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

Summary/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.

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