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统计计算手册AI 解读

1. Organizing Data and Some Simple Computations. 2. Confidence Intervals. 3. Correlation and Related Topics. 4. Analysis of Variance. 5. Supplemental Computations for Analysis of Variance. 6. Multivariate Analyses. 7. Nonparametric Tests, Miscellaneous Tests of Significance, and Indexes of Relationships. Appendices. Normal-Curve Areas. Critical Values of Student's t Statistic. Critical Values for Sandler's A Statistic. Values of the Chi-Square Statistic. Probabilities of the…

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动态计量经济模型的均衡协方差矩阵AI 解读

This paper presents a convenient form for the asymptotic, or equilibrium, covariance matrix of the endogenous variable vector of a dynamic econometric model.

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LAMST 与列联表的无三因素交互假设AI 解读

A new class of tests is presented for testing the hypothesis of no second order interaction in three-way contingency tables. This hypothesis is expressed first in the form of linear contrasts in logarithms of the parameters of a multinomial experiment and the test is based on the general theory of locally asymptotically most stringent tests. Specific test criteria are then given for testing no second order interaction in 2 × 2 × 2, 2 × 2 × K and I × J × K contingency tables.…

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多元分布中线性次序统计量的渐近联合分布AI 解读

The asymptotic joint distribution of an arbitrary number of linear systematic statistics (that is, linear combinations of order statistics), when observations are made on a random vector, is shown to be normal under fairly general conditions. The linear systematic statistics may correspond to the same or to different components of the vector. Formulas for evaluating the parameters of the asymptotic normal distribution are derived. As an illustration, these are applied to the…

多元概率密度的立方体与球形估计AI 解读

Two estimates of the density function f(x,y) of points in a plane are defined from a sample of n points by (1) counting how many points lie within a square of side 2h and center at (x,y), and (2) by counting how many points lie within a circle of diameter 2R and center at (x,y). Optimal values of h and R are shown to exist. This is done by expressing the principal part of the mean square errors of these estimates as the sum of two terms, an “error” and a “bias.” The error…

二项、F、Beta 及相关尾概率的正态近似（二）AI 解读

This paper describes and derives the asymptotic behavior of the new Normal approximation introduced in Part I and of a family of Normal approximations based on roots, including the square root approximations of Fisher, and Freeman and Tukey, and the cube root approximations of Wilson and Hilferty, Camp, and Paulson. Various asymptotic comparisons are made, all of which rank the new approximation first, the cube root approximations second, and the other root approximations…

规模显著变化时按规模概率区域样本的重新设计AI 解读

For purposes of obtaining statistical data by enumeration, systematic sampling with probability proportional to size in one or more stages is frequently employed. The article describes two methods of changing the measures of sizes without introducing a bias in the estimation procedure. They result in the reduction of the variance of sample take, and, in the illustrative material presented, result in varying degrees of overlap before and after the changes of sizes. These…

有限总体抽样理论的一种传统路径AI 解读

The main objective of this work is to relate classical inference and sampling theory (and current sampling practice) to recent advances toward formalizing and unifying the theory of sampling from finite populations. It is pointed out that the use of definitions which coincide with what seem to be the traditional notions of simple random sampling, and post-stratification (stratification after sampling) leads to the solution of such riddles which appear in the more recent…

一阶平稳马尔可夫残差下样本均值的效率AI 解读

The efficiency of the sample mean relative to the “best” linear unbiased estimator when residuals follow a first-order stationary Markoff process is studied. The minimum efficiency for correlation ρ ≧ 0 occurs at the unique root of a certain equation depending on the sample size n and decreases monotonically in n toward the value .878 obtained by Ylvisaker in the continuous case. It is tabulated for selected n ≦ 300, together with the value of p at which the minimum is…

因变量子集受约束的线性模型：估计与推断AI 解读

Subsets of the dependent variable of a linear model often conform to known constraints; for example, this situation arises with Engel curves and with models which estimate transition probabilities, market shares, or other classes of proportions. These models imply a variety of restrictions on the parameters, explanatory variables and residuals which must be treated explicitly in estimating and testing hypotheses about the parameters. This paper discusses these restrictions…

转移概率的极大似然与贝叶斯估计AI 解读

In this paper, maximum likelihood and Bayesian methods are presented for estimating transition probabilities when data in the form of aggregated proportions are available. The probability function for the observed proportions is assumed to have a multinomial distribution under the Lexis scheme. The multivariate beta distribution is used as the prior probability density function in formulating the Bayesian estimator. The results of some Monte Carlo experiments provide some…

逆高斯分布函数AI 解读

This note deals with a method of evaluating the distribution function of the Inverse Gaussian Distribution, from the Standard Normal Distribution.

双向完全随机分类中子组均值与子组观测数的统计依赖AI 解读

This paper deals with certain aspects of variance-component estimation for the unbalanced two-way completely-random classification where the numbers of observations in the subclasses are treated as random variables not necessarily independent of some of the random effects of the model. General results are given on the expectations of two commonly-used estimators of the vector of variance components. Numerical approximations are presented for these expectations for one…

二项、F、贝塔及其他相关常见分布尾概率的正态近似（一）AI 解读

This paper concerns a new Normal approximation to the beta distribution and its relatives, in particular, the binomial, Pascal, negative binomial, F, t, Poisson, gamma, and chi square distributions. The approximate Normal deviates are expressible in terms of algebraic functions and logarithms, but for desk calculation it is preferable in most cases to use an equivalent expression in terms of a function specially tabulated here. Graphs of the error are provided. They show…

离散总体与分组样本的次序统计量AI 解读

The aim of this paper is two-fold: (1) To give a unified treatment of the theory of order statistics when the parent distribution is not necessarily continuous. (2) To assess the effects of grouping on the distribution of order statistics and to indicate the convenience, under suitable conditions, of using order statistics for the estimation of parameters from grouped data with or without censoring.

基于 Kendall 秩相关系数的回归系数估计AI 解读

The least squares estimator of a regression coefficient β is vulnerable to gross errors and the associated confidence interval is, in addition, sensitive to non-normality of the parent distribution. In this paper, a simple and robust (point as well as interval) estimator of β based on Kendall's [6] rank correlation tau is studied. The point estimator is the median of the set of slopes (Yj - Yi )/(tj-ti ) joining pairs of points with ti ≠ ti , and is unbiased. The confidence…