Asymptotic normality of the local linear estimation of the conditional density for functional time-series data. Issue 14 (18th July 2018)

• Record Type: Journal Article
• Authors: Xiong, Xianzhu; Zhou, Peiqin; Ailian, Chen
• Is Part Of: Communications in statistics. Volume 47:Issue 14(2018)
• Page Start: 3418
• Page End: 3440
• Publication Date: 2018-07-18
• Subjects: α-mixing dependence -- Conditional density -- Functional data -- Joint asymptotic normality -- Local linear estimator; 62G05 -- 62G20; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2017.1359292
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: This article focuses on the conditional density of a scalar response variable given a random variable taking values in a semimetric space. The local linear estimators of the conditional density and its derivative are considered. It is assumed that the observations form a stationary α-mixing sequence. Under some regularity conditions, the joint asymptotic normality of the estimators of the conditional density and its derivative is established. The result confirms the prospect in Rachdi et al. (2014 ) and can be applied in time-series analysis to make predictions and build confidence intervals. The finite-sample behavior of the estimator is investigated by simulations as well.