Second Generation Wavelet Algorithms

Simple wavelet decompositions can be extended through lifting schemes to have better smoothness properties. This can lead to simpler algorithms for nonparametric regression problems with uneven or random designs.

Asymptotic Equivalence in Function Estimation

The asymptotic behavior of density estimation and nonparametric regression problems is linked to the problem of estimating a smooth function in a continuous white noise experiment. Bibliography of work on deficiency distance between experiments

Likelihood Ratio Tests in Mixture Models

Standard asymptotic results no longer apply in mixture models because under the null hypothesis there is lack of identifiability.

Asymptotics of Cluster-Robust Variance Estimation

Sandwich estimators have been used to estimate the variance in models with cluster observations (repeated measures, longitudinal data). These are approximately normal only if the Effective Number of Groups is large.

Student Projects

Nonparametric Regression of Presidential Approval Rating with Correlated Observations

The Presidential Approval Rating is the result of a consistent series of surveys performed by Gallup Inc. It provides an interesting example of a nonparametric regression problem where there is a true unknown population value of the parameter of interest. Unfortunately, the way the data series is reported results in correlated observations. We explore methods for finding a bandwidth in a Nadaraya--Watson kernel estimator that are robust to local positive correlation between observations. We apply these results to some inferential questions regarding the popularity of President Barack Obama.