Kernel Smoothed Probability Mass Functions for Ordered Datatypes

McMaster University, Working Paper Series # 2017-14

31 Pages Posted: 6 Nov 2017 Last revised: 28 Oct 2018

See all articles by Jeffrey Racine

Jeffrey Racine

Department of Economics - McMaster University

Qi Li

Texas A&M University - Department of Economics

Karen Yan

Texas A&M University, Department of Economics

Date Written: November 3, 2017

Abstract

We propose a kernel function for ordered categorical data that overcomes certain limitations present in ordered kernel functions that have appeared in the literature on the estimation of probability mass functions for multinomial ordered data. Some of these limitations arise from assumptions made about the support of the random variable that may be at odds with the data at hand. Furthermore, many existing ordered kernel functions lack a particularly appealing property, namely the ability to deliver discrete uniform probability estimates for some value of the smoothing parameter. To overcome these limitations, we propose an asymmetric empirical support kernel function that adapts to the data at hand and possesses certain desirable features. In particular, there are no difficulties arising from zero counts caused by gaps in the data while it encompasses both the empirical proportions and the discrete uniform probabilities at the lower and upper boundaries of the smoothing parameter. We propose using likelihood and least squares cross-validation for smoothing parameter selection, and study the asymptotic behaviour of these data-driven methods. We use Monte Carlo simulations to examine the finite sample performance of the proposed estimator and we also provide a simple empirical example to illustrate the usefulness of the proposed estimator in applied settings.

Suggested Citation

Racine, Jeffrey and Li, Qi and Yan, Karen, Kernel Smoothed Probability Mass Functions for Ordered Datatypes (November 3, 2017). McMaster University, Working Paper Series # 2017-14, Available at SSRN: https://ssrn.com/abstract=3064732 or http://dx.doi.org/10.2139/ssrn.3064732

Jeffrey Racine (Contact Author)

Department of Economics - McMaster University ( email )

Hamilton, Ontario L8S 4M4
Canada

Qi Li

Texas A&M University - Department of Economics ( email )

5201 University Blvd.
College Station, TX 77843-4228
United States
979-845-7349 (Phone)

Karen Yan

Texas A&M University, Department of Economics ( email )

Langford Building A
798 Ross St.
College Station, TX 77843-3137
United States

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