A Sumca Approach to Measures of Uncertainty for Complex Inference in Surveys
报告人： 蒋继明(University of California，Davis and 江西财经大学)
时间：2019-07-30 10:00 - 11:00
地点：北大理科一号楼1513
Abstract:
We propose a simple, unified, Monte-Carlo assisted (Sumca)
approach to second-order unbiased estimation of mean squared
prediction error (MSPE) of a small area predictor. The proposed
MSPE estimator is easy to derive, has a simple expression, and
applies to a broad range of predictors that include the traditional
empirical best linear unbiased predictor (EBLUP), empirical best
predictor (EBP), and post model selection EBLUP and EBP as
special cases. Furthermore, the leading term of the proposed MSPE
estimator is guaranteed positive; the lower-order term corresponds
to a bias correction, which can be evaluated via a Monte-Carlo
method. The computational burden for the Monte-Carlo evaluation
is much lesser, compared to other Monte-Carlo based methods that
have been used for producing second-order unbiased MSPE
estimators, such as double bootstrap and Monte-Carlo jackknife.
The Sumca estimator also has a nice stability feature. Theoretical
and empirical results demonstrate properties and advantages of the
Sumca estimator.
About the Speaker:
蒋继明，毕业于世界顶级名校University of California的Berkeley分校，师从数理统计学领域的世界权威P.J. Bickel教授，在University of California的Davis有过近20年的工作经历，是美国统计协会(ASA) 和国际统计协会(IMS)的Fellow。候选人成果丰富，深得同行认可，长期担任Annals of Statistics、Journal of American Statistical Association等著名统计学杂志的副主编，曾获得过美国统计协会的Outstanding Statistical Application奖。其所从事的混合效应模型、广义线性模型、纵向数据分析、模型选择、大数据分析是当前数理统计学方向的前沿领域。其著有5本专著，包括《统计学中的大样本技巧》（2010年斯普林格出版社）。
