On a class of parameter estimator in linear models dominating the least square one
| العنوان: | On a class of parameter estimator in linear models dominating the least square one |
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| المؤلفون: | Isabella Lari, Piero Barone |
| المصدر: | Digital signal processing 54 (2016): 27–34. doi:10.1016/j.dsp.2016.04.001 info:cnr-pdr/source/autori:Barone, Piero; Lari, Isabella/titolo:On a class of parameters estimators in linear models dominating the least squares one/doi:10.1016%2Fj.dsp.2016.04.001/rivista:Digital signal processing (Print)/anno:2016/pagina_da:27/pagina_a:34/intervallo_pagine:27–34/volume:54 |
| سنة النشر: | 2016 |
| مصطلحات موضوعية: | Mathematical optimization, Mean squared error, 02 engineering and technology, noise model, l(1) norm minimization, 01 natural sciences, mean square error, 010104 statistics & probability, Bias of an estimator, Artificial Intelligence, 0202 electrical engineering, electronic engineering, information engineering, Applied mathematics, l 1 norm minimization, Ill-posed inverse problems, 0101 mathematics, Electrical and Electronic Engineering, Mathematics, Minimum mean square error, Applied Mathematics, Orthogonality principle, Estimator, 020206 networking & telecommunications, linear model, Efficient estimator, Computational Theory and Mathematics, biased estimates, Signal Processing, Ordinary least squares, Computer Vision and Pattern Recognition, Statistics, Probability and Uncertainty, Invariant estimator |
| الوصف: | The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented by random coefficients in a given deterministic basis. An extended underdetermined design matrix is then formed, and the estimator of the extended parameters with minimum l(1) norm is computed. It is proved that, if the noise variance is larger than a threshold, which depends on the unknown parameters and on the extended design matrix, then the proposed estimator of the original parameters dominates the least-squares estimator, in the sense of the mean square error. A small simulation illustrates its behavior. Moreover it is shown experimentally that it can be convenient, even if the design matrix is not known but only an estimate can be used. Furthermore the noise basis can eventually be used to introduce some prior information in the estimation process. These points are illustrated in a simulation by using the proposed estimator for solving a difficult inverse ill-posed problem, related to the complex moments of an atomic complex measure. (C) 2016 Elsevier Inc. All rights reserved. |
| اللغة: | English |
| DOI: | 10.1016/j.dsp.2016.04.001 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::782473073693114dc2f8242a4c599f08 http://hdl.handle.net/11573/871163 |
| Rights: | CLOSED |
| رقم الانضمام: | edsair.doi.dedup.....782473073693114dc2f8242a4c599f08 |
| قاعدة البيانات: | OpenAIRE |
| DOI: | 10.1016/j.dsp.2016.04.001 |
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