Density estimation for spatial-temporal models

In this paper a k-nearest neighbor type estimator of the marginal density function for a random field which evolves with time is considered. Considering dependence, the consistency and asymptotic distribution are studied for the stationary and nonstationary cases. In particular, the parametric rate of convergence <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\sqrt{T}$</EquationSource> </InlineEquation> is proven when the random field is stationary. The performance of the estimator is shown by applying our procedure to a real data example. Copyright Sociedad de Estadística e Investigación Operativa 2013