Nonconcave penalized estimation for partially linear models with longitudinal data. Issue 1 (2nd January 2016)

• Record Type: Journal Article
• Authors: Yang, Yiping; Li, Gaorong; Lian, Heng
• Is Part Of: Statistics. Volume 50:Issue 1(2016)
• Page Start: 43
• Page End: 59
• Publication Date: 2016-01-02
• Subjects: partially linear model -- longitudinal data -- variable selection -- smoothing clipped absolute deviation; Primary: 62G05 -- Secondary: 62G20; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2015.1074232
• Languages: English
• ISSNs: 0233-1888

Abstract

Abstract : A nonconcave penalized estimation method is proposed for partially linear models with longitudinal data when the number of parameters diverges with the sample size. The proposed procedure can simultaneously estimate the parameters and select the important variables. Under some regularity conditions, the rate of convergence and asymptotic normality of the resulting estimators are established. In addition, an iterative algorithm is proposed to implement the proposed estimators. To improve efficiency for regression coefficients, the estimation of the covariance function is integrated in the iterative algorithm. Simulation studies are carried out to demonstrate that the proposed method performs well, and a real data example is analysed to illustrate the proposed procedure.