Asymptotic Normality of Single Functional Index Quantile Regression for Functional Data with Missing Data at Random - Allal, Anis; Kadiri, Nadia; Rabhi, Abbes (Asymptotyczna normalność w regresji kwantylowej pojedynczego wskaźnika funkcyjnego dla danych funkcjonalnych z losowymi brakującymi danymi, 2024)
This work addresses the problem of the nonparametric estimation of the regression function, namely the conditional distribution and the conditional quantile in the single functional index model (SFIM) under the independent and identically distributed condition with randomly missing data. The main result of this study was the establishment of the asymptotic properties of the estimator, such as the almost complete convergence rates. Moreover, the asymptotic normality of the constructs was obtained under certain mild conditions. Lastly, the authors discussed how to apply the result to construct confidence intervals.
Econometrics = Ekonometria, 2024, Vol. 28, No. 1, s. 26-38
Keywords: asymptotic normality; functional data analysis; functional single index process; missing at random; nonparametric estimation; small ball probability; asymptotyczna normalność; funkcjonalna analiza danych; funkcjonalny proces pojedynczego indeksu; estymator jądra; losowe braki; estymacja nieparametryczna; prawdopodobieństwo małej kuli