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An isotonic trivariate statistical regression method

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Abstract

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.

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Notes

  1. Acrylamide (Marstokk et al. 2000) is a chemical compound with chemical formula C\(_3\)H\(_5\)NO. It is a white odorless crystalline solid, soluble in water, ethanol, ether and chloroform. Acrylamide decomposes in the presence of acids, bases, oxidizing agents, iron and iron salts. It decomposes non-thermally to form ammonia, while its thermal decomposition produces carbon monoxide, carbon dioxide and oxides of nitrogen.

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Acknowledgments

The author wishes to gratefully thank the anonymous referees and the associate editor who coordinated the review of the present paper for their thorough and stimulating comments and suggestions that helped improving and enriching the presentation of the technical content conveyed by the present manuscript.

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  1. Dipartimento di Ingegneria dell’Informazione (DII), Facoltà di Ingegneria, Università Politecnica delle Marche, Via Brecce Bianche, Ancona, 60131, Italy

    Simone Fiori

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  1. Simone Fiori
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Correspondence to Simone Fiori.

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Fiori, S. An isotonic trivariate statistical regression method. Adv Data Anal Classif 7, 209–235 (2013). https://doi.org/10.1007/s11634-013-0131-9

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