Physical Sciences and Mathematics Commons^™

Determination Of Spatial Strata For Environmental Regulatory Purposes, John Edward Daniels

Dissertations

This dissertation introduces spatial strata modelling, a methodology that combines spatial statistics, cluster analysis, and geographic information system theories to analyze the background level of naturally occurring contaminants of concern (COCs). The objective of spatial strata modelling is to divide a geographic area of interest into mutually exclusive geographic zones (spatial strata): with each stratum representing a different level of COC concentration. An estimate of each stratum's COC concentration level, representing an upper regulatory limit, will also be provided. Data provided by the Michigan Department of Environmental Quality describing the spatial location and arsenic concentrations of 211 Michigan sites (arsenic …

A Robust Two-Sample Procedure To Estimate A Shift Parameter, Feridun Tasdan

Dissertations

This study estimates the location shift parameter in the two-sample problem. The classical method, Least Square(LS), obtains the shift parameter estimate under the normality assumption. A departure from normality assumption makes the estimate inefficient and unreliable. One alternative to the least square estimate is Hodges-Lehmann (HL) estimate which uses Wilcoxon ranks to estimate the shift parameter. This estimate is robust against contaminations and large outliers. The proposed method in this study combines two samples and uses convolution technique to find a density function for the combined sample. This new density function is later used in the construction of the log …

Spearman Rank Regression, Jason C. Parcon

Dissertations

The main purpose of this dissertation is to obtain an estimate of the slope parameter in a regression model that is robust to outlying values in both the x - and Y-spaces. The least squares method, though known to be optimal for normal errors, can yield estimates with infinitely large MSE's if the error distribution is thick-tailed. Regular rank-based methods like the Wilcoxon method are known to be robust to outlying values in the Y -space, but it is still grossly affected by outlying values in x -space.

This dissertation derives an estimate of the slope from an estimating …

New Graphical Approach On The Analysis Of Experimental Data, Suha Sari

Dissertations

This study presents a new graphical method to identify significant effects in factorial experiments. The proposed methods are obtained for the different cases in which the design can be of full factorial or fractional factorial and the factor levels can be pure or mixed.

We focus on the different decomposition methods, for example orthogonal components system and orthogonal contrast method, to make use of the chisquare plot which requires that the sums of squares are of the same degrees of freedom. Examples and simulations illustrating the different cases of the procedure are presented.

A Comparison Of Different Schemes For Selecting And Estimating Score Functions Based On Residuals, Ali A. Al-Shomrani

Dissertations

In a linear model when the errors follow a normal distribution, least squares methodology is most powerful. However, when the assumption of normality of the error distribution is not met then there exist methods which are more powerful than least squares methods. Rank-based methods form one such class. These methods depend on the selection of a score function [varphi]( u ). The correct choice of [varphi] leads to an optimal (efficient) analysis, but its selection depends on the error distribution which is not known.

In this thesis, we explore different schemes for score selection. Some of these schemes are functions …