Hierarchical Bayesian Model for Small Area Estimation of Poisson Means

다국어 초록 (Multilingual Abstract)

Small area estimation is a statistical method to estimate the parameters of sub- populations having small sample sizes. Hierarchical Bayesian approach has been (relatively) recently proposed for small area estimation problems. The Poisson-gamma model is usually used to formulate a dataset consisting of counts. This study investigates the hierarchical Bayes estimators comparing the empirical Bayes estimators of mean rates for the small areas. We explain the suggested method through a practical dataset. We also implement the statistical computations via R2WINBUGS to compare the estimates and their mean squared errors in a Monte Carlo study.

참고문헌 (Reference)

1 이우주, "생명보험의 보험계약대출 수요에 대한 통계적 예측" 한국통계학회 17 (17): 697-712, 2010

2 Dempster, A. P, "The Analysis of Census Undercount from a Post-enumeration Study" 88-94, 1980

3 Ghosh, M, "Small Area Estimation: An Appraisal" 9 : 55-76, 1994

4 Rao,J.N.K, "Small Area Estimation" Wiley 2003

5 Lord,D, "Modeling Motor Vehicle Crashes Using Poisson-Gamma Models: Examining the Effects of Low Sample Mean Values and Small Sample Size on the Estimation of the Fixed Dispersion Parameter" 38 : 751-766, 2006

6 Stern, H. S, "Inference about Batter-pitcher Matchups in Baseball from Small Samples, In Statistical Thinking in Sports" Chapman & Hall 153-165, 2007

7 Christiansen, C, "Hierarchical Poisson Regression Models" 92 : 618-632, 1997

8 Datta, G. S., "Hierarchical Bayes estimation of unemployment rate for the states of the U.S" 94 (94): 1074-1082, 1999

9 Fay, R. E, "Estimates of Income for Small Places: An Application of James- Stein Procedures to Census Data" 74 : 269-277, 1979

10 정광모, "Dispersion Parameter of Poisson-Gamma Model in the Small Area Estimation" 한국자료분석학회 11 (11): 23-32, 2009

11 Steffey, D, "Comment on Robinson, G. K., "That BLUP is a Good Thing: The Estimation of Random Effects,"" 6 : 45-47, 1991

12 Kim,H.J, "Bayesian Estimation of the Ratio of Two Means Using Dirichlet Process Prior" 3 : 387-395, 2001

13 Nandram, B., "Bayesian Analysis and Mapping of Mortality Rates for Chronic Obstructive Pulmonary Disease" 95 : 1110-1118, 2000

14 홍연웅, "Bayes Estimation of the Stress-Strength Model Reliability When the Mean Strength Is Greater Than the Mean Stress" 한국자료분석학회 6 (6): 961-969, 2004

15 ChanKeunPark, "Bayes Estimation of Component Steady-State Availability" 한국자료분석학회 5 (5): 33-44, 2003

16 Allenby,G, "An Introduction to Hierachical Bayesian Modeling, Tutorial Notes, Advanced Research Techniques Forum" 1997

17 Australian Bureau of Statistics, "A Guide to Small Area Estimation"

18 Train K., "A Comparison of Hierarchical Bayes and Maximum Simulated Likelihood for Mixed Logit, Working Paper" Department of Economics, University of California 2001