Time：2021/1/7日  9:00

Form：Tencent Meeting

Topic：Maximum sampled conditional likelihood estimation for informative  subsample

Abstract:

Subsampling is an effective approach to extract useful information from massive data sets when computing resources are limited. Existing investigations focus on developing better sampling procedures and deriving probabilities with higher estimation efficiency. After a subsample is taken from the full data, most available methods use an inverse probability weighted target function to define the estimator. This type of weighted estimator reduces the contributions of more informative data points, and thus it does not fully utilize information in the selected subsample. This paper focuses on parameter estimation with selected subsample, and proposes to use the maximum sampled conditional likelihood estimator (MSCLE) based on the sampled data. We established the asymptotic normality of the MSCLE, and prove that its variance covariance matrix reaches the lower bound of asymptotically unbiased estimators. Specifically, the MSCLE has a higher estimation efficiency than the weighted estimator. We further discuss the asymptotic results with the L-optimal subsampling probabilities, and illustrate the estimation procedure with generalized linear models. Numerical experiments are provided to evaluate the practical performance of the proposed method.

Resume:

HaiYing Wang is an Assistant Professor in the Department of Statistics at the University of Connecticut. He was an Assistant Professor in the Department of Mathematics and Statistics at the University of New Hampshire from 2013 to 2017. He obtained his Ph.D. from the Department of Statistics at the University of Missouri in 2013, and his M.S. from the Academy of Mathematics and Systems Science, Chinese Academy of Sciences in 2006. His research interests include informative subdata selection for big data, model selection, model averaging, measurement error models, and semi-parametric regression.