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Shrinkage estimation analysis of correlated binary data with a diverging number of parameters

Science China Mathematics 2013年第2期56卷 359-377页

作者： XU PeiRong FU WenJiang ZHU LiXing School of Finance and Statistics East China Normal University Department of Epidemiology and Biostatistics Michigan State University Department of Mathematics Hong Kong Baptist University

For analyzing correlated binary data with high-dimensional covariates,we,in this paper,propose a two-stage shrinkage ***,we construct a weighted least-squares(WLS) type function using a special weighting scheme on the non-conservative vector field of the generalized estimating equations(GEE) ***,we define a penalized WLS in the spirit of the adaptive LASSO for simultaneous variable selection and parameter *** proposed procedure enjoys the oracle properties in high-dimensional framework where the number of parameters grows to infinity with the number of ***,we prove the consistency of the sandwich formula of the covariance matrix even when the working correlation matrix is *** the selection of tuning parameter,we develop a consistent penalized quadratic form(PQF) function *** performance of the proposed method is assessed through a comparison with the existing methods and through an application to a crossover trial in a pain relief study.

关键词： correlated binary data variable selection diverging number of parameters adaptive LASSO GEE oracle properties sandwich covariance formula penalized quadratic form function

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Penalized profile least squares-based statistical inference for varying coefficient partially linear errors-in-variables models

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Science China Mathematics 2018年第9期61卷 1677-1694页

作者： Guo-liang Fan Han-ying Liang Li-xing Zhu Institute of Statistics and Big Data Renmin University of China School of Mathematics and Physics Anhui Polytechnic University School of Mathematical Science Tongji University Department of Mathematics Hong Kong Baptist University School of Statistics Beijing Normal University

The purpose of this paper is two fold. First, we investigate estimation for varying coefficient partially linear models in which covariates in the nonparametric part are measured with errors. As there would be some spurious covariates in the linear part, a penalized profile least squares estimation is suggested with the assistance from smoothly clipped absolute deviation penalty. However, the estimator is often biased due to the existence of measurement errors, a bias correction is proposed such that the estimation consistency with the oracle property is proved. Second, based on the estimator, a test statistic is constructed to check a linear hypothesis of the parameters and its asymptotic properties are studied. We prove that the existence of measurement errors causes intractability of the limiting null distribution that requires a Monte Carlo approximation and the absence of the errors can lead to a chi-square limit. Furthermore, confidence regions of the parameter of interest can also be constructed. Simulation studies and a real data example are conducted to examine the performance of our estimators and test statistic.

关键词： diverging number of parameters varying coefficient partially linear model penalized likelihood SCAD variable selection

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