Asymptotic normality of conditional density and conditional mode in the functional single index model

Akkal, Fatima; Kadiri, Nadia; Rabhi, Abbes

doi:10.15611/eada.2021.1.01

Cited by 2 publications

(1 citation statement)

References 23 publications

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“…Functional Statistics was published by Ferraty, Laksaci, and Vieu (2006), who obtained some properties in the case i.i.d. The study of statistical models for infinite-dimensional (functional) data has been the subject of several works in recent statistical literature; the reader can consult the studies by Akkal, Kadiri, and Rabhi (2021), Kadiri, Rabhi, Khardani, and Akkal (2021), and references therein. The recent result on nonparametric estimation was obtained by Hamri, Mekki, Rabhi, and Kadiri (2022), who introduced a kernel estimator of the conditional distribution function and proved some asymptotic properties (with rate) in various situations including censored and/or independent variables.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic properties of the estimator of the conditional distribution for associated functional data

Hamri¹,

Dib²,

Rabhi³

2022

Econometrics

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The purpose of the paper was to investigate by the kernel method a nonparametric estimate of the conditional density function of a scalar response variable given a random variable taking values in a separable real Hilbert space when the observations are quasi-associated dependent. Under some general conditions, the authors established the pointwise almost complete consistencies with rates of this estimator. The principal aim is the investigate the convergence rate of the proposed estimator.

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