Partially functional linear varying coefficient model. Issue 4 (3rd July 2016)

• Record Type: Journal Article
• Authors: Feng, Sanying; Xue, Liugen
• Is Part Of: Statistics. Volume 50:Issue 4(2016)
• Page Start: 717
• Page End: 732
• Publication Date: 2016-07-03
• Subjects: partially functional linear varying coefficient model -- functional principal components -- convergence rate -- mean squared prediction error -- bootstrap; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2016.1138954
• Languages: English
• ISSNs: 0233-1888

Abstract

Abstract : In this paper, we introduce a new partially functional linear varying coefficient model, where the response is a scalar and some of the covariates are functional. By means of functional principal components analysis and local linear smoothing techniques, we obtain the estimators of coefficient functions of both function-valued variable and real-valued variables. Then the rates of convergence of the proposed estimators and the mean squared prediction error are established under some regularity conditions. Moreover, we develop a hypothesis test for the model and employ the bootstrap procedure to evaluate the null distribution of test statistic and the p -value of the test. At last, we illustrate the finite sample performance of our methods with some simulation studies and a real data application.