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Full-Text Articles in Applied Statistics
A Copula Model Approach To Identify The Differential Gene Expression, Prasansha Liyanaarachchi
A Copula Model Approach To Identify The Differential Gene Expression, Prasansha Liyanaarachchi
Mathematics & Statistics Theses & Dissertations
Deoxyribonucleic acid, more commonly known as DNA, is a complex double helix-shaped molecule present in all living organisms and hosts thousands of genes. However, only a few genes exhibit differential expression and play a vital role in a particular disease such as breast cancer. Microarray technology is one of the modern technologies developed to study these gene expressions. There are two major microarray technologies available for expression analysis: Spotted cDNA array and oligonucleotide array. The focus of our research is the statistical analysis of data that arises from the spotted cDNA microarray. Numerous models have been proposed in the literature …
The Doubly Inflated Poisson And Related Regression Models, Manasi Sheth-Chandra
The Doubly Inflated Poisson And Related Regression Models, Manasi Sheth-Chandra
Mathematics & Statistics Theses & Dissertations
Most real life count data consists of some values that are more frequent than allowed by the common parametric families of distributions. For data consisting of only excess zeros, in a seminal paper Lambert (1992) introduced Zero-Inflated Poisson (ZIP) model, which is a mixture model that accounts for the inflated zeros. In this thesis, two Doubly Inflated Poisson (DIP) probability models, DIP (p, λ) and DIP ( p1, p2, λ), are discussed for situations where there is another inflated value k > 0 besides the inflated zeros. The distributional properties such as identifiability, moments, and conditional probabilities …
Efficient Unbiased Estimating Equations For Analyzing Structured Correlation Matrices, Yihao Deng
Efficient Unbiased Estimating Equations For Analyzing Structured Correlation Matrices, Yihao Deng
Mathematics & Statistics Theses & Dissertations
Analysis of dependent continuous and discrete data has become an active area of research. For normal data, correlations fully quantify the dependence. And historically, maximum likelihood method has been very successful to estimate the correlations and unbiased estimating equation approach has become a popular alternative when there may be a departure from normality. In this thesis we show that the optimal unbiased estimating equation coincides with the likelihood equations for normal data. We then introduce a general class of weighted unbiased estimating equations to estimate parameters in a structured correlation matrix. We derive expressions for asymptotic covariance of the estimates, …