On Integrated L1 Convergence Rate of an Isotonic Regression Estimator for Multivariate Observations
| Autor: | Anne Leucht, Konstantinos Fokianos, Michael H. Neumann |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Multivariate statistics
Estimator 020206 networking & telecommunications 02 engineering and technology Function (mathematics) Library and Information Sciences Computer Science Applications Rate of convergence Convergence (routing) 0202 electrical engineering electronic engineering information engineering Applied mathematics Isotonic regression Parametric equation Smoothing Information Systems Mathematics |
| Zdroj: | IEEE Transactions on Information Theory. 66:6389-6402 |
| ISSN: | 1557-9654 0018-9448 |
| Popis: | We consider a general monotone regression estimation where we allow for independent and dependent regressors. We propose a modification of the classical isotonic least squares estimator and establish its rate of convergence for the integrated $L^{1}$ -loss function. The methodology captures the shape of the data without assuming additivity or a parametric form for the regression function. Furthermore, the degree of smoothing is chosen automatically and no auxiliary tuning is required for the theoretical analysis. Some simulations and two real data illustrations complement the study of the proposed estimator. |
| Databáze: | OpenAIRE |
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