, for the test being suggested…

离散均匀有限总体的极差抽样分布与齐性极差检验AI 解读

The sampling distribution of the range from a discrete uniform finite population is obtained. Its relation to the sampling distribution from a discrete uniform population is studied, and conditions under which one can approximate the other are given. A range test for homogeneity which is based on these distributions is proposed. An intuitive discussion of the test is given and then the power is determined for some alternative hypotheses. The test is found to be quite…

消费者态度数据的预测准确性AI 解读

This note evaluates the forecasting accuracy of the index of consumer sentiment constructed by the Michigan Survey Research Center. For the most part, other analyses have focused on the interpretation which should be given to an attitude variable or broadly described movements of the index of consumer sentiment in the vicinity of cyclical turning points. None of the studies have compared the accuracy of equations in which the attitude index is an independent variable against…

考虑未知方差不等的共同均值无偏估计量组合AI 解读

The problem considered in this paper is how to combine estimators of the common mean from two samples corresponding to normal populations with different unknown variances. Attention is confined to the case where it is known that the variance of one specific population exceeds that of the other. Three classes of unbiased estimators are presented, one of which is based on a preliminary test of significance regarding the ratio of the population variances. The gain achieved by…

回归百分位点的判别区间AI 解读

In simple linear regression the 100pth percentile of the distribution of Y for a given value of X is β0 + β1 X + Zp σ, where Zp is the 100pth percentile of the standard normal distribution. The problem considered is to estimate the value of X for which this percentile is equal to some specified value, Yp . Both point and interval estimates are considered. A procedure for obtaining exact confidence intervals is derived, and in addition, two approximate and two conservative…

平衡不完全区组设计中的方差分量估计量AI 解读

Estimation of variance components when the design is a balanced incomplete block, the model is additive, and error, block and treatment components are normal, independent, with zero expectations, is considered using variance as a criterion. The sections are arranged in the following manner: 1—The results are summarized. 2—The notation, model, statistics and analysis of variance tables are introduced. 3—A 1–1 (linear) transformation of the sufficient statistics is performed,…

尺度参数比的检验与估计AI 解读

Let X 1, …, Xm and Y 1, …, Yn be independent random samples from populations having continuous d.f.'s Ψ((x-μ)/σ) and Ψ ((y-v)/τ) respectively. The classical F-test of a hypothesis concerning λ = τ/σ is known to be non-robust. This paper examines several robust alternative procedures and compares them on the basis of Pitman a.r.e. and Monte Carlo studies of power functions. An approximate permutation test [13] and a “jackknife” procedure [9] are found to be most satisfactory;…