Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/105022
Title: Asymptotic distributions of M-estimators in a spatial regression model under some fixed and stochastic spatial sampling designs
Authors: Lahiri, S.N.
Mukherjee, K. 
Keywords: Central limit theorem
Increasing-domain asymptotics
Infill sampling
Long range dependence
Random field
Spatial sampling design
Stochastic design
Strong mixing
Issue Date: 2004
Citation: Lahiri, S.N.,Mukherjee, K. (2004). Asymptotic distributions of M-estimators in a spatial regression model under some fixed and stochastic spatial sampling designs. Annals of the Institute of Statistical Mathematics 56 (2) : 225-250. ScholarBank@NUS Repository.
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 ψ-function and the sign functions (corresponding to the sample quantiles).
Source Title: Annals of the Institute of Statistical Mathematics
URI: http://scholarbank.nus.edu.sg/handle/10635/105022
ISSN: 00203157
Appears in Collections:Staff Publications

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