Asymptotic normality of a nonparametric estimator of the conditional mode function for functional data

We consider the estimation of the conditional mode function when the covariables take values in some abstract function space. It is shown that, under some regularity conditions, the kernel estimate of the conditional mode is asymptotically normally distributed. From this, we derive the asymptotic normality of a predictor and propose confidence bands for the conditional mode function. Simulations are drawn to show how our methodology can be implemented. We consider the estimation of the conditional mode function when the covariables take values in some abstract function space. It is shown that, under some regularity conditions, the kernel estimate of the conditional mode is asymptotically normally distributed. From this, we derive the asymptotic normality of a predictor and propose confidence bands for the conditional mode function. Simulations are drawn to show how our methodology can be implemented.