Statistica Sinica 23 (2013), 543-569

PENALIZED MINIMUM AVERAGE VARIANCE

ESTIMATION

Tao Wang$^1$, Peirong Xu$^2$ and Lixing Zhu$^1$

$^1$Hong Kong Baptist University and $^2$East China Normal University

Abstract: For simultaneous dimension reduction and variable selection for general regression models, including the multi-index model as a special case, we propose a penalized minimum average variance estimation method, combining the ideas of minimum average variance estimation in dimension reduction and regularization in variable selection. The resulting estimator can be found in a computationally efficient manner. Under mild conditions, the new method can consistently select all relevant predictors and has the oracle property. Simulations and a data example demonstrate the effectiveness and efficiency of the proposed method.

Key words and phrases: Dimension reduction, minimum average variance estimation, oracle property, single-index model, sufficient dimension reduction, variable selection.