Kernel Density Estimation by Stagewise Algorithm with a Simple Dictionary

TL;DR

This paper introduces a novel multivariate kernel density estimator using a stagewise minimization algorithm with a simple dictionary, achieving data-adaptive weighting and sparse representation, and demonstrating competitive performance through simulations.

Contribution

It presents a new stagewise minimization approach for kernel density estimation that incorporates a simple dictionary for adaptivity and sparsity.

Findings

The estimator achieves data-adaptive weights and bandwidth matrices.

Non-asymptotic error bounds are established for the estimator.

Simulation results show competitive or superior performance to existing methods.

Abstract

This study proposes multivariate kernel density estimation by stagewise minimization algorithm based on $U$-divergence and a simple dictionary. The dictionary consists of an appropriate scalar bandwidth matrix and a part of the original data. The resulting estimator brings us data-adaptive weighting parameters and bandwidth matrices, and realizes a sparse representation of kernel density estimation. We develop the non-asymptotic error bound of estimator obtained via the proposed stagewise minimization algorithm. It is confirmed from simulation studies that the proposed estimator performs competitive to or sometime better than other well-known density estimators.