Physical Sciences and Mathematics Commons^™

Comparison Of The Performance Of Simple Linear Regression And Quantile Regression With Non-Normal Data: A Simulation Study, Marjorie Howard

Theses and Dissertations

Linear regression is a widely used method for analysis that is well understood across a wide variety of disciplines. In order to use linear regression, a number of assumptions must be met. These assumptions, specifically normality and homoscedasticity of the error distribution can at best be met only approximately with real data. Quantile regression requires fewer assumptions, which offers a potential advantage over linear regression. In this simulation study, we compare the performance of linear (least squares) regression to quantile regression when these assumptions are violated, in order to investigate under what conditions quantile regression becomes the more advantageous method …

Robust And Efficient Regression, Qi Zheng

All Dissertations

This dissertation aims to address two problems in regression
analysis. One problem is the model selection and robust parameter estimation in high dimensional linear regressions. The other is concerning developing a robust and efficient estimator in nonparametric regressions.
In Chapter 1, we introduce the robust and efficient regression analysis, discuss those two interesting problems and our motivations, and present several exciting results.
We propose a novel robust penalized method for high dimensional linear regression in Chapter 2. Asymptotic properties are established and a data-driven procedure is developed to select adaptive penalties. We show it is the very first estimator to …

Statistical Analysis And Modeling Of Brain Tumor Data: Histology And Regional Effects, Keshav Prasad Pokhrel

USF Tampa Graduate Theses and Dissertations

Comprehensive statistical models for non-normally distributed cancerous tumor sizes are

of prime importance in epidemiological studies, whereas a long term forecasting models

can facilitate in reducing complications and uncertainties of medical progress. The statistical

forecasting models are critical for a better understanding of the disease and supply

appropriate treatments. In addition such a model can be used for the allocations of budgets,

planning, control and evaluations of ongoing efforts of prevention and early detection of

the diseases.

In the present study, we investigate the effects of age, demography, and race on primary

brain tumor sizes using quantile regression methods to …