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A Direct Test of Friedman's Permanent Income Theory

对 Friedman 永久收入理论的直接检验

After reviewing Friedman's time series model, this article presents a test of whether or not permanent consumption and transitory income are correlated. We conclude utilizing essentially the same data series and the same measure of permanent income as Friedman that a significant positive correlation exists between these variables as well as between permanent and transitory income.

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Measurement of Citrus Demands When all Variables are Subject to Error

所有变量均有测量误差时的柑橘需求估计

The hypothesis that consumers use a two-stage procedure to maximize a utility function in which food items are strongly separable from non-food items is combined with prior information about food price correlations to derive statistically manageable demand equations for fresh oranges and frozen orange concentrate. Special attention is given to the problem of measuring demand when all the variables are measured with error. A new statistical method, which yields consistent…

AI 解读阅读原文 ↗BibTeX ↓

Predictive Accuracy of Quarterly and Annual Aggregate Saving Functions

季度与年度总量储蓄函数的预测准确性

Aggregate saving functions have been grouped into several models which have similar theoretical underpinnings. They are then tested under criteria pertaining to their predictive accuracy and their economic reasonableness. It is found that saving is predicted much more accurately when it includes net investment in consumer durables (i.e., “use value” saving, D S) as opposed to when it is defined as only personal saving (S). In predicting D S, the functions which use current…

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Balanced Repeated Replications for Standard Errors

用于标准误估计的平衡重复复制法

Balanced repeated replications (BRR) is a general method for computing standard errors. It is useful when mathematical distribution theory is impractical or lacking, and especially for analytical statistics based on complex samples where clustering destroys the independence of observations. Presented are results of methods used to measure standard errors of regression coefficients for several multivariate techniques. The basic designs of the several samples comprised two…

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Systematic Biases in Panel Surveys Due to Differential Nonresponse

差异性无回应导致的面板调查系统偏差

Panel surveys involve repeated observations made on the same sample of populalation units. In some of these studies systematic biases have appeared; specifically, if Ri is an estimate made from panels appearing in the sample for the i th time, then it has been observed that these estimates sometimes vary systematically with i. It is tempting to interpret these phenomena as being due to conditioning of the panel of respondents. In this article it is shown that these…

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A Test for a Shifting Slope Coefficient in a Linear Model

线性模型中斜率系数发生变化的检验

A locally most powerful test is developed for the hypothesis that a slope coefficient in a linear time series model is stable, against the alternative that the slope shifts exactly once somewhere in the series. Analysis of the procedure using artificial data indicates good power characteristics even when the ratio of the shift size to the error variance is moderate—especially if the shift does not occur very near either end of the series. Power also depends on the pattern of…

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Properties of a Rank Test of Cronholm and Revusky

Cronholm–Revusky 秩检验的性质

Cronholm and Revusky [4] have proposed a rank test based on independent subexperiments for the comparison of a treatment effect with a control when the treatment is destructive but the control produces at most a transient effect. This article provides a thorough study of its performance under two sampling situations. With the aid of a computer, the exact small sample power of the test is evaluated for some important alternatives. A modification of the test is proposed for…

AI 解读阅读原文 ↗BibTeX ↓

Some Probability Inequalities of Multivariate Normal and Multivariate t

多元正态与多元 t 分布的若干概率不等式

Applying the result of expectations of non-negative random variables, inequalities for the one-sided and two-sided rectangular probabilities of higher-dimensional multivariate normal and multivariate t distributions are obtained. It is shown that their k-dimensional rectangular probabilities is lower bounded by the (k/m)th power of their m-dimensional rectangular probabilities for every k≥ m ≥ 1, and this bound is quite good when k/m is close to one. Applications to multiple…

AI 解读阅读原文 ↗BibTeX ↓

Zipf's Law and Prior Distributions for the Composition of a Population

齐普夫定律与总体构成的先验分布

The limiting distribution of frequencies of frequencies as the population size becomes large is obtained under Bose-Einstein and Maxwell-Boltzmann forms of the classical occupancy problem, when the number of cells is random and has a prior distribution. A rich variety of limiting distributions is obtained, including weak forms of Zipf's Law and the Fisher logarithmic series distribution. Lizards are compared to the weak form of Zipf's Law, and some speculations are made in…

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A Test Procedure for the Simulated Plant-Record Method of Life Analysis

模拟厂产记录寿命分析法的检验程序

A chi-square test procedure is proposed that would establish the reasonableness of assuming a dispersion and average service life selected by the Simulated Plant-Record method of life analysis to be descriptive of the mortality characteristics of an industrial property plant account.

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Piecewise Regression

分段回归

A difficult regression parameter estimation problem is posed when the data sample is hypothesized to have been generated by more than a single regression model. To find the best-fitting number and location of underlying regression systems, the investigator must specify both the statistical criterion and the search-estimation procedure to be used. The approach outlined in this article is essentially a wedding of hierarchical clustering and standard regression theory. As the…

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On the Nonparametric Tests of David and Fix for the Bivariate Two-Sample Location Problem

双变量两样本位置问题的 David–Fix 非参数检验

Some large-sample properties of the three nonparametric tests of David and Fix for the two-sample bivariate location problem are given. In particular the Pitman A.R.E.s of the tests against some ‘normal-theory’ competitors are shown to be satisfactory in most cases for a number of ‘near-normal’ bivariate distributions. Their performances in some mixtures of bivariate normal distributions prove to be particularly convincing. A useful relationship between the three test…

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Calibration and Statistical Inference

校准与统计推断

This article presents an elementary statistical model from which inferences in the form of probability statements are drawn. These are compared with the inferences derived from the corresponding classical and Bayesian models of the same phenomenon. The example concerns a measuring device, and the problem of calibration is discussed. The method of analysis extends to a wide range of common statistical applications, notably those described by multivariate and linear regression…

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Zipf's Law and Prior Distributions for the Composition of a Population

Zipf 定律与总体构成的先验分布

The limiting distribution of frequencies of frequencies as the population size becomes large is obtained under Bose-Einstein and Maxwell-Boltzmann forms of the classical occupancy problem, when the number of cells is random and has a prior distribution. A rich variety of limiting distributions is obtained, including weak forms of Zipf's Law and the Fisher logarithmic series distribution. Lizards are compared to the weak form of Zipf's Law, and some speculations are made in…

AI 解读阅读原文 ↗BibTeX ↓

Predictive Accuracy of Quarterly and Annual Aggregate Saving Functions

季度与年度总量储蓄函数的预测准确性

Aggregate saving functions have been grouped into several models which have similar theoretical underpinnings. They are then tested under criteria pertaining to their predictive accuracy and their economic reasonableness. It is found that saving is predicted much more accurately when it includes net investment in consumer durables (i.e., “use value” saving, D S) as opposed to when it is defined as only personal saving (S). In predicting D S, the functions which use current…

AI 解读阅读原文 ↗BibTeX ↓

Systematic Biases in Panel Surveys Due to Differential Nonresponse

差异性无应答导致的面板调查系统偏差

Panel surveys involve repeated observations made on the same sample of populalation units. In some of these studies systematic biases have appeared; specifically, if Ri is an estimate made from panels appearing in the sample for the i th time, then it has been observed that these estimates sometimes vary systematically with i. It is tempting to interpret these phenomena as being due to conditioning of the panel of respondents. In this article it is shown that these…

AI 解读阅读原文 ↗BibTeX ↓

On the Efficiency of Ordinary Least-Squares in Regression Models

回归模型中普通最小二乘估计的效率

For all regression models containing a common subset of explanatory variables, a necessary and sufficient condition for the ordinary least-squares estimators to be also best linear-unbiased estimators is given. The stochastic properties of the variances and covariances estimated by ordinary least-squares are derived. Five examples, especially useful in economic applications, are studied. The relevance of the basic result of this article for regression models containing a set…

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Properties of a Rank Test of Cronholm and Revusky

Cronholm–Revusky 秩检验的性质

Cronholm and Revusky [4] have proposed a rank test based on independent subexperiments for the comparison of a treatment effect with a control when the treatment is destructive but the control produces at most a transient effect. This article provides a thorough study of its performance under two sampling situations. With the aid of a computer, the exact small sample power of the test is evaluated for some important alternatives. A modification of the test is proposed for…

AI 解读阅读原文 ↗BibTeX ↓

Some Probability Inequalities of Multivariate Normal and Multivariate t

多元正态与多元t分布的若干概率不等式

Applying the result of expectations of non-negative random variables, inequalities for the one-sided and two-sided rectangular probabilities of higher-dimensional multivariate normal and multivariate t distributions are obtained. It is shown that their k-dimensional rectangular probabilities is lower bounded by the (k/m)th power of their m-dimensional rectangular probabilities for every k≥ m ≥ 1, and this bound is quite good when k/m is close to one. Applications to multiple…

AI 解读阅读原文 ↗BibTeX ↓

A Test Procedure for the Simulated Plant-Record Method of Life Analysis

模拟资产记录寿命分析法的检验程序

A chi-square test procedure is proposed that would establish the reasonableness of assuming a dispersion and average service life selected by the Simulated Plant-Record method of life analysis to be descriptive of the mortality characteristics of an industrial property plant account.

AI 解读阅读原文 ↗BibTeX ↓

A Direct Test of Friedman's Permanent Income Theory

After reviewing Friedman's time series model, this article presents a test of whether or not permanent consumption and transitory income are correlated. We conclude utilizing essentially the same data series and the same measure of permanent income as Friedman that a significant positive correlation exists between these variables as well as between permanent and transitory income.

阅读原文 ↗BibTeX ↓

Measurement of Citrus Demands When All Variables are Subject to Error

所有变量均存在误差时的柑橘需求测量

The hypothesis that consumers use a two-stage procedure to maximize a utility function in which food items are strongly separable from non-food items is combined with prior information about food price correlations to derive statistically manageable demand equations for fresh oranges and frozen orange concentrate. Special attention is given to the problem of measuring demand when all the variables are measured with error. A new statistical method, which yields consistent…

AI 解读阅读原文 ↗BibTeX ↓