On multivariate nonlinear regression models with stationary correlated errors
In this paper we consider the statistical analysis of multivariate multiple nonlinear regression models with correlated errors, using Finite Fourier Transforms. Consistency and asymptotic normality of the weighted least squares estimates are established under various conditions on the regressor vari...
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ftcdlib:qt6rz1d4b6 2023-05-15T13:50:53+02:00 On multivariate nonlinear regression models with stationary correlated errors Terdik, G Subba Rao, T Jammalamadaka, SR 3793 - 3814 2007-11-01 application/pdf http://www.escholarship.org/uc/item/6rz1d4b6 english eng eScholarship, University of California qt6rz1d4b6 http://www.escholarship.org/uc/item/6rz1d4b6 public Terdik, G; Subba Rao, T; & Jammalamadaka, SR. (2007). On multivariate nonlinear regression models with stationary correlated errors. Journal of Statistical Planning and Inference, 137(11), 3793 - 3814. doi:10.1016/j.jspi.2007.03.050. UC Santa Barbara: Retrieved from: http://www.escholarship.org/uc/item/6rz1d4b6 article 2007 ftcdlib https://doi.org/10.1016/j.jspi.2007.03.050 2018-07-13T22:52:21Z In this paper we consider the statistical analysis of multivariate multiple nonlinear regression models with correlated errors, using Finite Fourier Transforms. Consistency and asymptotic normality of the weighted least squares estimates are established under various conditions on the regressor variables. These conditions involve different types of scalings, and the scaling factors are obtained explicitly for various types of nonlinear regression models including an interesting model which requires the estimation of unknown frequencies. The estimation of frequencies is a classical problem occurring in many areas like signal processing, environmental time series, astronomy and other areas of physical sciences. We illustrate our methodology using two real data sets taken from geophysics and environmental sciences. The data we consider from geophysics are polar motion (which is now widely known as "Chandlers Wobble"), where one has to estimate the drift parameters, the offset parameters and the two periodicities associated with elliptical motion. The data were first analyzed by Arato, Kolmogorov and Sinai who treat it as a bivariate time series satisfying a finite order time series model. They estimate the periodicities using the coefficients of the fitted models. Our analysis shows that the two dominant frequencies are 12 h and 410 days. The second example, we consider is the minimum/maximum monthly temperatures observed at the Antarctic Peninsula (Faraday/Vernadsky station). It is now widely believed that over the past 50 years there is a steady warming in this region, and if this is true, the warming has serious consequences on ecology, marine life, etc. as it can result in melting of ice shelves and glaciers. Our objective here is to estimate any existing temperature trend in the data, and we use the nonlinear regression methodology developed here to achieve that goal. © 2007 Elsevier B.V. All rights reserved. Article in Journal/Newspaper Antarc* Antarctic Antarctic Peninsula Ice Shelves University of California: eScholarship Antarctic Antarctic Peninsula Faraday ENVELOPE(-64.256,-64.256,-65.246,-65.246) The Antarctic Vernadsky Station ENVELOPE(-64.257,-64.257,-65.245,-65.245) Journal of Statistical Planning and Inference 137 11 3793 3814 |
institution |
Open Polar |
collection |
University of California: eScholarship |
op_collection_id |
ftcdlib |
language |
English |
description |
In this paper we consider the statistical analysis of multivariate multiple nonlinear regression models with correlated errors, using Finite Fourier Transforms. Consistency and asymptotic normality of the weighted least squares estimates are established under various conditions on the regressor variables. These conditions involve different types of scalings, and the scaling factors are obtained explicitly for various types of nonlinear regression models including an interesting model which requires the estimation of unknown frequencies. The estimation of frequencies is a classical problem occurring in many areas like signal processing, environmental time series, astronomy and other areas of physical sciences. We illustrate our methodology using two real data sets taken from geophysics and environmental sciences. The data we consider from geophysics are polar motion (which is now widely known as "Chandlers Wobble"), where one has to estimate the drift parameters, the offset parameters and the two periodicities associated with elliptical motion. The data were first analyzed by Arato, Kolmogorov and Sinai who treat it as a bivariate time series satisfying a finite order time series model. They estimate the periodicities using the coefficients of the fitted models. Our analysis shows that the two dominant frequencies are 12 h and 410 days. The second example, we consider is the minimum/maximum monthly temperatures observed at the Antarctic Peninsula (Faraday/Vernadsky station). It is now widely believed that over the past 50 years there is a steady warming in this region, and if this is true, the warming has serious consequences on ecology, marine life, etc. as it can result in melting of ice shelves and glaciers. Our objective here is to estimate any existing temperature trend in the data, and we use the nonlinear regression methodology developed here to achieve that goal. © 2007 Elsevier B.V. All rights reserved. |
format |
Article in Journal/Newspaper |
author |
Terdik, G Subba Rao, T Jammalamadaka, SR |
spellingShingle |
Terdik, G Subba Rao, T Jammalamadaka, SR On multivariate nonlinear regression models with stationary correlated errors |
author_facet |
Terdik, G Subba Rao, T Jammalamadaka, SR |
author_sort |
Terdik, G |
title |
On multivariate nonlinear regression models with stationary correlated errors |
title_short |
On multivariate nonlinear regression models with stationary correlated errors |
title_full |
On multivariate nonlinear regression models with stationary correlated errors |
title_fullStr |
On multivariate nonlinear regression models with stationary correlated errors |
title_full_unstemmed |
On multivariate nonlinear regression models with stationary correlated errors |
title_sort |
on multivariate nonlinear regression models with stationary correlated errors |
publisher |
eScholarship, University of California |
publishDate |
2007 |
url |
http://www.escholarship.org/uc/item/6rz1d4b6 |
op_coverage |
3793 - 3814 |
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ENVELOPE(-64.256,-64.256,-65.246,-65.246) ENVELOPE(-64.257,-64.257,-65.245,-65.245) |
geographic |
Antarctic Antarctic Peninsula Faraday The Antarctic Vernadsky Station |
geographic_facet |
Antarctic Antarctic Peninsula Faraday The Antarctic Vernadsky Station |
genre |
Antarc* Antarctic Antarctic Peninsula Ice Shelves |
genre_facet |
Antarc* Antarctic Antarctic Peninsula Ice Shelves |
op_source |
Terdik, G; Subba Rao, T; & Jammalamadaka, SR. (2007). On multivariate nonlinear regression models with stationary correlated errors. Journal of Statistical Planning and Inference, 137(11), 3793 - 3814. doi:10.1016/j.jspi.2007.03.050. UC Santa Barbara: Retrieved from: http://www.escholarship.org/uc/item/6rz1d4b6 |
op_relation |
qt6rz1d4b6 http://www.escholarship.org/uc/item/6rz1d4b6 |
op_rights |
public |
op_doi |
https://doi.org/10.1016/j.jspi.2007.03.050 |
container_title |
Journal of Statistical Planning and Inference |
container_volume |
137 |
container_issue |
11 |
container_start_page |
3793 |
op_container_end_page |
3814 |
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1766254255339995136 |