Authors: Bagchi, Pramita
Dhar, Subhra Sankar
Title: A study on the least square estimator of multiple isotonic regression function
Language (ISO): en
Abstract: Consider the problem of pointwise estimation of f in a multiple isotonic regression model Z = f(X1, ... ,Xd) + ε , where Z is the response variable, f is an unknown non-parametric regression function, which is isotonic with respect to each component, and is the error term. In this article, we investigate the behaviour of the least square estimator of f and establish its asymptotic properties. We generalize the greatest convex minorant characterization of isotonic regression estimator for the multivariate case and use it to establish the asymptotic distribution of properly normalized version of the estimator. Moreover, we test whether the multiple isotonic regression function at a fixed point is larger (or smaller) than a specified value or not based on this estimator, and the consistency of the test is established. The practicability of the estimator and the test are shown on simulated and real data as well.
Subject Headings: consistency
rate of convergence
non-standard asymptotic distribution
cumulative sum diagram
convex function
Issue Date: 2018
Appears in Collections:Sonderforschungsbereich (SFB) 823

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