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Isotonic Regression for Multiple Independent Variables [PDF]

Algorithmica, 2013
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Quentin F Stout
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Testing Constancy for Isotonic Regressions

Scandinavian Journal of Statistics, 2006
Abstract.  In this paper, we propose a bootstrap method for testing the constancy of an isotonic regression. The technique we develop is completely non‐parametric and enlarges the appli‐cability of the classical chi‐bar‐squared tests, which require normality assumptions. We prove that our procedure is asymptotically correct and consistent. Moreover, by
Colubi, Ana, Domínguez-Menchero, J. Santos, Gonzáles-Rodrígues, Gil   +2 more
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A Multivariate Version of Isotonic Regression

Biometrika, 1983
A multivariate generalization of isotonic regression is given enabling the study of statistical inference for ordered vector-valued parameters or sets of ordered parameters, including multivariate extensions of Bartholomew's \({\bar \chi}{}^ 2_ k\) and \(\bar E^ 2_ k\).
Sasabuchi, Syoichi, Inutsuka, M., Kulatunga, D. D. S.   +2 more
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Algorithms for a Class of Isotonic Regression Problems

Algorithmica, 1999
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P M Pardalos, Pardalos P M
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Trimmed Mean Isotonic Regression

Scandinavian Journal of Statistics, 2015
AbstractThe trimmed mean is well‐known in literature for being more robust and for having better efficiency than the sample mean when data is generated from heavy‐tailed distributions. In this article, the trimmed mean in the isotonic regression setup is proposed, and the asymptotic as well as the robustness properties of the estimator are studied. The
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On the Consistency of the $L_P $-Isotonic Regression

Theory of Probability & Its Applications, 1993
In this paper we study the consistency of the empirical monotonic p-regression of a p-integrable, $1 \leqq p < \infty $, function both in pointwise convergence and in convergence of empirical p-norms.
Cuesta, J. A., Domínguez, J. S., Matrán, C.   +2 more
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Penalized isotonic regression

Journal of Statistical Planning and Inference, 2015
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Wu, Jiwen, Meyer, Mary C., Opsomer, Jean D.   +2 more
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Unimodal regression via prefix isotonic regression

Computational Statistics & Data Analysis, 2008
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An isotonic regression algorithm

Journal of Statistical Planning and Inference, 1981
Abstract A ‘pooling sets’ type of algorithm is developed and shown to be valid for computing an isotonic regression function for a general quasi-order. The method is direct and intuitive. The algorithm works best when the quasi-order is complex and the objective function is nearly isotonic. An example is worked out in detail.
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The Isotonic Regression Framework

2003
Die Kategorisierung von stetigen Merkmalen erweist sich als eine sehr wichtige Aufgabe innerhalb statistischer Analysen, ganz besonders in der Analyse von Dosis-Wirkungs-Beziehungen. Es ist in vielen Situationen wünschenswert, sinnvolle Gruppen innerhalb der Prädiktorvariablen zu finden und zu bilden.
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