View Submission - EcoSta2018

A0557
**Title: **Semi-parametric estimation of single-index models in modal regression
**Authors: **Hirofumi Ohta - The University of Tokyo (Japan) **[presenting]**

**Abstract: **Semi-parametric estimation methods in modal regression, especially for single index models, are considered. The modal regression estimates the conditional mode of the distribution of a continuous random variable Y given a continuous randon vector X in the usual regression sense. Since conditional modes are defined as maximizers of conditional densities, non-parametric density estimation should be needed, then it occurs ``the curse of dimensionality.'' To relax this effect, we propose a semi-parametric estimation procedures for single index models, which are familiar with dimensionality reduction methods. Particularly for weighted average derivatives of single index models, We construct the estimator based on sample-splitting/cross-fitting techniques. In estimating low-dimensional parameters of interest, these approaches is expected to reduce own-estimating bias from estimating highly complex nuisance parameters in full sample. We also derive some asymptotic results of the estimator and valid inference procedures based on sample-splitting/cross-fitting.