Conditional mode regression: Application to functional time series prediction

TL;DR

This paper develops a method for estimating the conditional mode of a response variable given a predictor in semi-metric spaces, with applications to functional time series prediction and convergence rate analysis.

Contribution

It introduces a new estimator for the conditional mode in semi-metric spaces and establishes its convergence rate, specifically tailored for functional time series prediction.

Findings

Provides a convergence rate in $L^p$ norm for the estimator.

Demonstrates application to functional time series prediction.

Addresses estimation under $\alpha$-mixing conditions.

Abstract

We consider $\alpha$-mixing observations and deal with the estimation of the conditional mode of a scalar response variable $Y$ given a random variable $X$ taking values in a semi-metric space. We provide a convergence rate in $L^p$ norm of the estimator. A useful and typical application to functional times series prediction is given.