Asymptotics and computations for approximation of method of regularization estimators

Simple item page
dc.contributorEubank, Randall L.
dc.creatorLee, Sang-Joon
dc.date.accessioned2005-08-29T14:37:13Z
dc.date.accessioned2017-04-07T19:50:01Z
dc.date.available2005-08-29T14:37:13Z
dc.date.available2017-04-07T19:50:01Z
dc.date.created2003-05
dc.date.issued2005-08-29
dc.description.abstractInverse problems arise in many branches of natural science, medicine and engineering involving the recovery of a whole function given only a finite number of noisy measurements on functionals. Such problems are usually ill-posed, which causes severe difficulties for standard least-squares or maximum likelihood estimation techniques. These problems can be solved by a method of regularization. In this dissertation, we study various problems in the method of regularization. We develop asymptotic properties of the optimal smoothing parameters concerning levels of smoothing for estimating the mean function and an associated inverse function based on Fourier analysis. We present numerical algorithms for an approximated method of regularization estimator computation with linear inequality constraints. New data-driven smoothing parameter selection criteria are proposed in this setting. In addition, we derive a Bayesian credible interval for the approximated method of regularization estimators.
dc.identifier.urihttp://hdl.handle.net/1969.1/2266
dc.language.isoen_US
dc.publisherTexas A&M University
dc.subjectMethod of Regularization
dc.subjectSpline Smoothings
dc.titleAsymptotics and computations for approximation of method of regularization estimators
dc.typeBook
dc.typeThesis

Files

Collections

Texas A&M University at College Station