We propose a novel way of forecasting the market shares of several brands simultaneously in a multiplicative competitive interaction model, which uses kernel regression technique incorporated with kernel machine technique applied in support vector machines and other machine learning techniques. Traditionally, the estimations of the market share attraction model are performed via a maximum likelihood estimation procedure under the assumption that the data are drawn from a normal distribution. The proposed method is shown to be a good candidate for forecasting method of the market share attraction model when normal distribution is not assumed. We apply the proposed method to forecast the market shares of 4 Korean car brands simultaneously and represent better performances than maximum likelihood estimation procedure.