Adaptive Group Lasso for Multivariate Linear Regression

• Main Authors: Shing-Hung Yeh, 葉世弘
• Other Authors: Sheng-Mao Chang
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/90910161360611684952

碩士 === 國立成功大學 === 統計學系碩博士班 === 97 === In traditional statistical method, estimation and variable selection are almost discussed separately. LASSO (Tibshirani, 1996) is a new method for estimation in linear model, it can estimate parameters and variable selection simultaneously. But Lasso is inconsistent for variable selection, Adaptive Lasso (Zou 2006) overcomes these problems and enjoys the oracle properties. In linear regression when categorical predictors (factors) are present, the Lasso solution only selects individual dummy variables instead of whole factors. The group Lasso(Yuan and Lin 2006) overcomes these problems. Group lasso is a natural extension of lasso and selects variable in a grouped manner, group lasso suffers from estimation inefficiency and selection inconsistency. Adaptive Group Lasso (Wang and Leng 2006) show it’s estimator can be as efficient as oracle. We propose the adaptive group lasso for multivariate linear regression. In our study, the definition of grouped variable is different with the definition defined by formed study, which is regard one column of model matrix as a group. We consider one row of parametric matrix as one group for finding the significant variable on Y.