Semiparametric and Nonparametric Inferences

Semiparametric and nonparametric inferences

Most scientific problems involving data and many medical research problems can be viewed as an investigation into the association between a response variable and a number of potential explanatory variables. Regression analysis, wavelet techniques, hierarchical Bayesian analysis, and neural networks are included in the set of tools that can be brought to bear on such problems. Recent advances in computer technology make it easier to collect large data sets, which in turn demand more complex scientific theories. Hence high-dimensional semiparametric and nonparametric techniques become powerful tools for analyzing data.

This research concerns several related statistical problems ranging from processing signals to analyzing survival data. The research includes the further development of methodologies and computational tools for model fitting and inference in two areas. In the first area, the research develops new techniques of random-sieve methodology and deterministic sieve methodology, each of which expands existing techniques in novel ways. In the second area, the research studies foundational issues of the connection between semiparametric and nonparametric Bayesian and maximum likelihood inference, and constructs confidence bands andintervals for function inference. The areas of application include survival analysis and signal processing. The knowledge gained in this investigation is expected to bring great benefit to many other statistical areas and will be useful in a variety of complex scientific problems.