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A Quarterly Econometric Model of the United States

美国季度计量经济模型

Simplicity in an econometric model may often be a virtue provided that the model performs its particular predictive function in a reasonably competent manner. The following model, while minimizing computational difficulties, demonstrates fairly accurate forecasting ability and a partial explanation, via an accelerator, of postwar fluctuations in the gross national product of the United States.

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Partial Correlations in Regression Computations

回归计算中的偏相关

The partial correlation between the dependent variable and the k-th independent variable in a regression can be calculated simply from the k-th regression coefficient and its standard error. Partial correlations are useful in determining relations among the estimates obtained under alternative assumptions about which variables in a regression are independent of the disturbances.

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A Note on Measurement Errors and Detecting Real Differences

测量误差与真实差异检出的简注

Two groups, N 1 = α1 + b 1 and N 2 = α2+ b 2, are compared in terms of their respective morbidity rates, p 1 and p 2, in the presence of errors of misclassification (α1 and α2 are sure components; b 1 and b 2 are potential error terms). The four extreme situations for the compositions of N 1 and N 2 are considered. Rate p 1 is assumed to apply to α1 and b 1; p 2 is assumed to apply to α1 and b 2. If there is a difference in rates for the error-free situation, then the…

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The Use of Sample Quasi-Ranges in Setting Confidence Intervals for the Population Standard Deviation

利用样本准极差构造总体标准差置信区间

The problem is the determination of an optimal selection method of quasi-range for setting one-sided confidence bounds and confidence intervals for the standard deviation from a given distribution. The proposed methods of optimal selection are applied to random ordered samples from the normal, exponential and rectangular distributions. Tables of confidence bounds for the standard deviation of these distributions are given for confidence levels commonly used in statistical…

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Confidence Curves: An Omnibus Technique for Estimation and Testing Statistical Hypotheses

置信曲线:统一估计与统计假设检验的方法

A standard practice of physical scientists is to report estimates (“measurements”) accompanied by their standard errors (or alternatively “average errors” or “probable errors”). Such reports are interpreted flexibly as appropriate in various contexts of application. With the usual normality assumption, such reports may be read as representing confidence intervals or limits at the various confidence levels, and this omnibus character largely accounts for the convenience and…

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A Quarterly Econometric Model of the United States

美国季度计量经济模型

Simplicity in an econometric model may often be a virtue provided that the model performs its particular predictive function in a reasonably competent manner. The following model, while minimizing computational difficulties, demonstrates fairly accurate forecasting ability and a partial explanation, via an accelerator, of postwar fluctuations in the gross national product of the United States.

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A Note on Measurement Errors and Detecting Real Differences

测量误差与真实差异检出的一个注记

Two groups, N 1 = α1 + b 1 and N 2 = α2+ b 2, are compared in terms of their respective morbidity rates, p 1 and p 2, in the presence of errors of misclassification (α1 and α2 are sure components; b 1 and b 2 are potential error terms). The four extreme situations for the compositions of N 1 and N 2 are considered. Rate p 1 is assumed to apply to α1 and b 1; p 2 is assumed to apply to α1 and b 2. If there is a difference in rates for the error-free situation, then the…

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The Use of Sample Quasi-Ranges in Setting Confidence Intervals for the Population Standard Deviation

用样本准极差构造总体标准差置信区间

The problem is the determination of an optimal selection method of quasi-range for setting one-sided confidence bounds and confidence intervals for the standard deviation from a given distribution. The proposed methods of optimal selection are applied to random ordered samples from the normal, exponential and rectangular distributions. Tables of confidence bounds for the standard deviation of these distributions are given for confidence levels commonly used in statistical…

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Partial Correlations in Regression Computations

回归计算中的偏相关

The partial correlation between the dependent variable and the k-th independent variable in a regression can be calculated simply from the k-th regression coefficient and its standard error. Partial correlations are useful in determining relations among the estimates obtained under alternative assumptions about which variables in a regression are independent of the disturbances.

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Randomized Rounded-Off Multipliers in Sampling Theory

抽样理论中的随机取整乘数

In a large scale survey, where a non-self-weighting design is used, the work at the tabulation stage becomes time consuming and costly due to the large number of multipliers (inflation factors) involved in obtaining the estimates. In this paper a technique is developed to substitute the multipliers by a very small number of multipliers called “randomized rounded-off multipliers” by a suitable randomizing process, thereby reducing the work at the tabulation stage. A suitable…

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A Parametric Estimate of the Standard Error of the Survival Rate

生存率标准误的参数化估计

This paper proposes a simplification of Greenwood's estimate of the standard error of the survival rate. The simplifying assumptions are (a) that cases enter the follow-up study at a uniform rate, (b) there are no losses to follow-up, and (c) the mortality risk for successive follow-up intervals is constant. Numerical examples drawn from cancer registry data indicate that the proposed estimate yields acceptable results under certain realistic circumstances despite some…

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Unbiased Ratio Estimators in Stratified Sampling

分层抽样中的无偏比率估计量

Several unbiased ratio estimators (URE) in stratified random sampling are presented. The “separate” URE is a direct application of the Hartley-Ross URE within strata. The “combined” URE, for equal sample size k per stratum, is obtained by means of a complete replacement, repeated k times, of a sample of size one per stratum. The relative efficiencies of these estimators with respect to the usual biased RE are discussed. An approximately URE is developed and it is shown that,…

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Some Nonparametric Tests for Comovements between Time Series

时间序列共同变动的若干非参数检验

The test, proposed by Moore and Wallis [23], of the existence of correlation between the movements in two time series (eliminating at least the primary effects of trends) was justified by them in “the special case of randomly arranged [signs of the] first differences” in both series. Moore and Wallis also noted that the signs of the first differences in a time series will have a negative serial correlation if the time series is a purely random process (or if it is a…

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Note on Stepwise Least Squares

分步最小二乘简注

A stepwise procedure is often used to estimate one coefficient in a multiple linear regression. The relation between this stepwise estimate and the estimate obtained by direct multiple regression is spelled out.

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Residual Analysis

残差分析

Individual value of residuals from a least squares regression equation can be analyzed as a set of originally observed quantities. If the analysis of residuals is in the form of another regression analysis, the total analysis of the data can be described as a two-stage regression. Such a two-stage approach is not equivalent to the usual, one-stage analysis, and therefore the resulting estimates and tests are biased. It is the purpose of this paper to obtain expressions for…

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Multiple Comparisons among Means

多个均值之间的多重比较

Methods for constructing simultaneous confidence intervals for all possible linear contrasts among several means of normally distributed variables have been given by Scheffé and Tukey. In this paper the possibility is considered of picking in advance a number (say m) of linear contrasts among k means, and then estimating these m linear contrasts by confidence intervals based on a Student t statistic, in such a way that the overall confidence level for the m intervals is…

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