On latent process models in multi-dimensional space

Zuofeng Shang

Statistics & Probability Letters, 2012, vol. 82, issue 7, 1259-1266

Abstract: 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.

Keywords: M-estimation; Asymptotic normality; Mixing conditions; Spatial Poisson model; Spatial linear quantile regression (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spl.2012.03.022

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