Local polynomial quasi-likelihood regression on random fields

Summary In this paper, local quasi-likelihood regression is considered for stationary random fields of dependent variables. In the case of independent data, local polynomial quasi-likelihood regression is known to have several appealing features such as minimax efficiency, design adaptivity and good boundary behaviour. These properties are shown to carry over to the case of random fields. The asymptotic normality of the regression estimator is established and explicit formulae for its asymptotic bias and variance are derived for strongly mixing stationary random fields. The extension to multi-dimensional covariates is also provided in full generality. Moreover, evaluation of the finite sample performance is made through a simulation study.