Local linear estimation of conditional cumulative distribution function in the functional data: uniform consistency with convergence rates. (English) Zbl 07478642

Hebchi, Chaima; Chouaf, Abdelhak

Kybernetika 57, No. 5, 819-839 (2021).

The paper under review deals with estimation of conditional cumulative distribution function of a scalar response variable given a random variable taking values in a semi-metric space. The paper is organized as follows. In introductory Section 1, the authors discuss published results pertinent to the studied topic. In Section 2 they detail the considered model. The main result (namely, the uniform almost complete consistency of the considered estimator) is stated in Section 4, while assumptions for establishing it are given in Section 3. In Section 5, the result is applied to derivation of asymptotic properties of the local linear estimator of the conditional functional quantile. Simulation study is conducted in Section 6.

Reviewer: Joseph Melamed (Los Angeles)

MSC:

62G08	Nonparametric regression and quantile regression
62G20	Asymptotic properties of nonparametric inference

Keywords:

functional data; local linear estimator; conditional cumulative; conditional quantile; nonparametric regression; small balls probability