Estimation of Location and Scale Parameters and Their Joint Density in a Random Effects Model
Abstract
This thesis provides a framework for estimating the location-scale parameters in random
effects models. A secondary goal, which is necessary to efficiently achieve the main goal, is
to estimate the joint density of the location-scale parameters.
The main setting considered here is having a large number of small data sets whose
locations and scales vary randomly but have a common joint distribution. The goal is to
estimate the location-scale parameters and their joint density assuming the scaled error
density is standard normal. This thesis relaxes the assumption that location and scale are
independent and introduces a Bayesian semi-parametric approach based on a mixture of
normal-inverse gamma densities. Also, this thesis further relaxes the assumption that the
scaled error density is standard normal, instead allowing any known scaled error density.
The joint density of location and scale is estimated by a bivariate histogram. Estimation
algorithms are proposed and their usefulness is illustrated with both simulated and real data.
Subject
normal mean and variance estimationbivariate density estimation
heteroscedasticity
shrinkage estimator
dirichlet process mixture model
Citation
Sinha, Shyamalendu (2018). Estimation of Location and Scale Parameters and Their Joint Density in a Random Effects Model. Doctoral dissertation, Texas A & M University. Available electronically from https : / /hdl .handle .net /1969 .1 /174513.