By: Aselia Urmanbetova
In joint research with Jeffrey Racine and Qi Li (research paper published by the Journal of Nonparametric Statistics), Assistant Professor Karen Yan considers nonparametric estimation of smoothed probability mass functions for ordered categorical data.
Ordered categorical data often appear in economics and other social sciences. For example, age group, educational level and number of successful patent applications are categorical ordered data. Previous nonparametric smoothed estimation methods have shortcomings — such as inability to deal with gaps in the data or to replicate the empirical proportions and give a discrete uniform distribution for different values of the smoothing parameter — properties that have been shown to be useful.
The authors assume that the data has finite support and exploit this to construct an empirical support kernel function and thus probability mass function estimation. Further, the authors give two different data-driven methods for calculating the smoothing parameter and compare their performance to other estimators using Monte Carlo experiments, showing that they are not only simpler to calculate but also perform significantly better.
"Kernel smoothed probability mass functions for ordered datatypes" appeared in Journal of Nonparametric Statistics in May 2020: https://www.tandfonline.com/doi/abs/10.1080/10485252.2020.1759595