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辅助变量信息不完整时的双重抽样AI 解读

It is well known that the precision of an estimator can be improved if auxiliary variables are used. In particular, if the relationship is linear, a linear regression estimator is constructed. When the mean of the auxiliary variable is completely unknown, double sampling techniques can be adopted. If the experimenter has partial information about the mean, he may perform a preliminary test and construct a preliminary test estimator. The bias, mean square error and relative…

有限总体中的稳健估计（二）：按规模变量分层AI 解读

It has been established in Part I [3] that for estimating a finite population total, the estimators which are optimal under simple super-population models can be made insensitive to certain departures from the models by the choice of balanced samples. Here stratification on a size variable is considered as another technique for protecting against model failure. Together the two techniques, stratification and balanced sampling, are shown to provide more efficient protection…

有限总体中的稳健估计（一）AI 解读

This is an application of a least-squares prediction approach to finite population sampling theory. One way in which this approach differs from the conventional one is its focus on characteristics of particular samples rather than on plans for choosing samples. Here we study samples in which many superpopulation models lead to the same optimal (BLU) estimator. Random sampling is considered in the light of these results.

Simon Newcomb、Percy Daniell 与稳健估计史：1885—1920AI 解读

This article reviews some of the history of robust estimation, emphasizing the period 1885–1920 and the work of Newcomb, Edgeworth, Sheppard, and Daniell. Particular attention is paid to lines of development which have excited recent interest, including linear functions of order statistics and mixtures of normal densities as models for heavy-tailed populations.

广义 Logistic 函数及其在广告效果中的应用AI 解读

A generalization of the common logistic function is developed, incorporating a non-unit saturation level, a non-zero intercept, and a non-symmetric shape. The dependence of the three generalized characteristics on (estimated) parameter values is exhibited. The statistical properties of the function are developed for the case where the dependent variable is a relative frequency. An empirical application shows that the effect of advertising on market share is best depicted by…

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用于比较相关比例的 Cochran Q 检验注记AI 解读

Cochran's Q-test, proposed to test the equality of three proportions for correlated observations, may have a larger asymptotic significance level than the nominal one, unless the admissible family of distributions is restricted to ensure that under the hypothesis the correlations between the observations are also equal. For a large class of such restricted families, optimal C 2(α) tests of the hypothesis are obtained, and the family for which the Q-test is an optimal C 2(α)…

关于使用正交展开进行密度估计的一则札记AI 解读

The estimation of probability density functions is frequently approached through the use of orthogonal series. The goodness of the estimator can be conveniently measured in terms of Mean Integrated Squared Error, or MISE. To reduce MISE to a minimum, for fixed sample size, the experimenter would like to determine an optimal truncation point for the orthogonal series estimator. Presented here are some general MISE properties of a commonly used type of density estimator.

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一般线性回归中标准化最小二乘残差的联合分布AI 解读

In this article the p-variate joint distribution is derived for a subset of p of the n standardized least squares residuals from a general linear regression. The resulting distribution is a standardized version of the Inverted-Student Function [8, p. 259]. An application of this result to the problem of detection of outliers is discussed.

不完整观测下二元正态分布的贝叶斯分析AI 解读

We consider the problem of drawing inferences on the difference of the population means when an incomplete sample from a bivariate normal population is available. Whereas Mehta and Gurland [7] have considered this problem from the sampling theory point of view, we tackle here the same problem from a Bayesian approach.

调查数据多变量回答误差模型及其在子类均值估计中的应用AI 解读

Indicator functions are used as the basis for the formulation of a multivariate extension of the response error model developed by the U.S. Bureau of the Census. This approach allows a more complete characterization for general survey designs of the nature of the various components of the total variance of linear sample estimators and is particularly useful with respect to the role of the interaction component. These results are then applied to study the effect of response…

It has been established in Part I [3] that for estimating a finite population total, the estimators which are optimal under simple super-population models can be made insensitive to certain departures from the models by the choice of balanced samples. Here stratification on a size variable is considered as another technique for protecting against model failure. Together the two techniques, stratification and balanced sampling, are shown to provide more efficient protection…

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广义 Logistic 函数及其广告效果应用AI 解读

A generalization of the common logistic function is developed, incorporating a non-unit saturation level, a non-zero intercept, and a non-symmetric shape. The dependence of the three generalized characteristics on (estimated) parameter values is exhibited. The statistical properties of the function are developed for the case where the dependent variable is a relative frequency. An empirical application shows that the effect of advertising on market share is best depicted by…

基于随机游走的流行病模拟AI 解读

An epidemic simulation is presented in which the population occupies a rectangular grid and individuals or germs move about the grid using a two-dimensional random walk. It is shown that the model can simulate the Providence measles data and also a distemper epidemic in ferrets.

美联储敏感价格指数预测能力的评价AI 解读

This article reviews the historical performance of the Federal Reserve Board Sensitive Price Index (SPI) in accord with the standards established for such an index by the Price Statistics Review Committee. Several empirical tests are outlined which can be used to assess the predictive performance of any leading indicator. These tests indicate that the SPI performs well as an indicator for business conditions but has little to offer for the problem of predicting price level…

非线性响应函数的实验设计AI 解读

W. G. COCHRAN* This article reviews work on the planning of experiments with response functions nonlinear in some parameters. Apart from older work on dilution series experiments and quantal bioassays, this field is relatively recent, the mathematical and computing aspects being more complex than for linear responses. An efficient design requires good advance estimates of the parameters. Research has concentrated on (1) optimum estimation of the parameters, under an…

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独栋住宅开工的短期不稳定性AI 解读

This article provides a statistical analysis of an inventory-theoretic approach to the study of the speculative sector of the single-family housing starts. Seen as a source of supply of new housing units the speculative housing starts are found to be heavily affected by the short-term interest rate and the monetary base.