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指数族分布有限混合模型的估计AI 解读

General “successive substitutions” iteration equations are developed for obtaining estimates for finite mixtures of distributions from the exponential family. These, in general, correspond to relative maximums of the likelihood function. It is assumed that the number of distributions is known, and that the mixtures are from distributions of the same type, but with different parameter values. The particular equations for the Poisson, binomial, and exponential distributions…

离散均匀有限总体的极差抽样分布与同质性检验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…

随机变量乘积的精确协方差AI 解读

For the general case of jointly distributed random variables x and y, Goodman [3] derives the exact variance of the product xy. For the special case where x and y are stochastically independent, he provides a simpler expression for the exact variance. We offer a weaker set of assumptions which suffices to yield the simpler expression. We then extend Goodman's analysis to present the exact covariance of two products xy and uv, and sketch several specializations and…

方差分量估计量的均方误差效率AI 解读

Various estimators of components of variance for the balanced one way layout are compared using mean squared error as a measure of performance. Several modifications of the maximum likelihood estimator and several formal Bayes estimators are compared and mean square error relationships are given. Inadmissibility is established for a large class of translation and scale invariant estimators. Numerical results are tabled and graphed to exhibit the relative efficiency of the…

独立异方差抽样误差下加权回归估计量的方差AI 解读

General results are obtained for an approximation to the variance of a weighted regression estimator in which the weights are sample estimators of unknown unpatterned variances. Independent normally distributed errors are specified for the linear response model used in the development. Applications to four examples of weighted sample means and linear regression in a single factor are studied. The most important practical conclusion drawn from the results of these examples is…

方形列联表的对称性与边际齐性AI 解读

The principle of minimum discrimination information estimation is employed to obtain RBAN (Regular Best Asymtotically Normal) estimates of the cell frequencies of an r×r contingency table under hypotheses of either symmetry or marginal homogeneity. For the latter, a convergent iterative procedure is given to compute the estimates. The associated minimum discrimination information statistics are distributed asymptotically as χ2 under the null hypotheses. The procedures differ…

关于 Scheffé 对 Behrens–Fisher 问题解法的若干讨论AI 解读

The problem considered here is a multivariate generalization of the classical Behrens-Fisher problem. Based on samples of size ni , i = 1, …, k, from k multivariate normal populations (of perhaps different dimension), a test statistic is proposed to test null hypotheses about linear relationships between components of the mean vectors of the k populations. Under the null hypothesis, the test statistic has a central F distribution and under alternatives, a non-central F…

南亚部分国家女性死亡率高于男性：概要AI 解读

This paper presents statistical evidence, which seems to be conclusive, that there exists a particular pattern of mortality in Ceylon, India and Pakistan where, contrary to general experience, female mortality is higher than that of the males. The sex ratios of the enumerated population in these three countries are among the highest in the world, and the age pattern of the sex ratios is such that they increase from childhood to adulthood to the old ages. Abnormally high sex…

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…

图书使用的统计模型及其在馆藏储存问题中的应用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…

回归中精确线性约束的均方误差检验表AI 解读

A table is presented containing critical points for the non-central F with non-centrality of one-half for type one error .05, .10, .25 and .50 and numerator and denominator d.f. including 1–30, 40, 60, 120, 200, 400, 1000. The critical points may be used to test the hypothesis that a set of exact linear restrictions imposed on the parameters of a linear model yield estimators that are better in generalized MSE than the unrestricted, o.l.s., estimators. Tabulation is…

双样本 Kolmogorov–Smirnov 统计量的精确与近似抽样分布AI 解读

The size of errors of the Smirnov approximation to the exact null distribution of the two sample Kolmogorov-Smirnov criterion Dmn, m≤n is investigated. It is shown that a sample size n of 100 is necessary before the overestimating effect of the Smirnov distribution becomes negligible. Several improvements over the Smirnov approximation are considered. With continuity correction of order of , the Smirnov approximation accomplishes for n = 50 about what it does for n = 100…

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.

Friedman 秩检验的多元扩展AI 解读

This paper deals with a multivariate extension of Friedman's χ2 r -test. A rank permutation distribution and the large sample properties of the criterion are studied. The asymptotic relative efficiency (A.R.E.) for a sequence of translation alternatives is studied and bounds are given for certain special cases. It is shown that, under specified conditions, the A.R.E. of this test with respect to the likelihood ratio test is largest when the block dispersion matrices differ…

利用矩阵导数判定多元极大值与极小值AI 解读

The purpose of this paper is the presentation of formulae for obtaining matrix derivatives of the second order to use in making tests for maxima and minima. The theory of such second order derivatives is presented. These formulae require the rearrangment of the parameter elements in vector form and the transformed results feature Kronecker products, which have certain desirable properties. Application is made to several types of problems.

序贯概率比检验所需样本量分布的矩AI 解读

Approximate expressions are given for the first four moments of the distribution of sample size required by a sequential probability ratio test. Some possible uses of these moments are also discussed.

关于一种两阶段抽样检验的札记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…

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…

高效率估计方法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…

使简单最小二乘与方差分析程序仍具最优性的参数扩充及误差结构AI 解读

Conditions are presented under which in all linear models with a common specified systematic part every linear simple least squares estimator is also best. The behaviour of mean squares and test ratios in ordinary analysis of variance tables under these and also less stringent conditions is discussed with illustrative examples given.

关于“必要最优估计量”的一则注记AI 解读

This note presents a simple proof that the Horvitz-Thompson estimator (where πi is the total probability of selecting unit i over all possible samples), satisfies Ajgaonkar's criterion for the “necessary best estimator” for all sample designs.

对称性条件下的 Student t 检验AI 解读

The size and power of Student's t-test are discussed under weaker than normal conditions. It is shown that assuming only a symmetry condition for the null hypothesis leads to effective bounds on the dispersion of the t-statistic. (The symmetry condition is weak enough to include all cases of independent but not necessarily identically distributed observations, each symmetric about the origin.) The connection between Student's test and the usual non-parametric tests is…

以随机场作为解释变量的回归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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