Asymptotic Properties of the Semi-Parametric Estimators of the Conditional Density for Functional Data in the Single Index Modelwith Missing Data at Random

Statistica

Sanaà DounyaMekki¹  Abbes Rabhi²  Nadia Kadiri² 

[1] University center Salhi Ahmed of Naâma;University of Sidi Bel Abbes;

关键词: ergodic processes;    functional data analysis;    functional single-index process;    missing at random;    small ball probability;   

DOI  :  10.6092/issn.1973-2201/10472

来源: DOAJ

【 摘 要 】

The main objective of this work is to estimate, semi-parametrically, the mode of a conditional density when the response is a real valued random variable subject to censored phenomenon and the predictor takes values in a semi-metric space. We assume that the explanatory and the response variables are linked through a single-index structure. First, we introduce a type of kernel estimator of the conditional density function when the data are supposed to be selected from an underlying stationary and ergodic process with missing at random (MAR). Under some general conditions, both the uniform almost-complete consistencies with convergence rates of the model are established. Further, the asymptotic normality of the considered model is given. As an application, the asymptotic (1−α) confidence interval of the conditional density function and the conditional mode are also presented for 0 < α < 1.

【 授权许可】

Unknown