In this article,we propose a nonconcave penalized M-estimation of least product relative error(penalized M-LPRE)method for multiplicative regression models whose dimension of parameters is sparse and can increase with the sample size.Under some mild conditions,consistency and asymptotic normality of the penalized M-LPRE estimator are established.Numerical simulations and a real data analysis on the body fat are carried out to assess the performance of the proposed method.
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