Asymptotic analysis of statistical estimators of parameters for binomial conditionally autoregressive model of spatio-temporal data

Authors

  • Maryna K. Dauhaliova Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus
  • Yuriy S. Kharin Research Institute for Applied Problems of Mathematics and Informatics, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus; Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

Keywords:

spatio-temporal data, inhomogeneous Markov chain, ergodic principle, maximum likelihood estimator, consistency of estimator, asymptotic normality

Abstract

The binomial conditionally autoregressive model of discrete spatio-temporal data is considered in this paper. This model is a multidimensional inhomogeneous Markov chain with a finite state space. Conditions, under which the binomial conditionally autoregressive model satisfies the ergodic principle, are found in case when exogenous factors depend on time. The maximum likelihood approach is used for statistical estimation of model parameters. It is proved that the constructed maximum likelihood estimators are consistent and asymptotically normal distributed for any bounded values of the model parameters and any bounded values of the exogenous factor in case of statistical identifiability of model parameters. Results of computer experiments on simulated data illustrate consistency of maximum likelihood estimators. 

Author Biographies

  • Maryna K. Dauhaliova, Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus

    junior researcher

  • Yuriy S. Kharin, Research Institute for Applied Problems of Mathematics and Informatics, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus; Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

    corresponding member of the National Academy of Sciences of Belarus, doctor of science (physics and ma the matics); director, Research Institute for Applied Problems of Mathematics and Informatics, Belarusian State University; professor at the department of mathematical modeling and data analysis, faculty of applied mathematics and informatics, Belarusian State University

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Published

2019-01-19

Issue

No. 2 (2018): Journal of the Belarusian State University. Mathematics and Informatics

Section

Probability Theory and Mathematical Statistics

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How to Cite

[1]
Dauhaliova, M.K. and Kharin, Y.S. 2019. Asymptotic analysis of statistical estimators of parameters for binomial conditionally autoregressive model of spatio-temporal data. Journal of the Belarusian State University. Mathematics and Informatics. 2 (Jan. 2019), 47–57.