Degree Type

Dissertation

Date of Award

1999

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Wayne A. Fuller

Second Advisor

F. Jay Breidt

Abstract

The estimation of the distribution function of a random variable X measured with error is studied. It is assumed that the measurement error is normally distributed with mean zero and known variance sigma 2. The random variable X is assumed to have a continuous density function. Let the i-th observation on X be denoted by Yi=Xi+ei , where ei , is the measurement error. Let Yi ( i = 1,2,...,n) be a sample of independent observations. It is assumed that Xi and ei are mutually independent and each is identically distributed;Three spline estimators of the density function of X are proposed. The first is a weighted quantile regression spline obtained by acting as if the observations were generated by a set of n X*-values. The n X*-values are defined as a transformation of the original Y-values such that the mean and variance of the X* are consistent estimators of the mean and variance of X. The other two procedures estimate the parameters of the spline function by maximum likelihood. Both use the quantile regression spline estimator as an initial estimator. In all cases, the number of parameters of the spline function is determined by the data with a sample criterion, such as AIC. The proposed spline estimators perform better than a normal mixture estimator and better than a kernel estimator in a simulation study.

DOI

https://doi.org/10.31274/rtd-180813-13824

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

Copyright Owner

Cong Chen

Language

en

Proquest ID

AAI9924707

File Format

application/pdf

File Size

118 pages

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