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An isotonic trivariate statistical regression method. (English) Zbl 1267.62078

Summary: The present research work outlines the main ideas behind statistical regression by a two-independent-variates and one-dependent-variate model based on the invariance of measures in probabilistic spaces. The principle of probabilistic measure invariance, applied under the assumption that the model be isotonic, leads to a system of differential equations. Such differential system is reformulated in terms of an integral equation that affords an iterative numerical solution. Numerical tests performed on the devised statistical regression procedure illustrate its features.

MSC:

62J02 General nonlinear regression
62G08 Nonparametric regression and quantile regression
35Q62 PDEs in connection with statistics
65C60 Computational problems in statistics (MSC2010)
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