Non-parametric Estimator for Conditional Mode with Parametric Features*

Abstract

We in this paper propose a new approach for estimating conditional mode non-parametrically to capture the ‘most likely’ effect built on local linear approximation, in which a parametric pilot modal regression is locally adjusted through a kernel smoothing fit to potentially reduce the bias asymptotically without affecting the variance of the estimator. Specifically, we first estimate a parametric modal regression utilizing prior information from initial studies or economic analysis, and then estimate the non-parametric modal function based on the additive correction by eliminating the parametric feature. We derive the asymptotic normal distribution of the proposed modal estimator for both fixed and estimated parametric feature cases, and demonstrate that there is substantial room for bias reduction under certain regularity conditions. We numerically estimate the suggested modal regression model with the use of a modified modal-expectation-maximization (MEM) algorithm. Monte Carlo simulations and one empirical analysis are presented to illustrate the finite sample performance of the developed modal estimator. Several extensions, including multiplicative correction, generalized guidance, modal-based robust regression and the incorporation of categorical covariates, are also discussed for the sake of completeness.