Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Entire DC Network
Functional Data Analysis And Its Application To Cancer Data, Evgeny Martinenko
Functional Data Analysis And Its Application To Cancer Data, Evgeny Martinenko
Electronic Theses and Dissertations
The objective of the current work is to develop novel procedures for the analysis of functional data and apply them for investigation of gender disparity in survival of lung cancer patients. In particular, we use the time-dependent Cox proportional hazards model where the clinical information is incorporated via time-independent covariates, and the current age is modeled using its expansion over wavelet basis functions. We developed computer algorithms and applied them to the data set which is derived from Florida Cancer Data depository data set (all personal information which allows to identify patients was eliminated). We also studied the problem of …
Nonparametric And Empirical Bayes Estimation Methods, Rida Benhaddou
Nonparametric And Empirical Bayes Estimation Methods, Rida Benhaddou
Electronic Theses and Dissertations
In the present dissertation, we investigate two different nonparametric models; empirical Bayes model and functional deconvolution model. In the case of the nonparametric empirical Bayes estimation, we carried out a complete minimax study. In particular, we derive minimax lower bounds for the risk of the nonparametric empirical Bayes estimator for a general conditional distribution. This result has never been obtained previously. In order to attain optimal convergence rates, we use a wavelet series based empirical Bayes estimator constructed in Pensky and Alotaibi (2005). We propose an adaptive version of this estimator using Lepski’s method and show that the estimator attains …