A relative error-based approach for variable selection

The accelerated failure time model or the multiplicative regression model is well-suited to analyze data with positive responses. For the multiplicative regression model, the authors investigate an adaptive variable selection method via a relative error-based criterion and Lasso-type penalty with desired theoretical properties and computational convenience. With fixed or diverging number of variables in regression model, the resultant estimator achieves the oracle property. An alternating direction method of multipliers algorithm is proposed for computing the regularization paths effectively. A data-driven procedure based on the Bayesian information criterion is used to choose the tuning parameter. The finite-sample performance of the proposed method is examined via simulation studies. An application is illustrated with an analysis of one period of stock returns in Hong Kong Stock Exchange.