Asymptotic properties of rank estimators in a simple spatial linear regression model under spatial sampling designs

Asymptotic properties of rank estimators in a simple spatial linear regression model under... Jpn J Stat Data Sci https://doi.org/10.1007/s42081-018-0014-6 Asymptotic properties of rank estimators in a simple spatial linear regression model under spatial sampling designs Eika Yamada Received: 28 November 2017 / Accepted: 21 May 2018 Japanese Federation of Statistical Science Associations 2018 Abstract In this study, we derive the asymptotic normality of a class of rank estimators in a simple spatial linear regression model, when errors form a strongly mixing random field and when the spatial data are both on the lattice and on the irregularly spaced spatial sites. This result in turn is used to investigate the asymptotic relative efficiency (ARE) of these estimators relative to the LSE. In addition, we conduct numerical experiments under both the lattice and the irregu- larly spaced sampling, which lends support to the robustness of these estimators compared to the LSE. Keywords Spatial regression  Strong-mixing random field  Spatial sampling designs  Rank estimator  Robustness  Asymptotic normality 1 Introduction The least-squares estimator (LSE) is a popular estimator because it has desirable properties under regularity conditions and is always easily available. However, it is well known that it is not robust against heavy-tail error distributions. On the other hand, rank estimators are http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Japanese Journal of Statistics and Data Science Springer Journals

Asymptotic properties of rank estimators in a simple spatial linear regression model under spatial sampling designs

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Publisher
Springer Singapore
Copyright
Copyright © 2018 by Japanese Federation of Statistical Science Associations
Subject
Statistics; Statistical Theory and Methods; Statistics and Computing/Statistics Programs; Statistics for Business/Economics/Mathematical Finance/Insurance; Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences; Statistics for Life Sciences, Medicine, Health Sciences; Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law
ISSN
2520-8756
eISSN
2520-8764
D.O.I.
10.1007/s42081-018-0014-6
Publisher site
See Article on Publisher Site

Abstract

Jpn J Stat Data Sci https://doi.org/10.1007/s42081-018-0014-6 Asymptotic properties of rank estimators in a simple spatial linear regression model under spatial sampling designs Eika Yamada Received: 28 November 2017 / Accepted: 21 May 2018 Japanese Federation of Statistical Science Associations 2018 Abstract In this study, we derive the asymptotic normality of a class of rank estimators in a simple spatial linear regression model, when errors form a strongly mixing random field and when the spatial data are both on the lattice and on the irregularly spaced spatial sites. This result in turn is used to investigate the asymptotic relative efficiency (ARE) of these estimators relative to the LSE. In addition, we conduct numerical experiments under both the lattice and the irregu- larly spaced sampling, which lends support to the robustness of these estimators compared to the LSE. Keywords Spatial regression  Strong-mixing random field  Spatial sampling designs  Rank estimator  Robustness  Asymptotic normality 1 Introduction The least-squares estimator (LSE) is a popular estimator because it has desirable properties under regularity conditions and is always easily available. However, it is well known that it is not robust against heavy-tail error distributions. On the other hand, rank estimators are

Journal

Japanese Journal of Statistics and Data ScienceSpringer Journals

Published: Jun 5, 2018

References

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