pagesWith the development of microarray technology, it is now possible to obtain the concentration levels of thousands of genes at a given time or in a given state. By following the changes in the gene expression levels, the responsible genes for cell differentiation or certain diseases can be identified. Gene expression changes are regulated by the interactions between the genes and their products. Gene regulatory networks (GRNs) identify these interactions using the gene expression changes. There are a number of statistical methods to infer GRNs, however, most of them depend on the normality assumption of noises in the data. This thesis considers the multiple linear regression analysis for the reconstruction of GRNs when the error term comes from a Weibull distribution. Since nonnormality complicates the data analysis and results in inefficient estimators, it is proposed to use the modified maximum likelihood (MML) estimation procedure which produces efficient and robust estimators. Also, explanatory variables representing the gene expression levels come from a Weibull distribution. Therefore, they are considered as stochastic and stochastic multiple linear regression analysis is used for inferring GRNs by implementing MML method to estimate the model vi parameters. Robustness and power analyses for both stochastic and nonstochastic multiple linear regression model parameters are also given.

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