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Likelihood‐based inference for spatiotemporal data with censored and missing responses

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  • Katherine A. L. Valeriano
  • Victor H. Lachos
  • Marcos O. Prates
  • Larissa A. Matos

Abstract

This paper proposes an alternative method to deal with spatiotemporal data with censored and missing responses using the SAEM algorithm. This algorithm is a stochastic approximation of the widely used EM algorithm and is an important tool for models in which the E‐step does not have an analytic form. Besides the algorithm developed to estimate the model parameters from a likelihood‐based perspective, we present analytical expressions to compute the observed information matrix. Global influence measures are also developed and presented. Several simulation studies are conducted to examine the asymptotic properties of the SAEM estimates. The proposed method is illustrated by environmental data analysis. The computing codes are implemented in the new R package StempCens.

Suggested Citation

  • Katherine A. L. Valeriano & Victor H. Lachos & Marcos O. Prates & Larissa A. Matos, 2021. "Likelihood‐based inference for spatiotemporal data with censored and missing responses," Environmetrics, John Wiley & Sons, Ltd., vol. 32(3), May.
    • Handle: RePEc:wly:envmet:v:32:y:2021:i:3:n:e2663
    DOI: 10.1002/env.2663
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    References listed on IDEAS

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    1. Hong‐Tu Zhu & Sik‐Yum Lee, 2001. "Local influence for incomplete data models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 111-126.
    2. Victor H. Lachos & Dipankar Bandyopadhyay & Dipak K. Dey, 2011. "Linear and Nonlinear Mixed-Effects Models for Censored HIV Viral Loads Using Normal/Independent Distributions," Biometrics, The International Biometric Society, vol. 67(4), pages 1594-1604, December.
    3. Ma, Chunsheng, 2003. "Spatio-temporal stationary covariance models," Journal of Multivariate Analysis, Elsevier, vol. 86(1), pages 97-107, July.
    4. Zaida C. Quiroz & Marcos O. Prates & Håvard Rue, 2015. "A Bayesian approach to estimate the biomass of anchovies off the coast of Perú," Biometrics, The International Biometric Society, vol. 71(1), pages 208-217, March.
    5. Víctor H. Lachos & Larissa A. Matos & Thais S. Barbosa & Aldo M. Garay & Dipak K. Dey, 2017. "Influence diagnostics in spatial models with censored response," Environmetrics, John Wiley & Sons, Ltd., vol. 28(7), November.
    6. Bakar, Khandoker Shuvo & Sahu, Sujit K., 2015. "spTimer: Spatio-Temporal Bayesian Modeling Using R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i15).
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    Cited by:

    1. Galarza, Christian E. & Matos, Larissa A. & Castro, Luis M. & Lachos, Victor H., 2022. "Moments of the doubly truncated selection elliptical distributions with emphasis on the unified multivariate skew-t distribution," Journal of Multivariate Analysis, Elsevier, vol. 189(C).

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