A difference based approach to the semiparametric partial linear model
Name
Wang - semiparametric.pdf
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256.89 KB
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Adobe PDF
Checksum (MD5)
7fa56f5cab4ee8e5c742ef5104a85066
Author(s)
Wang, Lie
Brown, Lawrence D.
Cai, T. Tony
Date Issued
2011
Journal
Electronic Journal of Statistics
Publisher
Institute of Mathematical Statistics
Citation
Wang, Lie, Lawrence D. Brown, and T. Tony Cai. “A difference based approach to the semiparametric partial linear model.” Electronic Journal of Statistics 5, no. 0 (2011): 619-641.
Version
Author's final manuscript
Abstract
A commonly used semiparametric partial linear model is considered. We propose analyzing this model using a difference based approach. The procedure estimates the linear component based on the differences of the observations and then estimates the nonparametric component by either a kernel or a wavelet thresholding method using the residuals of the linear fit. It is shown that both the estimator of the linear component and the estimator of the nonparametric component asymptotically perform as well as if the other component were known. The estimator of the linear component is asymptotically efficient and the estimator of the nonparametric component is asymptotically rate optimal. A test for linear combinations of the regression coefficients of the linear component is also developed. Both the estimation and the testing procedures are easily implementable. Numerical performance of the procedure is studied using both simulated and real data. In particular, we demonstrate our method in an analysis of an attitude data set.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1214/11-ejs621
