Asymptotic Normality of Conditional Density and Conditional Mode in the Functional Single Index Model

Akkal Fatima (), Kadiri Nadia () and Rabhi Abbes ()
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Akkal Fatima: Statistics Laboratory Stochastic Processes, University Djillali LIABES of Sidi Bel Abbes, Sidi Bel Abbes, Algeria
Kadiri Nadia: University Djillali LIABES of Sidi Bel Abbes, Sidi Bel Abbes, Algeria
Rabhi Abbes: University Djillali LIABES of Sidi Bel Abbes, Sidi Bel Abbes, Algeria

Econometrics. Advances in Applied Data Analysis, 2021, vol. 25, issue 1, 1-24

Abstract: The main objective of this paper is to investigate the nonparametric estimation of the conditional density of a scalar response variable Y, given the explanatory variable X taking value in a Hilbert space when the sample of observations is considered as an independent random variables with identical distribution (i.i.d) and are linked with a single functional index structure. First of all, a kernel type estimator for the conditional density function (cond-df) is introduced. Afterwards, the asymptotic properties are stated for a conditional density estimator when the observations are linked with a single-index structure from which one derives a central limit theorem (CLT) of the conditional density estimator to show the asymptotic normality of the kernel estimate of this model. As an application the conditional mode in functional single-index model is presented, and the asymptotic (1 – ζ) confidence interval of the conditional mode function is given for 0

Keywords: asymptotic normality; conditional density; functional single index model; functional random variable; nonparametric estimation (search for similar items in EconPapers)
JEL-codes: C13 C14 C15 (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:eaiada:v:25:y:2021:i:1:p:1-24:n:4

DOI: 10.15611/eada.2021.1.01

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