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Market share analysis using semi-parametric attraction models
Institution:1. Division of Computational Sciences in Mathematics, National Institute for Mathematical Sciences, Daejeon, Republic of Korea;2. Brain Korea 21 PLUS Project for Medical Science, Yonsei University, Seoul, Republic of Korea;3. Department of Psychiatry and Institute of Behavioral Science in Medicine, Yonsei University College of Medicine, Seoul, Republic of Korea;4. Department of Nuclear Medicine, Yonsei University College of Medicine, Seoul, Republic of Korea;1. Department of Statistics and Operations Research, University of Murcia, Spain;2. Institute of Mathematics and Informatics, Vilnius University, Lithuania;1. Centre of New Technologies, University of Warsaw, Warsaw, Poland;2. Department of Computer Science and Engineering, Jadavpur University, Kolkata, India;3. Faculty of Mathematics and Information Science, Warsaw University of Technology, Warsaw, Poland;4. Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland;5. Computer Science Department, University of California, 2063 Kemper Hall, One Shields Avenue, Davis, CA 95616-8562, United States;1. Division of Pediatric Nephrology, Johns Hopkins University School of Medicine, Baltimore, Maryland, USA;2. The Children''s Hospital Association, Alexandria, Virginia, USA, and Overland Park, Kansas, USA;3. Divisions of Pediatric Nephrology and Infectious Diseases, Children''s Mercy Hospital, Kansas City, Missouri, USA;4. Seattle Children’s Hospital, Seattle, Washington, USA
Abstract:Attraction models used to analyze the effects of marketing instruments on market share hitherto assume certain strict functional forms. We introduce semi-parametric models whose parametric components are equivalent to an exponential or multiplicative function. The nonparametric part is estimated on the basis of penalized generalized least squares taking into account smoothness of nonlinear functions. In the empirical study presented market share models with semi-parametric additive brand attractions attain better fits both according to an information criterion that penalizes a model for degrees of freedom (df) consumed and according to error measures determined by bootstrapping.
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