Electronic Journal of Statistics

A difference based approach to the semiparametric partial linear model

Lie Wang, Lawrence D. Brown, and T. Tony Cai

Full-text: Open access

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.

Article information

Source
Electron. J. Statist., Volume 5 (2011), 619-641.

Dates
First available in Project Euclid: 27 June 2011

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1309180102

Digital Object Identifier
doi:10.1214/11-EJS621

Mathematical Reviews number (MathSciNet)
MR2813557

Zentralblatt MATH identifier
1329.62179

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Asymptotic efficiency difference-based method kernel method wavelet thresholding method partial linear model semiparametric model

Citation

Wang, Lie; Brown, Lawrence D.; Cai, T. Tony. A difference based approach to the semiparametric partial linear model. Electron. J. Statist. 5 (2011), 619--641. doi:10.1214/11-EJS621. https://projecteuclid.org/euclid.ejs/1309180102


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