A Functional Non-Parametric Model for Scalar Response with Bootstrap Confidence Intervals: Some Computational Tools and Applications

Alessandra Durio and Aldo Goia

Abstract

The purpose of this work is to describe some applications of non-parametric regression models where the dependent variable is a curve and the response is scalar (Ramsay and Silverman, 1997). The estimator we will use is a generalization of the classical Nadaraya-Watson regression estimator with a local window. Such a model may be used both for independent and identically distributed data and for dependent observations. These methods may also be used for forecasting of time series where the variable Y is a time series value and X are portions of the same series.

With the aim to find a local confidence interval for the mean of the estimator, that is biased, we will use bootstrap techniques in order to approximate the law of statistic. In particular, adapting the bootstrap techniques (Efron, 1983) for non-parametric regression (see Hall, 1992 and Bowman and Azzalini, 1997) to the case of functional regression, we will find a variability band for regression mean by bootstrapping the residuals.