Souad Mekkaoui , Nadia Kadiri , Abbes Rabhi

© Souad Mekkaoui, Nadia Kadiri, Abbes Rabhi. Article available under the CC BY-SA 4.0 licence


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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.


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


C10, C13, C14, C19, C24


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