@misc{Akkal_Fatima_Asymptotic_2021,
 author={Akkal, Fatima and Kadiri, Nadia and Rahbi, Abbes},
 identifier={DOI: 10.15611/eada.2021.1.01},
 year={2021},
 rights={Pewne prawa zastrzeżone na rzecz Autorów i Wydawcy},
 publisher={Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu},
 description={Econometrics = Ekonometria, 2021, Vol. 25, No. 1, s. 1-24},
 language={eng},
 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 singleindex 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 < ζ < 1. A simulation study is also presented to illustrate the validity and finite sample performance of the considered estimator. Finally, the estimation of the functional index via the pseudo-maximum likelihood method is discussed},
 type={artykuł},
 title={Asymptotic normality of conditional density and conditional mode in the functional single index model},
 keywords={asymptotic normality, conditional density, functional single index model, functional random variable, nonparametric estimation, asymptotyczna normalność, gęstość warunkowa, funkcjonalny model pojedynczego wskaźnika, funkcjonalna zmienna losowa, estymacja nieparametryczna},
}