Asymptotic Normality of Single Functional Index Quantile Regression for Functional Data with Missing Data at Random

• Authors: Anis Allal , Nadia Kadiri , Abbes Rabhi

Title variants

PL

Asymptotyczna normalność regresji kwantylowej pojedynczego wskaźnika funkcyjnego dla danych funkcjonalnych z losowymi brakującymi danymi

Abstracts

PL

W artykule autorzy prowadzą rozważania dotyczące problemu nieparametrycznej estymacji funkcji regresji, a mianowicie rozkładu warunkowego i kwantyla warunkowego w modelu pojedynczego indeksu funkcjonalnego (SFIM) przy założeniu niezależnych i z identycznym rozkładem danych z losowymi brakami danych. Głównym rezultatem przeprowadzonych badań było ustalenie asymptotycznych właściwości estymatora, takich jak prawie całkowite współczynniki zbieżności. Co więcej, asymptotyczną normalność konstruktów uzyskano dla pewnych łagodnych warunków. Na koniec omówiono, jak zastosować uzyskany wynik do skonstruowania przedziałów ufności.

EN

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.

Keywords

EN

asymptotic normality; functional data analysis; functional single-index process; missing at random; nonparametric estimation; small ball probability

PL

asymptotyczna normalność; funkcjonalna analiza danych; funkcjonalny proces poje- dynczego indeksu; estymator jądra; losowe braki; estymacja nieparametryczna; prawdopodobieństwo małej kuli

• Publisher: Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
• Journal: Econometrics. Ekonometria. Advances in Applied Data Analytics
• Year: 2024
• Volume: 28
• Issue: 1
• Pages: 26-38

Dates

published

2024

Contributors

author

Anis Allal

• University Djillali LIABES of Sidi Bel Abbes, Algeria

• https://orcid.org/0000000215538132

author

Nadia Kadiri

• University Djillali LIABES of Sidi Bel Abbes, Algeria

• https://orcid.org/0000000234057414

author

Abbes Rabhi

• University Djillali LIABES of Sidi Bel Abbes, Algeria

• https://orcid.org/0000000167400226

References

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Identifiers

DOI

10.15611/eada.2024.1.03

Biblioteka Nauki

31233546