Free Access
Issue
ESAIM: PS
Volume 16, 2012
Page(s) 25 - 47
DOI https://doi.org/10.1051/ps/2011153
Published online 22 March 2012
  1. R.C. Bradley, Basic properties of strong mixing conditions. A survey and some open questions. Probab. Surveys 2 (2005) 107–144. [CrossRef] [MathSciNet] [Google Scholar]
  2. D. Dacunha-Castelle and E. Gassiat, The estimation of the order of a mixture model. Bernoulli 3 (1997) 279–299. [CrossRef] [MathSciNet] [Google Scholar]
  3. D. Dacunha-Castelle and E. Gassiat, Testing in locally conic models and application to mixture models. ESAIM : PS 1 (1997) 285–317. [CrossRef] [EDP Sciences] [Google Scholar]
  4. D. Dacunha-Castelle and E. Gassiat, Testing the order of a model using locally conic parametrization : population mixtures and stationary ARMA processes. Ann. Stat. 27 (1999) 1178–1209. [CrossRef] [MathSciNet] [Google Scholar]
  5. R. Douc, E. Moulines and T. Rydén, Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime. Ann. Stat. 32 (2004) 2254–2304. [CrossRef] [MathSciNet] [Google Scholar]
  6. P. Doukhan, Mixing : properties and examples. Springer-Verlag, New York. Lect. Notes in Stat. 85 (1994). [Google Scholar]
  7. P. Doukhan, P. Massart and E. Rio, Invariance principles for absolutely regular empirical processes. Ann. Inst. Henri Poincaré 31 (1995) 393–427. [Google Scholar]
  8. Ch. Engel and J.D. Hamilton, Long swings in the dollar : are they in the data and do markets know it? Am. Econ. Rev. 80 (1990) 689–713. [Google Scholar]
  9. C. Francq and M. Roussignol, Ergodicity of autoregressive processes with Markov-switching and consistency of the maximum likelihood estimator. Statistics 32 (1998) 151–173. [CrossRef] [MathSciNet] [Google Scholar]
  10. K. Fukumizu, Likelihood ratio of unidentifiable models and multilayer neural networks. Ann. Stat. 31 (2003) 833–851. [CrossRef] [Google Scholar]
  11. R. Garcia, Asymptotic null distribution of the likelihood ratio test in Markov switching models. Internat. Econ. Rev. 39 (1998) 763–788. [CrossRef] [Google Scholar]
  12. E. Gassiat, Likelihood ratio inequalities with applications to various mixtures. Ann. Inst. Henri Poincaré 38 (2002) 897–906. [CrossRef] [Google Scholar]
  13. E. Gassiat and C. Keribin, The likelihood ratio test for the number of components in a mixture with Markov regime. ESAIM : PS 4 (2000) 25–52. [CrossRef] [EDP Sciences] [Google Scholar]
  14. J.D. Hamilton, A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57 (1989) 357–384. [CrossRef] [MathSciNet] [Google Scholar]
  15. J.D. Hamilton, Analysis of time series subject to changes in regime. J. Econom. 64 (1990) 307–333. [CrossRef] [Google Scholar]
  16. B.E. Hansen, The likelihood ratio test under nonstandard conditions : testing the Markov switching model of GNP. J. Appl. Econom. 7 (1992) 61–82. [CrossRef] [Google Scholar]
  17. B.E. Hansen, Erratum : The likelihood ratio test under nonstandard conditions : testing the Markov switching model of GNP. J. Appl. Econom. 11 (1996) 195–198. [CrossRef] [Google Scholar]
  18. B.E. Hansen, Inference when a nuisance parameter is not identified under the null hypothesis. Econometrica 64 (1996) 413–430. [CrossRef] [MathSciNet] [Google Scholar]
  19. J. Henna, On estimating the number of constituents of a finite mixture of continuous distributions. Ann. Inst. Statist. Math. 37 (1985) 235–240. [CrossRef] [MathSciNet] [Google Scholar]
  20. A.J. Izenman and C. Sommer, Philatelic mixtures and multivariate densities. J. Am. Stat. Assoc. 83 (1988) 941–953. [CrossRef] [Google Scholar]
  21. C. Keribin, Consistent estimation of the order of mixture models. Sankhya : The Indian Journal of Statistics 62 (2000) 49–66. [Google Scholar]
  22. V. Krishnamurthy and T. Rydén, Consistent estimation of linear and non-linear autoregressive models with Markov regime. J. Time Ser. Anal. 19 (1998) 291–307. [CrossRef] [MathSciNet] [Google Scholar]
  23. P.-S. Lam, The Hamilton model with a general autoregressive component : estimation and comparison with other models of economic time series. J. Monet. Econ. 26 (1990) 409–432. [CrossRef] [Google Scholar]
  24. B.G. Leroux, Maximum penalized likelihood estimation for independent and Markov-dependent mixture models. Biometrics 48 (1992) 545–558. [CrossRef] [PubMed] [Google Scholar]
  25. B.G. Leroux, Consistent estimation of a mixing distribution. Ann. Stat. 20 (1992) 1350–1360. [CrossRef] [Google Scholar]
  26. B.G. Lindsay, Moment matrices : application in mixtures. Ann. Stat. 17 (1983) 722–740. [CrossRef] [Google Scholar]
  27. X. Liu and Y. Shao, Asymptotics for likelihood ratio tests under loss of identifiability. Ann. Stat. 31 (2003) 807–832. [CrossRef] [Google Scholar]
  28. R. Rios and L.A. Rodriguez, Penalized estimate of the number of states in Gaussian linear AR with Markov regime. Electron. J. Stat. 2 (2008) 1111–1128. [CrossRef] [MathSciNet] [Google Scholar]
  29. K. Roeder, A graphical technique for determining the number of components in a mixture of normals. J. Am. Stat. Assoc. 89 (1994) 487–495. [CrossRef] [Google Scholar]
  30. T. Ryden, Estimating the order of hidden Markov models. Statistics 26 (1995) 345–354. [CrossRef] [MathSciNet] [Google Scholar]
  31. G.W. Schwert, Business cycles, financial crises and stock volatility. Carnegie-Rochester Conf. Ser. Public Policy 31 (1989) 83–125. [CrossRef] [Google Scholar]
  32. A.W. Van der Vaart, Asymptotic Statistics. Cambridge University Press (2000). [Google Scholar]
  33. C.S. Wong and W.K. Li, On a mixture autoregressive model. J. R Stat. Soc. Ser. B 62 (2000) 95–115. [Google Scholar]
  34. J.F. Yao and J.G. Attali, On stability of nonlinear AR processes with Markov switching. Adv. Appl. Probab. 32 (2000) 394–407. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.