# Dissertation/Thesis Abstract

Hierarchical Bayesian Model for AK Composite Estimators in the Current Population Survey (CPS)
by Li, Yuan, Ph.D., The George Washington University, 2018, 137; 10748002
Abstract (Summary)

The Current Population Survey (CPS) is a multistage probability sample survey conducted by the U.S. Census Bureau and the Bureau of Labor Statistics (BLS). The 4-8-4 rotation design is applied to produce overlap in the sample across months. Several weighting steps are used to adjust the ultimate sample in each month to be representative of the population. In order to produce efficient estimates of labor force levels and month-to-month change, the so-called AK composite estimator combines current estimates from eight rotation panels and the previous month’s estimates to estimate current values. Values of coefficients A and K are chosen every decade or so for the nation. The Successive Difference Replicate (SDR) method and Balanced Repeated Replication (BRR) method are currently used by the CPS for estimating the variance of the AK Composite Estimates.

Instead of using constant CPS (A, K) values for AK Composite Estimator over time, one could find the monthly optimal coefficients ( A, K) that minimize the variance for measuring the monthly level of unemployment in the target population. The CPS (A, K) values are stable over time but can produce larger variance in some months, while the monthly optimal (A, K) values have lower variance within a month but high variability across months.

In order to make a compromise between the CPS (A, K) values and monthly optimal (A, K), a Hierarchical Bayesian method is proposed through modeling the obtained monthly optimal ( A, K)’s using a bivariate normal distribution. The parameters, including the mean vector and the variance-covariance matrix, are unknown in this distribution. In such case, a first step towards a more general model is to assume a conjugate prior distribution for the bivariate normal model. Computing the conditional posterior distribution can be approximated through simulation. In particular, it can be achieved by the Gibbs sampling algorithm with its sequential sampling. As the key to the success of this Hierarchical Bayesian method is that approximated distributions are improved as iteration goes on in the simulation, one needs to check the convergence of the simulated sequences. Then, the sample mean after a number of iterations in the simulation will serve as the Hierarchical Bayesian (HB) (A, K). The HB (A, K) estimates in effect produce a shrinkage between the CPS (A, K) values and the monthly optimal (A, K) values. The shrinkage of the estimates of the coefficients ( A, K) occurs by manipulating the certain hyperparameter in the model.

In this dissertation, detailed comparisons are made among the three estimators. The AK Estimator using the CPS (A, K) values, using the monthly optimal (A, K) values, and using the Hierarchical Bayesian (A,K) values are compared in terms of estimates produced, estimated variance, and estimated coefficients of variation. In each month of the data set, separate estimates using the three methods are produced.

In order to assess the performance of the proposed methods, a simulation study is implemented and summarized. In the CPS, eight rotating survey panels contribute to the overall estimate in each month. Each panel is measured in a month at one of its month-in- sample. The month-in- sample range from one to eight. In the simulation, month-in- sample values are generated as if replicate panels were available for estimation. These month-in-sample values are used as the original monthly panel estimates of unemployment to produce CPS-style (A, K) estimates, AK-estimates using monthly optimal ( A, K) values, and AK-estimates using Hierarchical Bayesian ( A, K) values. Performance of each method is evaluated on the simulated data by examining several criteria including bias, variance, and mean squared error.

Indexing (document details)
 Advisor: Hu, Feifang, Larsen, Michael D. Commitee: Bose, Sudip, Cheng, Yang, Hu, Feifang, Kundu, Subrata, Larsen, Michael D., Nayak, Tapan K. School: The George Washington University Department: Statistics School Location: United States -- District of Columbia Source: DAI-B 79/08(E), Dissertation Abstracts International Source Type: DISSERTATION Subjects: Statistics Keywords: AK composite estimator, Current Population Survey, Gibbs sampler, Hierarchical Bayesian model, Unemployment Publication Number: 10748002 ISBN: 978-0-355-83022-4