A Statistical Technique to Construct Data-Driven Decision Rules Based on Prediction Intervals of Nonlinear Regressions

A statistical technique to build data-driven decision rules based on prediction intervals of nonlinear regressions created using multivariate normalizing transformations is proposed. In the general case, the proposed technique is iterative since there may be outliers in the process of building the decision-making rule based on prediction intervals of nonlinear regression. To construct nonlinear regressions and their prediction intervals we use the appropriate techniques based on multivariate normalizing transformations that take into account the correlation between dependent and independent variables. We give examples of constructing data-driven decision rules based on prediction intervals of nonlinear regression with two predictors created using the Johnson three-variate normalizing transformation for the S
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family for three-dimensional non-Gaussian data from 33 auto companies, 32 of which were from the S&P 500 Index in 2020. The above rules are constructed to make a decision in which stocks it is better to invest in. We have found that as of December 2020, the shares of two auto companies were overvalued, and the shares of one, on the contrary, were undervalued, so the shares of this company could be bought.