Functional lasso kernel smoothing for additive regression with interaction effects

초록

This paper proposes a nonparametric additive regression technique that can be used to analyze the interaction effects as well as the individual effects of the covariates. A powerful method of estimating the component functions that represent the individual and interaction effects is introduced and studied in a high-dimensional regime that allows the number of covariates to be much larger than the sample size. Asymptotic L2 error bounds are derived for the estimators under mild technical conditions in sparse settings where the number of nonzero components is smaller than the sample size but is allowed to increase to infinity as the sample size grows. The L2 error bounds reduce to the rate that can be achieved in bivariate smoothing, up to a logarithmic factor, when the number of significant effects is bounded. Numerical evidences are also provided via some simulation studies and a real data example.

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