ML, PL, QL in Markov chain models

Scandinavian Journal of Statistics

Volumn 35, Issue 1, 2008, Pages 64-82

  Hjort, Nils Lid ^a   Varin, Cristiano ^b  

^a UNIVERSITY OF OSLO   (Norway)

^b UNIVERSITY OF PADOVA   (Italy)

Author keywords

Composite likelihood; DNA; Estimator performance; Markov chains; Pseudo likelihood; Quasi likelihood; Spatial models

Indexed keywords

EID: 38849199252     PISSN: 03036898     EISSN: 14679469     Source Type: Journal    
DOI: 10.1111/j.1467-9469.2007.00559.x     Document Type: Article

References (35)

1. Anderson, T. W. Goodman, L. A. (1957). Statistical inference about Markov chains. Ann. Math. Stat. 28, 89 110.
2. Barry, D. Hartigan, J. A. (1987). Asynchronous distance between homologous DNA sequences. Biometrics 43, 261 276.
3. Basawa, I. V. Prakasa Rao, B. L. S. (1980). Statistical inference for stochastic processes. Academic Press, London.
4. Besag, J. (1974). Spatial interaction and the statistical analysis of lattice systems (with discussion contributions). J. Roy. Statist. Soc. Ser. B 36, 192 236.
5. Besag, J. (1975). Statistical analysis of non-lattice data. Statistician 24, 179 195.
6. Besag, J. (1977). Some methods of statistical analysis for spatial data. Bull. Inst. Int. Stat. 47, 77 92.
7. Billingsley, P. (1961a). Statistical inference for Markov processes. Statistical Research Monographs, Vol, University of Chicago Press, Chicago, IL.
8. Billingsley, P. (1961b). Statistical methods in Markov chains. Ann. Math. Stat. 32, 12 40.
9. Blaisdell, B. E. (1985). A method for estimating from two aligned present day DNA sequences their ancestral composition and subsequent rates of composition and subsequent rates of substitution, possibly different in the two lineages, corrected for multiple and parallel substitutions at the same site. J. Mol. Evol. 22, 69 81.
10. Cox, D. R. Reid, N. (2004). A note on pseudolikelihood constructed from marginal densities. Biometrika 91, 729 737.
11. Davison, A. C. (2003). Statistical models. Cambridge University Press, Cambridge.
12. Durret, R. (2002). Probability models for DNA sequence evolution. Probability and its applications. Springer-Verlag, New York.
13. Fearnhead, P. Donnelly, P. (2002). Approximate likelihood methods for estimating local recombination rates. J. Roy. Statist. Soc. Ser. B 64, 657 680.
14. Fokianos, K. Kedem, B. (2003). Regression theory for categorical time series. Stat. Science 18, 357 375.
15. Glasbey, C. A. (2001). Non-linear autoregressive time series with multivariate Gaussian mixtures as marginal distributions. Appl. Statist. 50, 143 154.
16. Heagerty, P. J. Lele, S. R. (1998). A composite likelihood approach to binary spatial data. J. Amer. Statist. Assoc. 93, 1099 1111.
17. Henderson, R. Shimakura, S. (2003). A serially correlated gamma frailty model for longitudinal count data. Biometrika 90, 355 366.
18. Hjort, N. L. Mohn, E. (1987). Topics in the statistical analysis of remotely sensed data (with discussion contributions). Bull. Int. Stat. Inst. 52 (Proceedings of the ISI Meeting, Tokyo), 23 44.
19. Hjort, N. L. Omre, H. (1994). Topics in spatial statistics (with discussion contributions). Scand. J. Stat. 21, 289 357.
20. Hjort, N. L. Varin, C. (2005). ML, PL, QL in Markov chain models. Statistical Research Report, Department of Mathematics, University of Oslo, Oslo. Available at: http://homes.stat.unipd.it/sammy/.
21. Hobolth, A. Jensen, J. L. (2005). Statistical inference in evolutionary models of DNA sequences via the EM algorithm. Research report No. 455. Department of Theoretical Statistics, University of Aarhus, Aarhus.
22. Homleid, M. (1995). Statistical methods applied in meteorology. Cand. Scient. Thesis. Department of Mathematics, University of Oslo, Oslo.
23. Karlin, S. Taylor, H. M. (1975). A first course in stochastic processes. Academic Press, New York.
24. Kimura, M. (1980). A simple method for estimating evolutionary rates of base substitutions through comparative studies of nucleotide sequences. J. Mol. Evol. 16, 111 120.
25. Kimura, M. (1981). Estimation of evolutionary distances between homologous nucleotide sequences. Proc. Natl. Acad. Sci. USA 78, 454 458.
26. de Leon, A. R. (2005). Pairwise likelihood approach to grouped continuous model and its extension. Statist. Prob. Lett. 75, 49 57.
27. Lindsay, B. (1988). Composite likelihood methods. Contemporary Mathematics 80, 221 239.
28. Markov, A. A. (1906). Rasprostranenie zakona bol'shih chisel na velichiny, zavisyashchie drug ot druga. [Extending the law of large numbers for variables that are dependent of each other.] Izvestiya Fiziko-matematicheskogo obshchestva pri Kazanskom universitete 15 (2-ya seriya 124 156.
29. Markov A. A. (1913). Primer statisticheskogo issledovaniya nad tekstom 'Evgeniya Onegina', illyustriruyushchij svyaz' ispytanij v tsep'. [Example of a statistical investigation illustrating the transitions in the chain for the 'Evgenii Onegin' text.] Izvestiya Akademii Nauk, Sankt-Peterburg 7 (6-ya seriya 153 162.
30. Nott, D. J. Rydén, T. (1999). Pairwise likelihood methods for inference in image models. Biometrika 86, 661 676.
31. Parner, E. T. (2001). A composite likelihood approach to multivariate survival data. Scand. J. Statist. 28, 295 302.
32. Pushkin, A. S. (1977). Eugene Onegin [translated by C. H. Johnston Penguin Classics, London. (There are various later reprints of essentially the same translation of Pushkin's 1833 epic.)
33. Renard, D., Molenberghs, G. Geys, H. (2004). A pairwise likelihood approach to estimation in multilevel probit models. Comput. Statist. Data Anal. 44, 649 667.
34. Varin, C., Høst, G. Skare, Ø. (2005). Pairwise likelihood inference in spatial generalized linear mixed models. Comput. Statist. Data Anal. 49, 1173 1191.
35. Wedderburn, R. W. M. (1974). Quasi-likelihood functions, generalized linear models and the Gauss-Newton method. Biometrika 61, 439 447.