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二项分布混合模型的参数估计AI 解读

Let Y 1, ···, Y m be independent, each having distribution where 0 < p 1 < ··· < p r < 1, 0 < α j , < 1, Σα j = 1, and n ≧ 2r − 1. This distribution is a mixture of r binomials. It is shown to be an identifiable mixture under the given restrictions on the parameters. Moment estimators for the 2r − 1 parameters p 1, ···, P r , α1, ···, α r − 1 are constructed and the covariance matrix of the joint asymptotic normal distribution of the estimators is obtained. It is found by…

重复调查的轮换抽样设计AI 解读

A unified finite population theory is developed for composite estimators of both the current level and change in level between consecutive occasions when a rotation sample design is employed. Explicit variance functions are given under the assumption that exponential and arithmetic correlation patterns hold over time for the characteristics of interest. Optimum values of the weight coefficients in the composite estimators, the optimum number of consecutive visits by a…

柯西样本估计的一则札记AI 解读

A class of estimators is proposed for the estimation of the center of the Cauchy distribution. Each estimator in the class is the arithmetic average of a central subset of the sample order statistics. Although the sample median is a member of the proposed class, it is not the most efficient. The average of roughly the middle quarter of the ordered sample has the lowest asymptotic variance.

非独立同分布观测的极端次序统计量近似分布AI 解读

The data are n univariate observations that are not necessarily from the same population, from continuous populations, or independent. The problem is to develop an approximate expression for a specified one of the upper (or lower) extremes of this set of observations when a type of m-dependence occurs. General expressions are developed that depend on n, the extreme considered, and the arithmetic average of the cumulative distribution functions (cdf's) for the individual…

季节性数据的回归分析AI 解读

When economists apply regression to monthly or quarterly data to estimate structural parameters, they generally either (a) use seasonally adjusted data or (b) use unadjusted data and allow for seasonal shifts in the intercept term. Starting from a more general model than either of these procedures, this paper spells out their implicit assumptions and derives expressions for the specification bias arising from incorrect assumptions. The expected values of the estimates in (a)…

列联表三因素交互作用的简便分析方法AI 解读

The earlier literature on three-factor interactions in a three-way contingency table was concerned mainly with the null hypothesis H 0 that these interactions are all nil. In the present article, we present methods for testing H 0 which are easier to apply than those suggested by earlier writers on this subject, and in addition we develop methods for obtaining simultaneous confidence intervals for estimating the magnitudes of the three-factor interactions in the three-way…

驻点位置受限的抛物线回归与最小二乘估计AI 解读

It is sometimes desired to fit a second degree polynomial E(y|x) = α + βx + γx 2 to a set of data so that its stationary point will fall in a given region. Methods are shown to calculate a, b, c, the least squares estimates of the regression coefficients α, β, and γ. An example is given in which this theory is applied to fit a parabolic regression to a set of data so that in a given contiguous and finite region of the independent variable, the regression function is strictly…

Wald 序贯概率比检验的最优性与操作特性曲线AI 解读

This paper examines “conjugate pairs” of points on the OC curve of a Wald Sequential Probability Ratio Test (SPRT). Such pairs are shown to exist for certain classes of SPRT's. For these classes, every point on the OC curve is a member of exactly one such pair. The well-known optimality property of a SPRT, which states that no other test of equal size and power (at the defining values of the parameter) can have a smaller expected sample size for either of the defining…

含系统性噪声的回归AI 解读

This paper identifies a type of highly correlated noise—systematic noise—that often arises in applications of linear regression to observations of spacecraft. An explicit formula is given for the inverse of the covariance matrix. The inverse matrix has a simple series expansion in ε2, where 1/ε is the amplitude of the systematic noise. When the leading term, the so-called filter matrix, is used in place of the exact inverse to estimate the regression parameters, the…

摘要暂缺

驻点位置受限的抛物线回归与最小二乘估计AI 解读

It is sometimes desired to fit a second degree polynomial E(y|x) = α + βx + γx 2 to a set of data so that its stationary point will fall in a given region. Methods are shown to calculate a, b, c, the least squares estimates of the regression coefficients α, β, and γ. An example is given in which this theory is applied to fit a parabolic regression to a set of data so that in a given contiguous and finite region of the independent variable, the regression function is strictly…

矩形分布总体中乘积统计量分布的若干推广AI 解读

This paper presents a unified approach to the distributions of the product of k (≥2) maximum values, and the product of k sample ranges from rectangular populations, both for equal and unequal sample sizes. The results obtained are generalisations based on some earlier work of Rider. It is proved that in all cases the distributions can be conveniently transformed to χ2's by the use of a well-known logarithmic transformation. It is also suggested that these results might be…

Wald 序贯概率比检验的最优性与操作特性曲线AI 解读

This paper examines “conjugate pairs” of points on the OC curve of a Wald Sequential Probability Ratio Test (SPRT). Such pairs are shown to exist for certain classes of SPRT's. For these classes, every point on the OC curve is a member of exactly one such pair. The well-known optimality property of a SPRT, which states that no other test of equal size and power (at the defining values of the parameter) can have a smaller expected sample size for either of the defining…

摘要暂缺

非同分布或相关观测的极端次序统计量近似分布AI 解读

The data are n univariate observations that are not necessarily from the same population, from continuous populations, or independent. The problem is to develop an approximate expression for a specified one of the upper (or lower) extremes of this set of observations when a type of m-dependence occurs. General expressions are developed that depend on n, the extreme considered, and the arithmetic average of the cumulative distribution functions (cdf's) for the individual…

含系统性噪声的回归AI 解读

This paper identifies a type of highly correlated noise—systematic noise—that often arises in applications of linear regression to observations of spacecraft. An explicit formula is given for the inverse of the covariance matrix. The inverse matrix has a simple series expansion in ε2, where 1/ε is the amplitude of the systematic noise. When the leading term, the so-called filter matrix, is used in place of the exact inverse to estimate the regression parameters, the…

两个多项式回归交点的估计AI 解读

Let t* denote an unknown abscissa of intersection of two true regression functions μ1(t) and μ2(t). Under normality assumptions with no restraints on t* the maximum likelihood estimator of t* is shown to be the corresponding intersection of the sample regressions. When this estimate exists confidence intervals J can usually be obtained for t* by an application of the Student t-distribution. When t* is restrained to some known interval I, the ML estimate may or may not fall…

非正态性对符号检验功效函数的影响AI 解读

The power function of the one sided, one-sample sign test is studied for populations which deviate from exact normality, either by skewness, kurtosis, or both. The terms of the Edgeworth asymptotic expansion of order more than N −3/2 are used to represent the population density. Three sets of hypotheses and alternatives, concerning the location of (1) the median, (2) the mean, and (3) the median as approximated by the mean and coefficient of skewness, are considered in an…

若干分布无关离散程度检验的一致性札记AI 解读

In this paper the consistency of the two-sample tests of Sukhatme [6], Ansari and Bradley [1], Siegel and Tukey [5], and Mood [3] is investigated. Each of these tests is a distribution-free analogue of the F-test for testing the equality of the variances of two normal distributions. If the two samples are taken from continuous distributions with the same median (say 0) and distribution functions F(x) and F(x/a) respectively, the hypothesis tested states that a = 1 and the…

费舍尔信任论证的内在困难AI 解读

The terms predictive and postdictive are introduced for two basic and implicitly well-known modes of interpreting probabilities, and the roles of these two modes in statistical inference are discussed with emphasis on the confidence argument of Neyman and the fiducial argument of Fisher. The conflicts between the confidence approach and the fiducial approach are analyzed in a way which generally supports Fisher's position. Finally, difficulties internal to the fiducial…

大规模调查中按规模成比例的系统抽样AI 解读

Based on a nationwide labour force survey the gain in precision arising from systematic pps (probability proportionate to size) sampling of the primary sampling units as compared to with-replacement pps sampling is obtained. The performance of a particular convenient but biased estimator of sampling variance is also studied.

恩格尔曲线分析中的有效分组、回归与相关AI 解读

Prais and Aitchison have shown that the common practice of grouping the individual observations in Engel curve analysis does not introduce a bias in the estimate of the regression coefficient, and that the classification of the individual households by income minimizes the increase in the variance of the estimate. The present paper provides an approximate numerical evaluation of the effects of such efficient grouping under the usual conditions of budget survey analysis. It…

观测落入指定类别的概率估计AI 解读

When observations in a random sample of n are classified into k categories with n i falling into a given class, the usual estimate of the corresponding probability is ni/n. When a priori information about the distribution of the probabilities is available, more precise estimates can be derived from data in any one sample of n. When the a priori distribution is not specified completely, but its general form can be inferred, the parameters of that distribution can be estimated…

直线回归的置信带AI 解读

This paper develops a method for obtaining confidence bands in polynomial regression when the observations are independently distributed with constant but unknown variance. The bands may be obtained, in principle, over arbitrary sets of the independent variable with exact preassigned confidence coefficients. In general, difficult distribution problems result when specific applications are attempted. The major portion of this paper is concerned with first degree polynomials…