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In many engineering and scientific applications, prediction variables aregrouped, for example, in biological applications where assayed genes orproteins can be grouped by biological roles or biological pathways. Commonstatistical analysis methods such as ANOVA, factor analysis, and functionalmodeling with basis sets also exhibit natural variable groupings. Existingsuccessful group variable selection methods such as Antoniadis and Fan (2001),Yuan and Lin (2006) and Zhao, Rocha and Yu (2009) have the limitation ofselecting variables in an "all-in-all-out" fashion, i.e., when one variable ina group is selected, all other variables in the same group are also selected.In many real problems, however, we may want to keep the flexibility ofselecting variables within a group, such as in gene-set selection. In thispaper, we develop a new group variable selection method that not only removesunimportant groups effectively, but also keeps the flexibility of selectingvariables within a group. We also show that the new method offers the potentialfor achieving the theoretical "oracle" property as in Fan and Li (2001) and Fanand Peng (2004).

Group Variable Selection via a Hierarchical Lasso and Its Oracle Property