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August 2010 Fractals with point impact in functional linear regression
Ian W. McKeague, Bodhisattva Sen
Ann. Statist. 38(4): 2559-2586 (August 2010). DOI: 10.1214/10-AOS791


This paper develops a point impact linear regression model in which the trajectory of a continuous stochastic process, when evaluated at a sensitive time point, is associated with a scalar response. The proposed model complements and is more interpretable than the functional linear regression approach that has become popular in recent years. The trajectories are assumed to have fractal (self-similar) properties in common with a fractional Brownian motion with an unknown Hurst exponent. Bootstrap confidence intervals based on the least-squares estimator of the sensitive time point are developed. Misspecification of the point impact model by a functional linear model is also investigated. Non-Gaussian limit distributions and rates of convergence determined by the Hurst exponent play an important role.


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Ian W. McKeague. Bodhisattva Sen. "Fractals with point impact in functional linear regression." Ann. Statist. 38 (4) 2559 - 2586, August 2010.


Published: August 2010
First available in Project Euclid: 11 July 2010

zbMATH: 1196.62116
MathSciNet: MR2676898
Digital Object Identifier: 10.1214/10-AOS791

Primary: 62E20 , 62G08 , 62M09
Secondary: 60J65

Keywords: Bootstrap methods , Empirical processes , fractional Brownian motion , Functional linear regression , M-estimation , misspecification , Nonstandard asymptotics

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 4 • August 2010
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