Annals of Mathematical Sciences and Applications

Volume 3 (2018)

Number 2

A unified Monte-Carlo jackknife for small area estimation after model selection

Pages: 405 – 438



Jiming Jiang (Department of Statistics, University of California at Davis)

P. Lahiri (Joint Program in Survey Methodology, University of Maryland, College Park, Md., U.S.A.)

Thuan Nguyen (School of Public Health, Oregon Health & Science University, Portland, Or., U.S.A.)


We consider estimation of measure of uncertainty in small area estimation (SAE) when a procedure of model selection is involved prior to the estimation. A unified Monte-Carlo jackknife method, called McJack, is proposed for estimating the logarithm of the mean squared prediction error. We prove the second-order unbiasedness of McJack, and demonstrate the performance of McJack in assessing uncertainty in SAE after model selection through empirical investigations that include simulation studies and real-data analyses.


Computer intensive, jackknife, log-MSPE, measure of uncertainty, model selection, Monte-Carlo, second-order unbiasedness, small area estimation

The research of Jiming Jiang, Partha Lahiri, and Thuan Nguyen are partially supported by the NSF grants SES-1121794, SES-1534413 and SES-1118469, respectively. The research of Jiming Jiang and Thuan Nguyen are partially supported by the NIH grant R01-GM085205A1.

Received 16 February 2016

Published 9 August 2018