Asymptotic distributions of M-estimators in a spatial regression model under some fixed and stochastic spatial sampling design

Lahiri, Soumendra and Mukherjee, Kanchan (2004) Asymptotic distributions of M-estimators in a spatial regression model under some fixed and stochastic spatial sampling design. Annals of the Institute of Statistical Mathematics, 56 (2). pp. 225-250. ISSN 1572-9052

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Abstract

In this paper, we consider M-estimators of the regression parameter in a spatial multiple linear regression model. We establish consistency and asymptotic normality of the M-estimators when the data-sites are generated by a class of deterministic as well as a class of stochastic spatial sampling schemes. Under the deterministic sampling schemes, the data-sites are located on a regular grid but may have an infill component. On the other hand, under the stochastic sampling schemes, locations of the data-sites are given by the realizations of a collection of independent random vectors and thus, are irregularly spaced. It is shown that scaling constants of different orders are needed for asymptotic normality under different spatial sampling schemes considered here. Further, in the stochastic case, the asymptotic covariance matrix is shown to depend on the spatial sampling density associated with the stochastic design. Results are established for M-estimators corresponding to certain non-smooth score functions including Huber's e-function and the sign functions (corresponding to the sample quantiles).

Item Type: Journal Article
Journal or Publication Title: Annals of the Institute of Statistical Mathematics
Uncontrolled Keywords: /dk/atira/pure/subjectarea/asjc/2600/2613
Subjects:
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 65680
Deposited By: ep_importer_pure
Deposited On: 15 Jul 2013 09:11
Refereed?: Yes
Published?: Published
Last Modified: 11 Jun 2019 00:12
URI: https://eprints.lancs.ac.uk/id/eprint/65680

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