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Wilcoxon 符号秩统计量的正态与 Edgeworth 近似精度AI 解读

Cumulative probabilities from the null distribution of the Wilcoxon signed rank statistic were approximated by the normal approximation and by Edgeworth expansions to terms of order 1/N and of order 1/N 2 for selected values of the statistic for values of N from 30 through 100. Use of the usual correction for continuity is advantageous at all probability levels in the Edgeworth expansions and in the normal approximation for probability levels greater than about 0.035. The…

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Theil相容性检验统计量的精确有限样本分布及应用AI 解读

In this article we derive the exact finite sample distribution of a statistic utilized by Theil [10] to test whether sample and prior information are in conflict with each other. A weighted estimator for the slope coefficient in a simple regression equation with one independent variable is obtained by using weights which are determined by the observed value of Theil's test statistic. This weighted estimator is particularly useful when we are uncertain about the compatibility…

离散分布的逼近及其应用AI 解读

This article presents a generalized procedure of finding the discrete distribution which minimizes, subject to a set of linear constraints on the probabilities, the “discrimination information” with respect to a given probability distribution. A convergent iterative algorithm is modified to serve this purpose. Many applications are discussed including analyses of contingency tables and some discrete analogues of the one-sample and several-samples problem. A test for the…

相关系数非零相关情形下分布的改进近似AI 解读

If r is the correlation coefficient based on a sample of n observations randomly drawn from a population having a bivariate normal distribution with correlation coefficient ρ, it is shown that is approximately distributed as t with (n − 2) degrees of freedom where ρ′ is a function of ρ and n satisfying certain constraints.

正态混合与正态 A 型分布抽样分布的讨论（统计量缺失）AI 解读

The asymptotic method described in an earlier article (Bowman and Shenton [2]) is applied to derive the power of the test of normality against skewed alternatives. In particular, normal mixtures of two components and Type A distributions, each depending on four parameters, are considered. Comparisons of the assessment of percentage points of using Cornish-Fisher expansions based on the normal and Monte Carlo simulations are given.

多样本 Kolmogorov–Smirnov 检验统计量的临界值表AI 解读

Let x 1j , x 2j , ···, xnj ; j=1, 2, ···, k be k independent random samples drawn, respectively, from the distributions with cdf's Fj (x). Let F* j (x) denote the empirical distribution function of the jth sample. Conover [3] and Wolf [6] derive the null distribution for the statistic sup x;i < k [F* i (x) – F* i+1(x)]. This article presents tables of exact probabilities for this statistic for k = 3(1)10, and n = 5(1)20. An approximation based on Conover's limiting…

关于比较相关比例的 Cochran Q 检验的注记AI 解读

Cochran's Q-test, proposed to test the equality of three proportions for correlated observations, may have a larger asymptotic significance level than the nominal one, unless the admissible family of distributions is restricted to ensure that under the hypothesis the correlations between the observations are also equal. For a large class of such restricted families, optimal C 2(α) tests of the hypothesis are obtained, and the family for which the Q-test is an optimal C 2(α)…

顺其自然：将尾部面积解释为后验概率或似然比AI 解读

Consider a problem in which a certain statistic X has a specified distribution function F(x) if a given hypothesis H is true, and suppose that the hypothesis H is evaluated by calculating the tail area 1 – F(x) corresponding to the observed value x of the statistic X. Examples are given in which this tail area is equal to the posterior probability that H is true and in which it is equal to the likelihood ratio comparing H to a certain class K of alternatives. The purpose of…

点估计与风险偏好AI 解读

The decision-theoretic approach to point estimation involves the choice of an estimate to minimize the expected loss associated with the estimate. The purpose of this paper is to indicate the influence of risk aversion on point estimates for classes of payoff functions including the piecewise linear and quadratic payoff functions. Increased risk aversion results in a point estimate closer to zero for a quadratic payoff function and a lower estimate with a piecewise linear…

泊松分布数据的回归分析AI 解读

The principle of maximum likelihood is used to obtain estimates of the parameters in a regression model when the experimental observations are assumed to follow the Poisson distribution. The maximum likelihood estimates are shown to be equivalent to those obtained by minimization of a quadratic form which reduces to a modified chi square under the Poisson assumption. Computationally, both of these estimation procedures are equivalent to a properly weighted least squares…

具有不完整观测的双变量正态分布的贝叶斯分析AI 解读

We consider the problem of drawing inferences on the difference of the population means when an incomplete sample from a bivariate normal population is available. Whereas Mehta and Gurland [7] have considered this problem from the sampling theory point of view, we tackle here the same problem from a Bayesian approach.

抽样调查多变量回答误差模型的另一种方法及子类均值应用AI 解读

Indicator functions are used as the basis for the formulation of a multivariate extension of the response error model developed by the U.S. Bureau of the Census. This approach allows a more complete characterization for general survey designs of the nature of the various components of the total variance of linear sample estimators and is particularly useful with respect to the role of the interaction component. These results are then applied to study the effect of response…

生存时间研究的简单回归方法AI 解读

Given a set of grouped survival data, least squares estimates are proposed for the parameters of four survival distributions that can be fit: exponential, linear hazard, Gompertz and Weibull. Sample estimates of the hazard function are utilized in the least squares procedures and a method is given for selecting a distribution for further investigation based on the likelihood under the four survival models. A Monte Carlo study demonstrated that the least squares estimates are…

期望频数较小时卡方拟合优度检验的不准确性AI 解读

In applied statistics there is an increasing tendency toward leniency regarding minimum expectation prerequisite to Pearson's X 2 test for goodness of fit, based on various empirical studies of the distribution of X2 in sampling from multinomial populations with given parameters. In this study it is shown that the chi-square probabilities of X 2 may differ markedly from the exact cumulative multinomial probabilities. Contrary to prevailing opinion, the approximation did not…

随机游走流行病模拟AI 解读

An epidemic simulation is presented in which the population occupies a rectangular grid and individuals or germs move about the grid using a two-dimensional random walk. It is shown that the model can simulate the Providence measles data and also a distemper epidemic in ferrets.

独栋住宅开工的短期不稳定性AI 解读

This article provides a statistical analysis of an inventory-theoretic approach to the study of the speculative sector of the single-family housing starts. Seen as a source of supply of new housing units the speculative housing starts are found to be heavily affected by the short-term interest rate and the monetary base.

联邦储备委员会敏感价格指数预测能力的评价AI 解读

This article reviews the historical performance of the Federal Reserve Board Sensitive Price Index (SPI) in accord with the standards established for such an index by the Price Statistics Review Committee. Several empirical tests are outlined which can be used to assess the predictive performance of any leading indicator. These tests indicate that the SPI performs well as an indicator for business conditions but has little to offer for the problem of predicting price level…

Wilcoxon 符号秩检验中并列值处理方法的比较AI 解读

Formulas are given for asymptotic efficiency of the Wilcoxon signed-rank test under several alternative ways of handling ties. Two methods of handling ties at zero, one suggested by Wilcoxon and the other by Pratt, are compared on the basis of their asymptotic efficiencies. Each method is shown to be better than the other in some situations. Two examples consider the discrete uniform distribution and the binomial distribution.

不同假设族之间的模型判别程序AI 解读

Procedures for discriminating between models from separate families of hypotheses are examined, with principal emphasis on procedures invariant under location and scale transformations. The discrimination procedures considered are compared using Monte Carlo samples as data for five pairs of invariant distributions. These comparisons are made with respect to the best invariant procedure, a procedure requiring no knowledge of sampling distributions, using approximate relative…

关于正交展开密度估计的一则札记AI 解读

The estimation of probability density functions is frequently approached through the use of orthogonal series. The goodness of the estimator can be conveniently measured in terms of Mean Integrated Squared Error, or MISE. To reduce MISE to a minimum, for fixed sample size, the experimenter would like to determine an optimal truncation point for the orthogonal series estimator. Presented here are some general MISE properties of a commonly used type of density estimator.

简单线性回归中 O-BLUE 估计量的相对效率AI 解读

This article is concerned with the estimators of the parameters of the linear model . The estimation procedure consists of using the Best Linear Unbiased Estimation method applied to ordered samples. These are denoted as “O-BLUE” estimators. The exact efficiences of such linear estimators based on censored samples relative to those based upon complete samples are given for some symmetric distributions as well as some scale contaminated distributions. Further, some percentage…

一般线性回归中标准化最小二乘残差的联合分布AI 解读

In this article the p-variate joint distribution is derived for a subset of p of the n standardized least squares residuals from a general linear regression. The resulting distribution is a standardized version of the Inverted-Student Function [8, p. 259]. An application of this result to the problem of detection of outliers is discussed.

因变量方差与其期望平方成比例时的回归分析AI 解读

In this article we consider a regression model where the variance of the dependent variable is proportional to the square of its expectation. First, we obtain the asymptotic efficiency of the weighted least squares estimator as compared to the maximum likelihood estimator for the cases when the dependent variable follows a normal, lognormal, or Gamma distribution. Second, we derive a test of whether the dependent variable follows a lognormal or a Gamma distribution. An…