On semiparametric inference of geostatistical models via local Karhunen–Loève expansion

type="main" xml:id="rssb12053-abs-0001"> <title type="main">Summary</title> <p>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.