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

Souad Mekkaoui; Nadia Kadiri; Abbes Rabhi

doi:https://doi.org/10.59139/ps.2023.02.2

Souad Mekkaoui Djillali LIABES University of Sidi Bel Abbes, Laboratory of Mathematics, Algeria ORCID:https://orcid.org/0009-0005-8611-3333 , Nadia Kadiri Djillali LIABES University of Sidi Bel Abbes, Higher School of Economics of Oran 22000, Sidi Bel Abbes, Algeria ORCID:https://orcid.org/0000-0002-3405-7414 , Abbes Rabhi Djillali LIABES University of Sidi Bel Abbes, Laboratory of Mathematics, Algeria ORCID:https://orcid.org/0000-0001-6740-0226 Przegląd Statystyczny. Statistical Review, vol. 70, 2023, 2, pages: 20-45 Published online: 30 November 2023 DOI https://doi.org/10.59139/ps.2023.02.2 Citation: Mekkaoui, S., Kadiri, N., & Rabhi, A. (2023). Some asymptotic results of the estimators for conditional mode for functional data in the single index model missing data at random. Przegląd Statystyczny. Statistical Review, 70(2), 20–45. https://doi.org/10.59139/ps.2023.02.2.

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ARTICLE

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ABSTRACT

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

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

JEL

C10, C13, C14, C19, C24

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