On latent process models in multi-dimensional space

Latent process models have been widely applied to time series and spatial data which involve complex correlation structures. However, the existing approaches assume a known distributional property of the observations given the latent process. Furthermore, there seems to be no literature treating the asymptotic properties of the latent process model in general multi-dimensional space (with dimension bigger than 2). In this paper, we propose to estimate the unknown model parameters of the latent process model in multi-dimensional space by an M-estimation approach, and derive the asymptotic normality, together with the explicit limiting variance matrix, for the estimates. The proposed method is of a distribution-free feature. Applications in three concrete situations are demonstrated.