Estimating the Market Share Attraction Model using Support Vector Regressions
提出用支持向量回归这一非参数技术来估计市场份额吸引力模型的参数，相比传统最大似然法，该方法对异常值更稳健且能避免过拟合，在36个汽车品牌的市场份额预测中表现良好。
We propose to estimate the parameters of the Market Share Attraction Model (Cooper and Nakanishi, 1988 Cooper , L. G. , Nakanishi , M. ( 1988 ). Market Share Analysis: Evaluating Competitive Marketing Effectiveness . Boston , MA : Kluwer Academic Publishers .[Crossref] , [Google Scholar]; Fok and Franses, 2004 Fok , D. , Franses , P. H. ( 2004 ). Analyzing the effects of a brand introduction on competitive structure using a market share attraction model . International Journal of Research in Marketing 21 : 159 – 177 .[Crossref] , [Google Scholar]) in a novel way by using a nonparametric technique for function estimation called Support Vector Regressions (SVR) (Smola, 1996 Smola , A. J. ( 1996 ). Regression Estimation with Support Vector Learning Machines. Master's thesis, Technische Universität München . [Google Scholar]; Vapnik, 1995 Vapnik , V. N. ( 1995 ). The Nature of Statistical Learning Theory. , 2nd ed . New York : Springer-Verlag .[Crossref] , [Google Scholar]). Traditionally, the parameters of the Market Share Attraction Model are estimated via a Maximum Likelihood (ML) procedure, assuming that the data are drawn from a conditional Gaussian distribution. However, if the distribution is unknown, Ordinary Least Squares (OLS) estimation may seriously fail (Vapnik, 1982 Vapnik , V. N. ( 1982 ). Estimation of Dependences Based on Empirical Data . Berlin : Springer . [Google Scholar]). One way to tackle this problem is to introduce a linear loss function over the errors and a penalty on the magnitude of model coefficients. This leads to qualities such as robustness to outliers and avoidance of the problem of overfitting. This kind of estimation forms the basis of the SVR technique, which, as we will argue, makes it a good candidate for estimating the Market Share Attraction Model. We test the SVR approach to predict (the evolution of) the market shares of 36 car brands simultaneously and report promising results.