Emanuel Parzen: A Memorial, and a Model With the Two Kernels That He Championed

TL;DR

This paper memorializes Emanuel Parzen's influential work on kernel density estimation and Reproducing Kernel Hilbert Spaces, highlighting his contributions and demonstrating how RKHS methods can be used to build risk models with personal density attributes.

Contribution

The paper introduces a model utilizing the two kernels championed by Parzen, applying RKHS penalized likelihood methods to risk modeling with individual density attributes.

Findings

Demonstrated how RKHS can be used for risk modeling

Showed the effectiveness of Parzen's kernels in new applications

Provided technical insights into kernel-based density estimation

Abstract

Manny Parzen passed away in February 2016, and this article is written partly as a memorial and appreciation. Manny made important contributions to several areas, but the two that influenced me most were his contributions to kernel density estimation and to Reproducing Kernel Hilbert Spaces, the two kernels of the title. Some fond memories of Manny as a PhD advisor begin this memorial, followed by a discussion of Manny's influence on density estimation and RKHS methods. A picture gallery of trips comes next, followed by the technical part of the article. Here our goal is to show how risk models can be built using RKHS penalized likelihood methods where subjects have personal (sample) densities which can be used as {\it attributes} in such models.