On latent process models in multi-dimensional space

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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.

Original languageEnglish (US)
Pages (from-to)1259-1266
Number of pages8
JournalStatistics and Probability Letters
Issue number7
StatePublished - Jul 2012
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Asymptotic normality
  • M-estimation
  • Mixing conditions
  • Spatial Poisson model
  • Spatial linear quantile regression


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