Journal
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
Volume 45, Issue 21, Pages 6436-6446Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/03610926.2014.921309
Keywords
B-spline; M-setimator; Partially functional linear regression
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Funding
- National Nature Science Foundation of China [11171293, 11225103, 11301464]
- Key Fund of Yunnan Province [2010CC003]
- Scientific Research Foundation of Yunnan Provincial Department of Education [2013Y360]
- National Natural Science Foundation of China [11501018, 11571340]
- Beijing University of Technology [006000514116003]
- Foundation of Academic Discipline Program at Central University of Finance and Economics
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M-estimation is a widely used technique for robust statistical inference. In this paper, we study robust partially functional linear regression model in which a scale response variable is explained by a function-valued variable and a finite number of real-valued variables. For the estimation of the regression parameters, which include the infinite dimensional function as well as the slope parameters for the real-valued variables, we use polynomial splines to approximate the slop parameter. The estimation procedure is easy to implement, and it is resistant to heavy-tailederrors or outliers in the response. The asymptotic properties of the proposed estimators are established. Finally, we assess the finite sample performance of the proposed method by Monte Carlo simulation studies.
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