Show simple item record

dc.contributor.advisor Cox, Dennis D.
dc.creatorGebert, Mark Allen
dc.date.accessioned 2009-06-04T07:00:47Z
dc.date.available 2009-06-04T07:00:47Z
dc.date.issued 1998
dc.identifier.citation Gebert, Mark Allen. "Nonparametric density contour estimation." (1998) Diss., Rice University. https://hdl.handle.net/1911/19261.
dc.identifier.urihttps://hdl.handle.net/1911/19261
dc.description.abstract Estimation of the level sets for an unknown probability density is done with no specific assumed form for that density, that is, non-parametrically. Methods for tackling this problem are presented. Earlier research showed existence and properties of an estimate based on a kernel density estimate in one dimension. Monte Carlo methods further demonstrated the reasonability of extending this approach to two dimensions. An alternative procedure is now considered that focuses on properties of the contour itself; procedures wherein we define and make use of an objective function based on the characterization of contours as enclosing regions of minimum area given a constraint on probability. Restricting our attention to (possibly non-convex) polygons as candidate contours, numeric optimization of this difficult non-smooth objective function is accomplished using pdsopt, for Parallel Direct Search OPTimization, a set of routines developed for minimization of a scalar-valued function over a high-dimensional domain. Motivation for this method is given, as well as results of simulations done to test it; these include exploration of a Lagrange-multiplier penalty on area and the need which arises for addition of a penalty on the "roughness" of a polygonal contour.
dc.format.extent 200 p.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.subjectMathematics
Statistics
dc.title Nonparametric density contour estimation
dc.type Thesis
dc.type.material Text
thesis.degree.department Statistics
thesis.degree.discipline Engineering
thesis.degree.grantor Rice University
thesis.degree.level Doctoral
thesis.degree.name Doctor of Philosophy


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record