Applications and Some Theory for a Nonparametric Approach Based on a Markov-Like Property for Classification with Water Applications
Clifford Spiegelman1, EunSug Park2, Jeongyoun Ahn3
1Statistics, Texas A&M University (and TTI), College Station, TX, United States; 2Mobility Analysis Group, Texas Transportation Institute, College Station, TX, United States; 3Statistics and Operations Research, University of Georgia, Athens, GA, United States

We suggest a new approach for classification based on nonparametricly estimated Likelihood ratios. Due to the scarcity of data in high dimensions, full nonparametric estimation of the likelihood ratios for each population is impractical. Instead, we build a class of estimated nonparametric candidate likelihood ratio models based on a Markov property and to provide multiple likelihood ratio estimates that are useful for guiding a classification algorithm. Our ratio estimates require only estimates for one and two- dimensional marginal distributions, which can effectively get around the curse of dimensionality problem. A classification algorithm based on those estimated likelihoods is presented. A modification to it utilizing variable selection of differences in log of estimated marginal densities is also suggested to specifically handle high dimensional data. The method is applied to water measurement data.

Keywords: Kernel estimation; Classification; Nonparametric; Fisher's LSD

Biography: Cliff Spiegelman is a Distinguished Professor of Statistics at Texas A&M. He is also a Senior Research Scientist at the Texas Transportation Institute. He is greatful for the oportunity to work on applied and methodological statistical problems.