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On semiparametric inference of geostatistical models via local Karhunen–Loève expansion
Author(s) -
Chu Tingjin,
Wang Haonan,
Zhu Jun
Publication year - 2014
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12053
Subject(s) - inference , consistency (knowledge bases) , mathematics , statistical inference , computer science , statistics , artificial intelligence
Summary We develop a semiparametric approach to geostatistical modelling and inference. In particular, we consider a geostatistical model with additive components, where the form of the covariance function of the spatial random error is not prespecified and thus is flexible. A novel, local Karhunen–Loève expansion is developed and a likelihood‐based method is devised for estimating the model parameters and statistical inference. A simulation study demonstrates sound finite sample properties and a real data example is given for illustration. Finally, the theoretical properties of the estimates are explored and, in particular, consistency results are established.