Statistical hypotheses testing for parameters of binomial conditionally autoregressive model of spatio-temporal data
Abstract
This paper is devoted to new binomial conditional autoregressive model of spatio-temporal data. This model is multidimensional non-homogeneous Markov chain with a finite state space. We use the maximum likelihood method for statistical estimation of the model parameters. We show that these estimators are consistent and asymptotically normally distributed. Fisher information matrix is calculated; it takes block-diagonal form and is nonsingular. The results of the analysis of the asymptotic properties of the maximum likelihood estimators are used to construct a statistic for statistical testing of hypotheses about the values of the parameters of the binomial conditional autoregressive model. Decision rule for statistical hypotheses testing is built and an asymptotic expression of the power of the test is obtained for a family of contiguous alternatives. Experiments have been conducted on simulated data to evaluate performance of the constructed decision rule. Plots of experimental and theoretical estimates of the first type error probability and power of the test in dependence on the length of the observation period are presented, they illustrate adequacy of theoretical and experimental results.
References
- Kang S., McGree1 J., Baade P., et al. Case Study for Modelling Cancer Incidence Using Bayesian Spatio-Temporal Models. Aust. & N. Z. J. Stat. 2015. Vol. 57, issue 3. P. 325–345.
- Xu G., Liang F., Genton M. G. A Bayesian spatio-temporal geostatistical model with an auxiliary lattice for large datasets. Stat. Sinica. 2015. Vol. 25. P. 61–79.
- Zhu X., Genton M. G., Gu Y., et al. Space-time wind speed forecasting for improved power system dispatch (with discussion and rejoinder). TEST. 2014. Vol. 23. P. 1–25.
- Zhu F., Liu S., Shi L. Local influence analysis for Poisson autoregression with an application to stock transaction data. Stat. Neerlandica. 2016. Vol. 7/1. P. 4 –25.
- Kharin Y. S., Zhurak M. K. Binomialʼnaya uslovno avtoregressionnaya modelʼ prostranstvenno-vremennykh dannykh i ee veroyatnostno-statisticheskii analiz [The binomial conditional autoregressive model of the spatio-temporal data and its probabilistic and statistical analysis]. Dokl. Nats. akad. nauk Belarusi. 2015. Vol. 59, No. 6. P. 5–12 (in Russ.).
- Kharin Y. S., Zhurak M. K. Asimptoticheskii analiz otsenok maksimalʼnogo pravdopodobiya parametrov binomialʼnoi uslovno avtoregressionnoi modeli prostranstvenno-vremennykh dannykh [Asymptotic analysis of maximum likelihood estimators for parameters of binomial conditionally autoregressive model of spatio-temporal data]. Izv. Nats. akad. nauk Belarusi. Ser. fiz.-mat. nauk. 2016. No. 1. P. 36 – 45 (in Russ.).
- Kharin Y. S., Zuev N. M., Zhuk E. E. Teoriya veroyatnostei, matematicheskaya i prikladnaya statistika [Probability theory, mathematical and applied statistics]. Minsk, 2011 (in Russ.).
The authors who are published in this journal agree to the following:
- The authors retain copyright on the work and provide the journal with the right of first publication of the work on condition of license Creative Commons Attribution-NonCommercial. 4.0 International (CC BY-NC 4.0).
- The authors retain the right to enter into certain contractual agreements relating to the non-exclusive distribution of the published version of the work (e.g. post it on the institutional repository, publication in the book), with the reference to its original publication in this journal.
- The authors have the right to post their work on the Internet (e.g. on the institutional store or personal website) prior to and during the review process, conducted by the journal, as this may lead to a productive discussion and a large number of references to this work. (See The Effect of Open Access.)
