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正态分布推断的两个定理及其在验收抽样中的应用AI 解读

Two theorems are presented which are useful in making inferences about the univariate normal distribution. Some applications of the theorems are given. It is thought that the theorems will prove useful in other contexts. Theorem 1 represents the normal (0, 1) random variable as a product of two independent random variables in infinitely many ways. Theorem 2 gives the expected value of the cumulative distribution function of the normal (0, 1) distribution, when the argument…

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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.

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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…

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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…

正态性假设下虚拟变量的多元回归AI 解读

The most frequently used practical regression model is that in which it is supposed that the dependent variate is normal for given values of the independent variate. In this paper it is pointed out that another regression model of wide applicability may be furnished by the contrary assumption—that the independent variate is normal for given values of the dependent variate. The particular case where the dependent variate is a vector of dummy variables is explored in detail.

准线性趋势与季节变动的估计AI 解读

Given a series of quarterly data, estimates may be obtained for both trend and seasonal variation by minimising the sum, or more generally a linear combination, of two sums of squares, one of them based on the second differences between trend values, the other on the deviations of the observations from seasonally corrected trend values. Exact solutions are obtained for 8 and 12 observations, and an approximate solution applicable to longer time series is given. A numerical…

似不相关回归方程估计量的若干精确有限样本结果AI 解读

The finite sample properties of an asymptotically efficient technique (JASA, June, 1962) for estimating coefficients in certain generally encountered sets of regression equations are studied in this paper. In particular, exact first and second moments of the asymptotically efficient coefficient estimator are derived and compared with those of the usual least squares estimator. Further, the exact probability density function of the new estimator is derived and studied as a…

构造房地产价格指数的回归方法AI 解读

Quality differences make estimation of price indexes for real properties difficult, but these can be largely avoided by basing an index on sales prices of the same property at different times. The problem of combining price relatives of repeat sales of properties to obtain a price index can be converted into a regression problem, and standard techniques of regression analysis can be used to estimate the index. This method of estimation is more efficient than others for…

十年消费者态度调查的预测表现AI 解读

Since 1951 the Survey Research Center has conducted surveys of consumer optimism and confidence two to four times a year in an attempt to improve methods of forecasting discretionary spending by consumers. The predictive success of these attitude surveys is tested here in conjunction with a number of financial variables by means of time series regressions covering the years 1952–61. The results indicate that attitude measurements contain information not obtainable from a…

残差分析札记AI 解读

In this note some aspects of residual analysis are considered critically. The relation between residual analysis in the sense of Freund, Vail, and Clunies-Ross and the analysis of covariance is clearly exhibited. The note establishes exact expressions for the difference between the “true” additional regression sum of squares obtained by simultaneous regression analysis and the regression sum of squares due to additional variables by residual analysis. The difference is given…

投资信托管理质量的变化（？）AI 解读

The paper compares year-to-year changes in the Wiesenberger Index of Return for investment funds of similar objectives. It is initially shown, using correlation techniques, that there was little consistency in yearly performance of the funds during the period from 1951 to 1960. This result serves as support for the assumption that a fund's relative performance in any one year is strictly a random occurrence. We might, therefore, define a “successful” management as one whose…

经济时间序列的季节调整与多元回归分析AI 解读

The logical implications of certain simple consistency requirements for appraising alternative procedures for seasonal adjustment constitute the first problem considered in this paper. It is shown that any sum preserving technique of seasonal adjustment that satisfies the quite reasonable requirements of orthogonality and idempotency can be executed on the electronic computer by standard least squares regression procedures. Problems involved in utilizing seasonally adjusted…

GCL 估计量精确有限样本分布函数在计量统计推断中的应用评述AI 解读

When employed in connection with econometric models that have a sufficiently high degree of cognitive significance (as measured by the extent to which underlying economic premises are actually elucidated into empirically testable implications) qualitative analysis of the exact finite sample distribution functions of GCL estimators of structural parameters finds its paramount use in delimiting the precision with which structural coefficients can be estimated. This kind of…

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关于残差分析的一则说明AI 解读

In this note some aspects of residual analysis are considered critically. The relation between residual analysis in the sense of Freund, Vail, and Clunies-Ross and the analysis of covariance is clearly exhibited. The note establishes exact expressions for the difference between the “true” additional regression sum of squares obtained by simultaneous regression analysis and the regression sum of squares due to additional variables by residual analysis. The difference is given…

正态假设下虚拟变量的多元回归AI 解读

The most frequently used practical regression model is that in which it is supposed that the dependent variate is normal for given values of the independent variate. In this paper it is pointed out that another regression model of wide applicability may be furnished by the contrary assumption—that the independent variate is normal for given values of the dependent variate. The particular case where the dependent variate is a vector of dummy variables is explored in detail.

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