1. Index-Model inference with Box-Cox transformations
- Author
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Luu, Hai Yen, Universitat de Barcelona, and Bolancé Losilla, Catalina
- Subjects
Box-Cox transformation ,Multivariate analysis ,Anàlisi multivariable ,Matemàtiques i estadística [Àrees temàtiques de la UPC] ,single index model ,62 Statistics::62H Multivariate analysis [Classificació AMS] ,car insurance - Abstract
The single-index model is a non-parametric model that is popular in statistics for the estimation of risk assessment, thanks to its flexibility. Many studies have approached the problem of finding the best estimators for the model parameters and smooth function. However, most of the real-world data is asymmetric. In this thesis, we consider the application of a Box-Cox transformation on the response variable to improve the performances of the single-index model. Indeed, the Box-Cox transformation addresses the skewness of the response and transform it into a normally-distributed variables. We consider also the log transformation of the response variable. We show through a simulation study that the parameters of the models fitted with the transformed response have more similarity with the true parameters, which shows that the model is more reliable. Finally, we perform a study on a real-world data set from the car insurance industry, where we build a single-index model to predict the expected cost per claim based on a set of variables, that concern the demographic characteristic and the driving style of the customer. We assess the performance of the model fitted on the original data as well the models that use the log and the Box-Cox transformation, that obtain better results than the original one.
- Published
- 2023