A study on the least squares estimator of multivariate isotonic regression function
Consider the problem of pointwise estimation of f in a multivariate isotonic regression model Z=f(X1,…,Xd)+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 investigat...
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| Veröffentlicht in: | Scandinavian journal of statistics 2020-12, Vol.47 (4), p.1192-1221, Article 1192 |
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| container_title | Scandinavian journal of statistics |
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| creator | Bagchi, Pramita Sankar Dhar, Subhra |
| description | Consider the problem of pointwise estimation of f in a multivariate isotonic regression model Z=f(X1,…,Xd)+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. |
| doi_str_mv | 10.1111/sjos.12459 |
| format | Article |
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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. 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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. 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| source | Wiley Online Library Journals Frontfile Complete; Business Source Complete |
| subjects | consistency convex function cumulative sum diagram Error analysis Fixed points (mathematics) Least squares Multivariate analysis nonstandard asymptotic distribution rate of convergence Regression models |
| title | A study on the least squares estimator of multivariate isotonic regression function |
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