Abstract
Researchers are often interested to study in the relationships between one variable and several other variables. Regression analysis is the statistical method for investigating such relationship and it is one of the most commonly used statistical Methods in many scientific fields such as financial data analysis, medicine, biology, agriculture, economics, engineering, sociology, geology, etc. But basic form of the regression analysis, ordinary least squares is not suitable for actuarial applications because the relationships are often nonlinear and the probability distribution of the response variable may be non-Gaussian distribution. One of the method that has been successful in overcoming these challenges is the generalized linear model (GLM), which requires that the response variable have a distribution from the exponential family. In this research work, we study copula regression as an alternative method to OLS and GLM. The major advantage of a copula regression is that there are no restrictions on the probability distributions that can be used. First part of this study, we will briefly discuss about copula regression by using several variety of marginal copula functions and copula regression is the most appropriate method in non Gaussian variable(violated normality assumption) regression model fitting. Also we validated our results by using real world example data and random generated (50000 observations) data. Second part of this study, we discussed about multiple regression model based on copula theory, and also we derived multiple regression line equation for Multivariate Non-Exchangeable Generalized Farlie-Gumbel-Morgenstern (FGM) copula function.
Advisor
Rahman Mezbahur
Committee Member
Han Wu
Committee Member
Deepak Sanjel
Date of Degree
2018
Language
english
Document Type
Thesis
Degree
Master of Science (MS)
Department
Mathematics and Statistics
College
Science, Engineering and Technology
Recommended Citation
Thevaraja, M. (2018). Copula Theory and Regression Analysis [Master’s thesis, Minnesota State University, Mankato]. Cornerstone: A Collection of Scholarly and Creative Works for Minnesota State University, Mankato. https://cornerstone.lib.mnsu.edu/etds/803/
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Included in
Ordinary Differential Equations and Applied Dynamics Commons, Other Applied Mathematics Commons
Rights Statement
