Journal
JOURNAL OF THE KOREAN STATISTICAL SOCIETY
Volume 49, Issue 4, Pages 1214-1237Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s42952-020-00052-x
Keywords
Robust estimation; Huber; Exponential squared loss; Partial functional linear models; B splines
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Funding
- National Natural Science Foundation of China [11971001]
- Beijing Natural Science Foundation [1182002]
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In this article, we consider a new robust estimation procedure for the partial functional linear model (PFLM) with the slope function approximated by spline basis functions. This robust estimation procedure applies a modified Huber's function with tail function replaced by the exponential squared loss (ESL) to achieve robustness against outliers. A data-driven procedure is presented for selecting the tuning parameters of the new estimation method, which enables us to reach better robustness and efficiency than other methods in the presence of outliers or non-normal errors. We construct robust estimators of both parametric coefficients and function coefficient in the PFLM. Moreover, some asymptotic properties of the resulting estimators are established. The finite sample performance of our proposed method is studied through simulations and illustrated with a data example.
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