Abstract: 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.