Piecewise Empirical Likelihood

TL;DR

This paper introduces a piecewise empirical likelihood method that combines multiple non-parametric likelihood components to improve computational efficiency and applicability for large data sets.

Contribution

It proposes a novel piecewise empirical likelihood approach that enhances computational speed while maintaining theoretical robustness.

Findings

Demonstrates computational gains over traditional empirical likelihood methods

Provides theoretical analysis of the new piecewise approach

Shows applicability to large data problems

Abstract

Non-parametric methods avoid the problem of having to specify a particular data generating mechanism, but can be computationally intensive, reducing their accessibility for large data problems. Empirical likelihood, a non-parametric approach to the likelihood function, is also limited in application due to the computational demands necessary. We propose a new approach that combines multiple non-parametric likelihood-type components to build a data-driven approximation of the true function. We will examine the theoretical properties of this piecewise empirical likelihood and demonstrate the computational gains of this methodology.