Some asymptotic results of the estimators for conditional mode for functional data in the single index model missing data at random

• Authors: Souad Mekkaoui , Nadia Kadiri , Abbes Rabhi

Abstracts

EN

In this work, we consider the problem of non-parametric estimation of a regression function, namely the conditional density and the conditional mode in a single functional index model (SFIM) with randomly missing data. The main result of this work is the establishment of the asymptotic properties of the estimator, such as almost complete convergence rates. Moreover, the asymptotic normality of the constructs is obtained under certain mild conditions. We finally discuss how to apply our result to construct confidence intervals.

Keywords

EN

functional data analysis; functional single-index process; kernel estimator; missing at random; non-parametric estimation; small ball probability

• Publisher: Główny Urząd Statystyczny
• Journal: Przegląd Statystyczny
• Year: 2023
• Volume: 70
• Issue: 2
• Pages: 20-45

Dates

published

2023

Contributors

author

Souad Mekkaoui

• Djillali LIABES University of Sidi Bel Abbes, Laboratory of Mathematics, Algeria

• https://orcid.org/0009000586113333

author

Nadia Kadiri

• Djillali LIABES University of Sidi Bel Abbes, Higher School of Economics of Oran 22000, Sidi Bel Abbes, Algeria

• https://orcid.org/0000000234057414

author

Abbes Rabhi

• Djillali LIABES University of Sidi Bel Abbes, Laboratory of Mathematics, Algeria

• https://orcid.org/0000000167400226

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Identifiers

DOI

10.59139/ps.2023.02.2

Biblioteka Nauki

31340028