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Mahalanobis kernel-based support vector data description for detection of large shifts in mean vector
Title
Mahalanobis kernel-based support vector data description for detection of large shifts in mean vector.
Creator
Nguyen, Vu, Maboudou, Edgard, Nickerson, David, Schott, James, University of Central Florida
Abstract / Description
Statistical process control (SPC) applies the science of statistics to various process control in order to provide higher-quality products and better services. The K chart is one among the many important tools that SPC offers. Creation of the K chart is based on Support Vector Data Description (SVDD), a popular data classifier method inspired by Support Vector Machine (SVM). As any methods associated with SVM, SVDD benefits from a wide variety of choices of kernel, which determines the...
Show moreStatistical process control (SPC) applies the science of statistics to various process control in order to provide higher-quality products and better services. The K chart is one among the many important tools that SPC offers. Creation of the K chart is based on Support Vector Data Description (SVDD), a popular data classifier method inspired by Support Vector Machine (SVM). As any methods associated with SVM, SVDD benefits from a wide variety of choices of kernel, which determines the effectiveness of the whole model. Among the most popular choices is the Euclidean distance-based Gaussian kernel, which enables SVDD to obtain a flexible data description, thus enhances its overall predictive capability. This thesis explores an even more robust approach by incorporating the Mahalanobis distance-based kernel (hereinafter referred to as Mahalanobis kernel) to SVDD and compare it with SVDD using the traditional Gaussian kernel. Method's sensitivity is benchmarked by Average Run Lengths obtained from multiple Monte Carlo simulations. Data of such simulations are generated from multivariate normal, multivariate Student's (t), and multivariate gamma populations using R, a popular software environment for statistical computing. One case study is also discussed using a real data set received from Halberg Chronobiology Center. Compared to Gaussian kernel, Mahalanobis kernel makes SVDD and thus the K chart significantly more sensitive to shifts in mean vector, and also in covariance matrix.
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Date Issued
2015
Identifier
CFE0005676, ucf:50170
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0005676
Sparse Ridge Fusion For Linear Regression
Title
Sparse Ridge Fusion For Linear Regression.
Creator
Mahmood, Nozad, Maboudou, Edgard, Schott, James, Uddin, Nizam, University of Central Florida
Abstract / Description
For a linear regression, the traditional technique deals with a case where the number of observations n more than the number of predictor variables p (n(>)p). In the case n(
Show moreFor a linear regression, the traditional technique deals with a case where the number of observations n more than the number of predictor variables p (n(>)p). In the case n(<)p, the classical method fails to estimate the coefficients. A solution of this problem in the case of correlated predictors is provided in this thesis. A new regularization and variable selection is proposed under the name of Sparse Ridge Fusion (SRF). In the case of highly correlated predictor , the simulated examples and a real data show that the SRF always outperforms the lasso, elastic net, and the S-Lasso, and the results show that the SRF selects more predictor variables than the sample size n while the maximum selected variables by lasso is n size.
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Date Issued
2013
Identifier
CFE0005031, ucf:49997
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0005031
Estimation for the Cox Model with Various Types of Censored Data
Title
Estimation for the Cox Model with Various Types of Censored Data.
Creator
Riddlesworth, Tonya, Ren, Joan, Mohapatra, Ram, Richardson, Gary, Ni, Liqiang, Schott, James, University of Central Florida
Abstract / Description
In survival analysis, the Cox model is one of the most widely used tools. However, up to now there has not been any published work on the Cox model with complicated types of censored data, such as doubly censored data, partly-interval censored data, etc., while these types of censored data have been encountered in important medical studies, such as cancer, heart disease, diabetes, etc. In this dissertation, we first derive the bivariate nonparametric maximum likelihood estimator (BNPMLE) Fn(t...
Show moreIn survival analysis, the Cox model is one of the most widely used tools. However, up to now there has not been any published work on the Cox model with complicated types of censored data, such as doubly censored data, partly-interval censored data, etc., while these types of censored data have been encountered in important medical studies, such as cancer, heart disease, diabetes, etc. In this dissertation, we first derive the bivariate nonparametric maximum likelihood estimator (BNPMLE) Fn(t,z) for joint distribution function Fo(t,z) of survival time T and covariate Z, where T is subject to right censoring, noting that such BNPMLE Fn has not been studied in statistical literature. Then, based on this BNPMLE Fn we derive empirical likelihood-based (Owen, 1988) confidence interval for the conditional survival probabilities, which is an important and difficult problem in statistical analysis, and also has not been studied in literature. Finally, with this BNPMLE Fn as a starting point, we extend the weighted empirical likelihood method (Ren, 2001 and 2008a) to the multivariate case, and obtain a weighted empirical likelihood-based estimation method for the Cox model. Such estimation method is given in a unified form, and is applicable to various types of censored data aforementioned.
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Date Issued
2011
Identifier
CFE0004158, ucf:49051
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0004158