Author

Izzet Sozucok

Graduation Semester and Year

2019

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Shan Sun-Mitchell

Abstract

The goal in functional data studies on failure time or on death time of the objects is to find a relationship between age-at-death (failure time) and current values of a functional predictors. In this study, a novel technique is applied to predict the failure time of devices (such as bearings in a mechanical system) and to try to predict the “age-at-death” distributions under censoring data. We concern ourselves with circumstances where all co-variate trajectories are observed until a current time t. The predictors observed up to current time can be shown by time-varying principal component scores which is continuously updated as time progresses. We establish the estimation of modified survival function for longitudinal trajectories by inspiring Kaplan-Meire method in order to predict mean residual life distribution. Projecting behavior of co-variate trajectories on single index we reduce their dimension to get predictions for each individual object. Furthermore, the uniform convergence rate is proved for mean and co-variance function for censored functional data based on some specified conditions. The proposed method is validated as the leave-one- out method and the approach is illustrated using the simulation study as well

Keywords

Functional data, Censored data, Remaining residual life, Mean remaining life functions, Uniform convergence rate

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons

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