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Asymptotic normality of conditional density estimation in the single index model for functional time series data

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  • Ling, Nengxiang
  • Xu, Qian

Abstract

In this paper, we investigate the estimation of conditional density function based on the single-index model for functional time series data. The asymptotic normality of the conditional density estimator and the conditional mode estimator for the α mixing dependence functional time series data are obtained, respectively. Furthermore, as applications, the asymptotic (1-ζ) confidence interval of the conditional density function and the conditional mode are also presented for 0<ζ<1.

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  • Ling, Nengxiang & Xu, Qian, 2012. "Asymptotic normality of conditional density estimation in the single index model for functional time series data," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2235-2243.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:12:p:2235-2243
    DOI: 10.1016/j.spl.2012.08.018
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    References listed on IDEAS

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    Cited by:

    1. Akkal Fatima & Kadiri Nadia & Rabhi Abbes, 2021. "Asymptotic Normality of Conditional Density and Conditional Mode in the Functional Single Index Model," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 25(1), pages 1-24, March.
    2. Nengxiang Ling & Lilei Cheng & Philippe Vieu & Hui Ding, 2022. "Missing responses at random in functional single index model for time series data," Statistical Papers, Springer, vol. 63(2), pages 665-692, April.

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