Estimation of Median Income of Four-Person Families: A Bayesian Time Series Approach
01 Dec 1996-Journal of the American Statistical Association (Taylor & Francis Group)-Vol. 91, Iss: 436, pp 1423-1431
TL;DR: The authors developed a general methodology for small domain estimation based on data from repeated surveys and applied it to the estimation of median income of four-person families for the 50 states and the District of Columbia.
Abstract: This article develops a general methodology for small domain estimation based on data from repeated surveys. The results are directly applied to the estimation of median income of four-person families for the 50 states and the District of Columbia. These estimates are needed by the U.S. Department of Health and Human Services (HHS) to formulate its energy assistance program for low income families. The U.S. Bureau of the Census, by an informal agreement, has provided such estimates to HHS through a linear regression methodology since the latter part of the 1970s. The current method is an empirical Bayes method (EB) that uses the Current Population Survey (CPS) estimates as well as the most recent decennial census estimates updated by the per capita income estimates of the Bureau of Economic Analysis. However, with the existing methodology, standard errors associated with these estimates are not easy to obtain. The EB estimates, when used naively, can lead to underestimation of standard errors. Mo...
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TL;DR: In this paper, the authors provide a critical review of the main advances in small area estimation (SAE) methods in recent years and discuss some of the earlier developments, which serve as a necessary background for the new studies.
Abstract: Summary The purpose of this paper is to provide a critical review of the main advances in small area estimation (SAE) methods in recent years. We also discuss some of the earlier developments, which serve as a necessary background for the new studies. The review focuses on model dependent methods with special emphasis on point prediction of the target area quantities, and mean square error assessments. The new models considered are models used for discrete measurements, time series models and models that arise under informative sampling. The possible gains from modeling the correlations among small area random effects used to represent the unexplained variation of the small area target quantities are examined. For review and appraisal of the earlier methods used for SAE, see Ghosh and Rao (1994).
256 citations
01 Jan 1999
TL;DR: This paper supplements Ghosh and Rao (1994) by covering the literature over the past five years or so on model-based estimation, and covers several small area models and empirical best linear unbiased prediction (EBLUP), empirical Bayes (EB) and hierarchicalBayes (HB) methods applied to these models.
Abstract: Small area estimation has received a lot of attention in recent years due to growing demand for reliable small area estimators. Traditional area-specific direct estimators do not provide adequate precision because sample sizes in small areas are seldom large enough. This makes it necessary to employ indirect estimators that borrow strength from related areas; in particular, model-based indirect estimators. Ghosh and Rao (1994) provided a comprehensive review and appraisal of methods for small area estimation, covering the literature to 1992-1993. This paper supplements Ghosh and Rao (1994) by covering the literature over the past five years or so on model-based estimation. In particular, we cover several small area models and empirical best linear unbiased prediction (EBLUP), empirical Bayes (EB) and hierarchical Bayes (HB) methods applied to these models. We also present several recent applications of small area estimation. 1. J.N.K. Rao, School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, K1S 5B6.
130 citations
TL;DR: In this paper, a preliminary analysis showed that the distributions of cancer screening and risk factors are different for telephone and non-telephone households. But, the distribution of cancer risk factors is similar for both types of households.
Abstract: Cancer surveillance research requires estimates of the prevalence of cancer risk factors and screening for small areas such as counties. Two popular data sources are the Behavioral Risk Factor Surveillance System (BRFSS), a telephone survey conducted by state agencies, and the National Health Interview Survey (NHIS), an area probability sample survey conducted through face-to-face interviews. Both data sources have advantages and disadvantages. The BRFSS is a larger survey and almost every county is included in the survey, but it has lower response rates as is typical with telephone surveys and it does not include subjects who live in households with no telephones. On the other hand, the NHIS is a smaller survey, with the majority of counties not included; but it includes both telephone and nontelephone households, and has higher response rates. A preliminary analysis shows that the distributions of cancer screening and risk factors are different for telephone and nontelephone households. Thus, informatio...
129 citations
Cites background or methods from "Estimation of Median Income of Four..."
...Although this is similar in spirit to treating sampling variances as fixed at estimates, which is common in small-area estimation (Fay and Herriott 1979; Datta et al. 1991; Ghosh et al. 1996; Rao 1999), it could result in underestimation of variability in the Bayesian procedure....
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...This is similar to the customary practice of assuming that the sampling variance is known when using many hierarchical models for small-area estimation (Fay and Herriott 1979; Datta, Fay, and Ghosh 1991; Ghosh, Nangia, and Kim 1996; Rao 1999)....
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TL;DR: An application with Spanish EU-SILC data is carried out to obtain estimates of poverty indicators for Spanish provinces in 2008, making use of survey data from years 2004-2008.
112 citations
Cites background from "Estimation of Median Income of Four..."
...Ghosh et al. (1996) proposed a slightly more complicated time correlated area level model to estimate the median income of four-person families for the fifty American states and the district of Columbia....
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TL;DR: In this article, a method based on bootstrap samples is proposed to measure the accuracy of the proposed empirical Bayes (EB) estimator of a small-area characteristic and a simple approximation of the method which does not require any bootstrap simulation is also proposed.
110 citations
Cites methods from "Estimation of Median Income of Four..."
...The current estimates are produced by an empirical Bayes procedure (see Ghosh et al., 1996)....
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References
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TL;DR: The analogy between images and statistical mechanics systems is made and the analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations, creating a highly parallel ``relaxation'' algorithm for MAP estimation.
Abstract: We make an analogy between images and statistical mechanics systems. Pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice-like physical system. The assignment of an energy function in the physical system determines its Gibbs distribution. Because of the Gibbs distribution, Markov random field (MRF) equivalence, this assignment also determines an MRF image model. The energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the MRF. For a range of degradation mechanisms, including blurring, nonlinear deformations, and multiplicative or additive noise, the posterior distribution is an MRF with a structure akin to the image model. By the analogy, the posterior distribution defines another (imaginary) physical system. Gradual temperature reduction in the physical system isolates low energy states (``annealing''), or what is the same thing, the most probable states under the Gibbs distribution. The analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations. The result is a highly parallel ``relaxation'' algorithm for MAP estimation. We establish convergence properties of the algorithm and we experiment with some simple pictures, for which good restorations are obtained at low signal-to-noise ratios.
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"Estimation of Median Income of Four..." refers background in this paper
...Also, following Gelfand and Smith (1991), "RaoBlackwellized" estimates of posterior means and variances of the Oj3 are given by...
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