Goodness of fit for lattice processes

The paper discusses tests for the correct specification of a model when data is observed in a d -dimensional lattice, extending previous work when the data is collected in the real line. As it happens with the latter type of data, the asymptotic distributions of the tests are functionals of a Gaussian sheet process, say B ( ν ) , ν ∈ [ 0 , π ] d . Since it is not easy to find a time transformation h ( ν ) such that B ( h ( ν ) ) becomes the standard Brownian sheet, a consequence is that the critical values are difficult, if at all possible, to obtain. So, to overcome the problem of its implementation, we propose employing a bootstrap approach, showing its validity in our context.