Local linear estimation for ergodic data under random censorship model in high dimensional statistics
by Rachida Rouane   Somia Ayad   Ali Laksaci   Saâdia Rahmani  

Vol. 18 No. 1 (2023) P.15~P.39

DOI:	https://doi.org/10.21915/BIMAS.2023102
	10.21915/BIMAS.2023102

ABSTRACT

This paper addresses the problem of estimating the conditional density function of a randomly censored scalar response variable given a functional random variable. Furthermore, we suppose that the data are sampled from stationary ergodic process. We introduce a local linear type estimator of the conditional density function. Under less restrictive assumptions closely related to the concentration of the probability of small balls of the underlying covariate we state the almost complete convergence with explicit rates as well as the asymptotic normality of the constructed estimator. As a direct application, the same properties are established for the conditional mode function.

KEYWORDS
Ergodic data, functional covariate, censored data, local linear fitting, conditional density, conditional mode nonparametric estimation, asymptotic properties

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 62G05, 62G08, 62G20, 62G35, 62H12

MILESTONES

Received: 2022-06-19
Revised :
Accepted:

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