This paper presents the estimator of the conditional density function of surrogated scalar response variable given a functional random one. We construct a conditional density function by using the available (true) response data and the surrogate data. Then, we build up some asymptotic properties...

We prove the strong consistency, uniformly in the bandwidth, of the smooth varying coefficient conditional least squares estimator. Our results justify data-driven choices of bandwidths, such as Silverman's rule-of thumb, or standard cross-validation, that are usually implemented by most...

In this paper we investigate the kernel estimator of the density for a stationary reversible Markov chain. The proofs are based on a new central limit theorem for a triangular array of reversible Markov chains obtained under conditions imposed to covariances, which has interest in itself.

The main purpose is to estimate the regression function of a real random variable with functional explanatory variable by using a recursive nonparametric kernel approach. The mean square error and the almost sure convergence of a family of recursive kernel estimates of the regression function...

Simple kernel-type estimators of integrals of general powers of general derivatives of probability densities are proposed. They are based on two simple properties, and in many circumstances enjoy optimal convergence rate.