Variable Selection For Multiplicative Model

Variable selection is a classic and essential research topic in the study of statisticalinference. In the analytic research of cancer, for example, only dozens of genes areresponsible for the outbreak of cancer, and it is of great importance finding an effectivemethod to select those determinant ones out of thousands of genes. It will not only lead betterunderstandings of molecular mechanisms, but also help the statisticians build betterclassification criteria. On the other hand, in practice we often encounter datasetswith positive responses, such as the income of companies and the duration of survival.Multiplicative model has great advantages in dealing with such data and is more and morepopular in many fields.This dissertation studies parameter estimation and variable selection for multiplicativemodel. In the first chapter, traditional methods for parameter estimation are discussed,including least square method, least absolute deviation method and least relative error method.The relative error usually used is the ratio of the error relative to the target value, not the errorrelative to the predictor value. LARE criterion proposed by Chen et al.(2010) combines theboth types of relative error. Chapter2reviews some variable selection methods, such assubset selection and LASSO. In the first part of Chapter3, we recall LARE estimator andits theoretical properties. Then we establish the variable selection based on LARE. We useadaptive lasso and SCAD to gain sparse solutions and prove that the estimators enjoy oracleproperties. We introduce BIC to select the tuning parameter and conduct some simulations toillustrate the finite performances of proposed methods. From the simulation, we can findadaptive lasso and SCAD successfully select the right model with possibility tending to1.Discussions and future work are summarized in the last chapter.