A non-parametric estimation of the conditional quantile for truncated and functional data

Abstract

In this paper, we propose a local linear estimator for the conditional distribution function in the case where the real response variable is subject to left-truncation by another random variable (r.v.) and the covariate is of functional type. Under regular assumptions, both of the pointwise and the uniform almost sure convergences, of the proposed estimator, are established. Then, we deduce the uniform almost sure convergence of the obtained conditional quantile estimator. A simulation study is used to illustrate the performance of our estimator with respect to the kernel method.

Local linear estimation of the conditional mode under left truncation for functional regressors

“…So, the feasible estimator f n (y|x) is also given by f n (y|x) = ∂Fn(y|x) ∂y , where F n (y|x) is the local linear estimator of F (y|x). It was introduced by [4] who studied its pointwise and uniform almost sure convergences.…”