Jungyoon Lee and Peter M Robinson

Published 26 January 2018

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We consider adaptive tests and estimates which are asymptotically efficient in the presence of unknown, nonparametric, distributional form in pure spatial models. A novel adaptive Lagrange Multiplier testing procedure for lack of spatial dependence is proposed and extended to linear regression with spatially correlated errors. Feasibility of adaptive estimation is verified and its efficiency improvement over Gaussian pseudo maximum likelihood is shown to be either less than, or more than, for models with explanatory variables. The paper covers a general class of semiparametric spatial models allowing nonlinearity in the parameters and/or the weight matrix, in addition to unknown distribution.