New Robust Analytic Tools (original) (raw)

Contributions to management science, 2016

Abstract

Uncertainty is one of the characteristic properties in the area of high-tech engineering and the environment, but also in finance and insurance, as the given data, in both input and output variables, are affected with noise of various kinds, and the scenarios which represent the developments in time, are not deterministic either. Since the global environmental and economic crisis has caused the necessity for an essential restructuring of the approach to risk and regulation in these areas, core elements of new global regulatory frameworks for serving the requirements of the real life have to be established in order to make regulatory systems more robust and suitable. The integration of uncertain is a significant issue for the reliability of any model of a highly interconnected system as the presence of noise and data uncertainty raises serious problems to be coped with on the theoretical and computational side. Therefore, nowadays, robustification has started to attract more attention with regard to complex interdependencies of global networks and Robust Optimization (RO) has gained great importance as a modeling framework for immunizing against parametric uncertainties. In this book, Robust (Conic) Multivariate Adaptive Regression Splines (R(C)MARS) approach has worked out through RO in terms of polyhedral uncertainty which brings us back to CQP naturally. By conducting a robustification in (C)MARS, the estimation variance is aimed to be reduced. Data uncertainty of real-world models is also integrated into regulatory systems and they are robustified by applying R(C)MARS. In (R)MARS and (R)CMARS, however, an extra problem has to be solved (by Software MARS, etc.), namely, the knot selection, which is not needed for the linear model part. Therefore, Robust (Conic) Generalized Partial Linear Models (R(C)GPLMs) are also developed and introduced by using the contributions of both regression models Linear Model/Logistic Regression and R(C)MARS. As semiparametric models, (C)GPLM and R(C)GPLM lead to reduce the complexity of (C)MARS and R(C)MARS in terms of the number of variables used in (C)MARS and R(C)MARS.

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