A Note on the Nonparametric Estimation of the Conditional Mode by Wavelet Methods

Abstract

The purpose of this note is to introduce and investigate the nonparametric estimation of the conditional mode using wavelet methods. We propose a new linear wavelet estimator for this problem. The estimator is constructed by combining a specific ratio technique and an established wavelet estimation method. We obtain rates of almost sure convergence over compact subsets of Rd. A general estimator beyond the wavelet methodology is also proposed, discussing adaptivity within this statistical framework.

Keywords

• conditional mode estimation
• strong consistency
• nonparametric estimation
• wavelet estimation