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An isotonic trivariate statistical regression method

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  • Simone Fiori

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. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Simone Fiori, 2013. "An isotonic trivariate statistical regression method," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 7(2), pages 209-235, June.
    • Handle: RePEc:spr:advdac:v:7:y:2013:i:2:p:209-235
    DOI: 10.1007/s11634-013-0131-9
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    References listed on IDEAS

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    1. Durot, Cécile, 2003. "A Kolmogorov-type test for monotonicity of regression," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 425-433, July.
    2. Velikova, M.V., 2006. "Monotone models for prediction in data mining," Other publications TiSEM d8ed8e5b-1061-4738-8ff9-a, Tilburg University, School of Economics and Management.
    3. Ana Colubi & J. Santos Domínguez‐Menchero & Gil González‐Rodríguez, 2006. "Testing Constancy for Isotonic Regressions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 463-475, September.
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    Cited by:

    1. Simone Fiori & Andrea Vitali, 2019. "Statistical Modeling of Trivariate Static Systems: Isotonic Models," Data, MDPI, vol. 4(1), pages 1-29, January.

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