Statistics and Applications

Case Western Reserve University, Cleveland OH

Investigators

Abstract

Four research topics are pursued. The first is on inverse problems and measurement error models. New adaptive wavelet denoising for 3-dimensional objects will be studied and new non-Fourier deconvolution methods for measurement error models will allow users to take into account non-homogeneous errors that occur often in astronomical data. The second area is on biased sampling. Nonparametric and semi-parametric methods will be studied for data from multiple surveys and semi-parametric methods will be developed for survival data. The third area is on high dimensional graphics and data mining. Efficient methods and software will be developed for (large) data analysis and modeling. The fourth area is on mixture problems. New tests and model selection procedures are proposed. The challenges for statistics arising from astronomy, genetics, medical imaging and computer science are multifaceted. Data can be complex due to measurement errors or other unobservable features; or large in size or dimension due to advances in sciences and information technology; or small due to some intrinsic nature of data, for example, halos, ancient stars, are scarce in comparison to other stars. This project develops new theories, practical methods and efficient computational tools to meet these challenges, via the above four major research topics. The interdisciplinary nature of the research will impact our knowledge in the sciences. The research will also benefit education and human development, via training of students, integration with research and mentorship and collaboration with scientists.