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Asymptotic normality of the local linear estimation of the conditional density for functional time-series data

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  • Xianzhu Xiong
  • Peiqin Zhou
  • Chen Ailian

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.

Suggested Citation

  • Xianzhu Xiong & Peiqin Zhou & Chen Ailian, 2018. "Asymptotic normality of the local linear estimation of the conditional density for functional time-series data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(14), pages 3418-3440, July.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:14:p:3418-3440
    DOI: 10.1080/03610926.2017.1359292
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