Higher-Order and Exact Methods for Statistical Inference

Cornell Univ - State: Awds Made Prior May 2010, Ithaca NY

Investigators

Abstract

DMS-020204252 PI: Thomas J DiCiccio Title: Higher Order and Exact Methods for Statistical Inference Abstract There has been burgeoning interest in the last decade or so in artificial likelihoods for nonparametric problems. The investigators also propose to develop tractable approximations to the usual and adjusted nonparametric likelihood ratio statistics. These approximations are intended both to make bootstrap inference feasible and to yield insight into inaccuracies of the standard asymptotic approximations. Maximizing the adjusted profile nonparametric likelihoods yields adjusted estimators, and the investigators propose to study their properties, particularly as a basis for the popular bootstrap-t method of inference. Small sample inference in discrete data problems, such as contingency tables, log-linear models, and logistic regression, has received much attention. One approach is saddlepoint approximations; another approach is the use of Monte Carlo methods to simulate from the relevant conditional distributions. Important new ideas from computational ring theory may pave the way for the next generation feasible methods in highly discrete problems, just as the network algorithm provided methods that are currently being implemented routinely in practice. The investigators propose to use analytic and computational concepts from the theory of Groebner bases and toric ideals to provide correct and feasible simulation methods in complex discrete problems. The proposed research concerns feasible methodologies for accurate inference in both nonparametric and parametric settings. In the nonparametric framework, the focus is on approximate inference based on pseudo-likelihoods, while in the parametric context, the focus is on simulation methods for exact inference in discrete models. The inferential methods that are to be addressed in the proposal have broad application in data analysis of numerous areas of modeling scientific phenomena.