Regression model for surrogate data in high dimensional statistics

Abstract

This paper deals with the problem of estimating the regression of a surrogated scalar response variable given a functional random one. We construct an estimator of the regression operator by using, in addition to the available (true) response data, a surrogate data. We then establish some asymptotic properties of the constructed estimator in terms of the almost-complete and the quadratic mean convergences. Notice that the obtained results generalize a part of the results obtained in the finite dimensional framework. Finally, an illustration on the applicability of our results on both simulated data and a real dataset was realized. We have thus shown the superiority of our estimator on classical estimators when we are lacking complete data.

KEYWORDS AND PHRASES:

• Functional data analysis (FDA)
• small ball probability
• surrogate data
• mean square convergence
• almost-complete convergence
• regression estimation
• classical kernel estimator
• k nearest neighbors (kNN)

AMS CLASSIFICATION:

• 62G05
• 62G08
• 62G20
• 62G35
• 62G07
• 62G32
• 62G30
• Secondary 62E20