Carnegie Mellon University - Statistics
In many scientific studies, researchers are interested in geometric structure in the underlying density function. Common examples are local modes, ridges, and level sets. In this talk, I will focus on two geometric structures: density ridges and modal regression. Density ridges are curve-like structures characterizing high density regions. I will first describe statistical models for ridges and then discuss their asymptotic theory and methods for constructing confidence sets. I will also show applications to astronomy. Modal regression is an alternative way to study the conditional structure of the response variable given covariates. Instead of estimating the conditional expectation, modal regression focuses on conditional local modes. I will present several useful statistical properties for modal regression, including asymptotic theory, confidence sets, prediction sets, and clustering.