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Full-Text Articles in Physical Sciences and Mathematics
On The Testing And Estimation Of High-Dimensional Covariance Matrices, Thomas Fisher
On The Testing And Estimation Of High-Dimensional Covariance Matrices, Thomas Fisher
All Dissertations
Many applications of modern science involve a large number of parameters. In
many cases, the number of parameters, p, exceeds the number of observations,
N. Classical multivariate statistics are based on the assumption that the
number of parameters is fixed and the number of observations is large. Many of
the classical techniques perform poorly, or are degenerate, in high-dimensional
situations.
In this work, we discuss and develop statistical methods for inference of
data in which the number of parameters exceeds the number of observations.
Specifically we look at the problems of hypothesis testing regarding and the
estimation of the covariance …
Survival Analysis With High-Dimensional Covariates: An Application In Microarray Studies, David Engler, Yi Li
Survival Analysis With High-Dimensional Covariates: An Application In Microarray Studies, David Engler, Yi Li
Faculty Publications
Use of microarray technology often leads to high-dimensional and low-sample size (HDLSS) data settings. A variety of approaches have been proposed for variable selection in this context. However, only a small number of these have been adapted for time-to-event data where censoring is present. Among standard variable selection methods shown both to have good predictive accuracy and to be computationally efficient is the elastic net penalization approach. In this paper, adaptations of the elastic net approach are presented for variable selection both under the Cox proportional hazards model and under an accelerated failure time (AFT) model. Assessment of the two …
Detecting Differentially Expressed Genes While Controlling The False Discovery Rate For Microarray Data, Shuo Jiao
Department of Statistics: Dissertations, Theses, and Student Work
Microarray is an important technology which enables people to investigate the expression levels of thousands of genes at the same time. One common goal of microarray data analysis is to detect differentially expressed genes while controlling the false discovery rate. This dissertation consists with four papers written to address this goal. The dissertation is organized as follows: In Chapter 1, a brief introduction of the Affymetrix GeneChip microarray technology is provided. The concept of differentially expressed genes and the definition of the false discovery rate are also introduced. In Chapter 2, a literature review of the related works on this …
Discrete Nonparametric Algorithms For Outlier Detection With Genomic Data, Debashis Ghosh
Discrete Nonparametric Algorithms For Outlier Detection With Genomic Data, Debashis Ghosh
Debashis Ghosh
In high-throughput studies involving genetic data such as from gene expression microarrays, differential expression analysis between two or more experimental conditions has been a very common analytical task. Much of the resulting literature on multiple comparisons has paid relatively little attention to the choice of test statistic. In this article, we focus on the issue of choice of test statistic based on a special pattern of differential expression. The approach here is based on recasting multiple comparisons procedures for assessing outlying expression values. A major complication is that the resulting p-values are discrete; some theoretical properties of sequential testing procedures …