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Asymptotics of Monte Carlo maximum likelihood estimators

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We describe Monte Carlo approximation to the maximum likelihood estimator in models with intractable norming constants and explanatory variables. We consider both sources of randomness (due to the initial sample and to Monte Carlo simulations) and prove asymptotical normality of the estimator.
Rocznik
Strony
295--310
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
  • Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland
autor
  • Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland
  • School of Mathematics, University of Leeds, Woodhouse Lane, Leeds LS2 9JT, United Kingdom
autor
  • Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
Bibliografia
  • [1] J. Besag, Spatial interaction and the statistical analysis of lattice systems, J. R. Stat. Soc. Ser. B. Stat. Methodol. 36 (1974), pp. 192-236.
  • [2] O. Cappé, R. Douc, E. Moulines, and C. Robert, On the convergence of the Monte Carlo maximum likelihood method for latent variable models, Scand. J. Stat. 29 (2002), pp. 615-635.
  • [3] A. P. Dempster, N. M. Laird, and D. B. Rubin, Maximum likelihood from incomplete data via the EM algorithm, J. R. Stat. Soc. Ser. B. Stat. Methodol. 39 (1977), pp. 1-38.
  • [4] T. S. Ferguson, A Course in Large Sample Theory, Chapman and Hall, London 2010.
  • [5] G. Fort and E. Moulines, Convergence of the Monte Carlo expectation maximization for curved exponential families, Ann. Statist. 31 (2003), pp. 1220-1259.
  • [6] C. J. Geyer, On the convergence of Monte Carlo maximum likelihood calculations, J. R. Stat. Soc. Ser. B. Stat. Methodol. 56 (1994), pp. 261-274.
  • [7] C. J. Geyer and E. A. Thompson, Constrained Monte Carlo maximum likelihood for dependent data, J. R. Stat. Soc. Ser. B. Stat. Methodol. 54 (1992), pp. 657-699.
  • [8] F. W. Huffer and H. Wu, Markov chain Monte Carlo for autologistic regression models with application to the distribution of plant species, Biometrics 54 (1998), pp. 509-524.
  • [9] R. A. Levine and G. Casella, Implementations of the Monte Carlo EM algorithm, J. Comput. Graph. Statist. 10 (2001), pp. 422-439.
  • [10] B. Miasojedow, W. Niemiro, J. Palczewski, and W. Rejchel, Adaptive Monte Carlo maximum likelihood, in: Challenges in Computational Statistics and Data Mining, S. Matwin and J. Mielniczuk (Eds.), Stud. Comput. Intell., Vol. 605, Springer, 2016, pp. 247-270.
  • [11] J. Møller, A. N. Pettitt, R. Reeves, and K. K. Berthelsen, An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants, Biometrika 93 (2006), pp. 451-458.
  • [12] W. Niemiro, Asymptotics for M-estimators defined by convex minimization, Ann. Statist. 20 (1992), pp. 1514-1533.
  • [13] D. Pollard, Convergence of Stochastic Processes, Springer, New York 1984.
  • [14] Y. J. Sung and C. J. Geyer, Monte Carlo likelihood inference for missing data models, Ann. Statist. 35 (2007), pp. 990-1011.
  • [15] A. W. van der Vaart, Asymptotic Statistics, Cambridge University Press, Cambridge 1998.
  • [16] G. C. G. Wei and M. A. Tanner, A Monte Carlo implementation of the EM algorithm and the poor man’s data augmentation algorithms, J. Amer. Statist. Assoc. 85 (1990), pp. 699-704.
  • [17] H. Wu and F. W. Huffer, Modeling the distribution of plant species using the autologistic regression model, Environ. Ecol. Stat. 4 (1997), pp. 49-64.
  • [18] M. Zalewska, W. Niemiro, and B. Samoliński, MCMC imputation in autologistic model, Monte Carlo Methods Appl. 16 (2010), pp. 421-438.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-5d0ca70f-7e3c-4124-b43d-c0700dff2016
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