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dc.contributor.supervisor Wang, Xikui (Statistics) en_US
dc.contributor.author Tan, Qi Er
dc.date.accessioned 2012-09-25T22:15:38Z
dc.date.available 2012-09-25T22:15:38Z
dc.date.issued 2012-09-25
dc.identifier.uri http://hdl.handle.net/1993/9147
dc.description.abstract The PhD thesis introduces two new types of correlation adjusted penalization methods to address the issue of multicollinearity in regression analysis. The main purpose is to achieve simultaneous shrinkage of parameter estimators and variable selection for multiple linear regression and logistic regression when the predictor variables are highly correlated. The motivation is that when there is serious issue of multicollinearity, the variances of parameter estimators are significantly large. The new correlation adjusted penalization methods shrink the parameter estimators and their variances to alleviate the problem of multicollinearity. The latest important trend to deal with multicollinearity is to apply penalization methods for simultaneous shrinkage and variable selection. In the literature, the following penalization methods are popular: ridge, bridge, LASSO, SCAD, and OSCAR. Few papers have used correlation based penalization methods, and these correlation based methods in the literature do not work when some correlations are either 1 or -1. This means that these correlation based methods fail if at least two predictor variables are perfectly correlated. We introduce two new types of correlation adjusted penalization methods that work whether or not the predictor variables are perfectly correlated. The types of correlation adjusted penalization methods introduced in my thesis are intuitive and innovative. We investigate important theoretical properties of these new types of penalization methods, including bias, mean squared error, data argumentation and asymptotic properties, and plan to apply them to real data sets in the near future. en_US
dc.subject Statistics en_US
dc.title Correlation adjusted penalization in regression analysis en_US
dc.degree.discipline Statistics en_US
dc.contributor.examiningcommittee Cheng, Smiley W. (Statistics) Mandal, Saumen (Statistics) Bohm, Eric (Surgery) Li, Deli (Lakehead University) en_US
dc.degree.level Doctor of Philosophy (Ph.D.) en_US
dc.description.note October 2012 en_US


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