Isotonic Regression for Variance Estimation and Its Role in Mean Estimation and Model Validation

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<dc:creator>Delong, Tukasz </dc:creator>
<dc:creator>Wüthrich, Mario V.</dc:creator>
<dc:date>2025-09-29</dc:date>
<dc:description xml:lang="es">Sumario: We study isotonic regression which is a nonparametric rank-preserving regression technique. Under the assumption that the variance function of a response is monotone in its mean functional, we investigate a novel application of isotonic regression as an estimator of this variance function. Our proposal of variance estimation with isotonic regression is used in multiple classical regression problems focused on mean estimation and model validation. In a series of numerical examples, we (1) explore the power variance parameter of the variance function within Tweedie's family of distributions, (2) derive a semi-parametric bootstrap under heteroscedasticity, (3) provide a test for auto calibration, (4) explore a quasi-likelihood approach to benefit from best-asymptotic estimation, and (5) deal with several difficulties under Lognormal assumptions. In all of these problems we verify that the variance estimation with isotonic regression is essential for proper mean estimation and beneficial compared to traditional statistical techniques based on local polynomial smoothers</dc:description>
<dc:identifier>https://documentacion.fundacionmapfre.org/documentacion/publico/es/bib/188559.do</dc:identifier>
<dc:language>spa</dc:language>
<dc:rights xml:lang="es">InC - http://rightsstatements.org/vocab/InC/1.0/</dc:rights>
<dc:subject xml:lang="es">Matemática del seguro</dc:subject>
<dc:subject xml:lang="es">Ciencias Actuariales y Financieras</dc:subject>
<dc:type xml:lang="es">Artículos y capítulos</dc:type>
<dc:title xml:lang="es">Isotonic Regression for Variance Estimation and Its Role in Mean Estimation and Model Validation</dc:title>
<dc:format xml:lang="es">30 p.</dc:format>
<dc:relation xml:lang="es">En: North American actuarial journal. - Schaumburg : Society of Actuaries, 1997- = ISSN 1092-0277. - 29/09/2025 Volume 29 Number 3 - 2025 </dc:relation>
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