Journal ArticleDOI
Estimates of Income for Small Places: An Application of James-Stein Procedures to Census Data
Robert E. Fay,Roger A. Herriot +1 more
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In this article, an adaptation of the James-Stein estimator is applied to sample estimates of income for small places (i.e., population less than 1,000) from the 1970 Census of Population and Housing.Abstract:
An adaptation of the James-Stein estimator is applied to sample estimates of income for small places (i.e., population less than 1,000) from the 1970 Census of Population and Housing. The adaptation incorporates linear regression in the context of unequal variances. Evidence is presented that the resulting estimates have smaller average error than either the sample estimates or an alternate procedure of using county averages. The new estimates for these small places now form the basis for the Census Bureau's updated estimates of per capita income for the General Revenue Sharing Program.read more
Citations
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Journal ArticleDOI
That BLUP is a Good Thing: The Estimation of Random Effects
TL;DR: In animal breeding, Best Linear Unbiased Prediction (BLUP) as mentioned in this paper is a technique for estimating genetic merits, which can be used to derive the Kalman filter, the method of Kriging used for ore reserve estimation, credibility theory used to work out insurance premiums, and Hoadley's quality measurement plan used to estimate a quality index.
Journal ArticleDOI
Parametric Empirical Bayes Inference: Theory and Applications
TL;DR: In this paper, a review of the state of the art in multiparameter shrinkage estimators with emphasis on the empirical Bayes viewpoint, particularly in the case of parametric prior distributions, is presented.
Book
Small Area Estimation
TL;DR: In this paper, the authors proposed a model-based approach for estimating small area statistics based on direct and indirect estimates of the total population of a given region in a given domain.
Journal ArticleDOI
An Error-Components Model for Prediction of County Crop Areas Using Survey and Satellite Data
TL;DR: In this article, a linear regression model was used to predict the area under corn and soybeans in 12 Iowa counties. But the model was not applied to the U.S. Department of Agriculture's 1978 June Enumerative Survey of the United States.
Journal ArticleDOI
Small Area Estimation: An Appraisal
Malay Ghosh,J. N. K. Rao +1 more
TL;DR: Empirical best linear unbiased prediction as well as empirical and hierarchical Bayes seem to have a distinct advantage over other methods in small area estimation.
References
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Book
Applied Regression Analysis
Norman R. Draper,Harry Smith +1 more
TL;DR: In this article, the Straight Line Case is used to fit a straight line by least squares, and the Durbin-Watson Test is used for checking the straight line fit.
Book
Linear statistical inference and its applications
TL;DR: Algebra of Vectors and Matrices, Probability Theory, Tools and Techniques, and Continuous Probability Models.
Journal ArticleDOI
Linear Statistical Inference and its Applications
P. G. Moore,C. Radhakrishna Rao +1 more
TL;DR: The theory of least squares and analysis of variance has been studied in the literature for a long time, see as mentioned in this paper for a review of some of the most relevant works. But the main focus of this paper is on the analysis of variance.
Book ChapterDOI
Estimation with Quadratic Loss
W. James,Charles Stein +1 more
TL;DR: In this paper, the authors consider the problem of finding the best unbiased estimator of a linear function of the mean of a set of observed random variables. And they show that for large samples the maximum likelihood estimator approximately minimizes the mean squared error when compared with other reasonable estimators.
Inadmissibility of the usual estimator for the mean of a multivariate normal distribution
TL;DR: In this article, the authors show that the possible improvement over the usual estimator seems to be large enough to be of practical importance if n is large, but the results are not in a form suitable for immediate practical application.