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A study on the least squares estimator of multivariate isotonic regression function
Author(s) -
Bagchi Pramita,
Sankar Dhar Subhra
Publication year - 2020
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12459
Subject(s) - isotonic regression , mathematics , estimator , statistics , pointwise , nonparametric regression , multivariate statistics , mathematical analysis
Consider the problem of pointwise estimation of f in a multivariate isotonic regression model Z = f ( X 1 ,…, X d )+ ϵ , where Z is the response variable, f is an unknown nonparametric regression function, which is isotonic with respect to each component, and ϵ is the error term. In this article, we investigate the behavior of the least squares estimator of f . 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 multivariate 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.