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Full-Text Articles in Physical Sciences and Mathematics
A Markov Transition Model To Dementia With Death As A Competing Event, Liou Xu
A Markov Transition Model To Dementia With Death As A Competing Event, Liou Xu
University of Kentucky Doctoral Dissertations
The research on multi-state Markov transition model is motivated by the nature of the longitudinal data from the Nun Study (Snowdon, 1997), and similar information on the BRAiNS cohort (Salazar, 2004). Our goal is to develop a flexible methodology for handling the categorical longitudinal responses and competing risks time-to-event that characterizes the features of the data for research on dementia. To do so, we treat the survival from death as a continuous variable rather than defining death as a competing absorbing state to dementia. We assume that within each subject the survival component and the Markov process are linked by …
Comparison Of Two Samples By A Nonparametric Likelihood-Ratio Test, William H. Barton
Comparison Of Two Samples By A Nonparametric Likelihood-Ratio Test, William H. Barton
University of Kentucky Doctoral Dissertations
In this dissertation we present a novel computational method, as well as its software implementation, to compare two samples by a nonparametric likelihood-ratio test. The basis of the comparison is a mean-type hypothesis. The software is written in the R-language [4]. The two samples are assumed to be independent. Their distributions, which are assumed to be unknown, may be discrete or continuous. The samples may be uncensored, right-censored, left-censored, or doubly-censored. Two software programs are offered. The first program covers the case of a single mean-type hypothesis. The second program covers the case of multiple mean-type hypotheses. For the first …
Nonparametric Estimation Of Derivatives With Applications, Benjamin Hall
Nonparametric Estimation Of Derivatives With Applications, Benjamin Hall
University of Kentucky Doctoral Dissertations
We review several nonparametric regression techniques and discuss their various strengths and weaknesses with an emphasis on derivative estimation and confidence band creation. We develop a generalized C(p) criterion for tuning parameter selection when interest lies in estimating one or more derivatives and the estimator is both linear in the observed responses and self-consistent. We propose a method for constructing simultaneous confidence bands for the mean response and one or more derivatives, where simultaneous now refers both to values of the covariate and to all derivatives under consideration. In addition we generalize the simultaneous confidence bands to account for heteroscedastic …