Scalar-on-function local linear regression and beyond

Summary It is common to want regress a scalar response on random function. This paper presents results that advocate local linear regression based projection as nonparametric approach this problem. Our asymptotic demonstrate functional outperforms its constant counterpart. Beyond the estimation of operator itself, also useful tool for predicting derivative operator, promising mathematical object in own right. The estimator shown be consistent. For both and derivative, theoretical properties are detailed. On simulated datasets we illustrate good finite-sample proposed methods. real data example single-functional index model, indicate how provides an original, fast widely applicable method.