Dokument

Summary:
The thesis consists of three papers. In the paper “Testing for the number of states in hidden Markov models” we generalize existing testing procedures for i.i.d. mixture models to hidden Markov models by considering penalized quasi-likelihood ratio tests. They can be applied in order to assess the number of states k of a hidden Markov model with univariate state-dependent distribution fulfilling certain regularity conditions. In the paper “Hidden Markov Models with state-dependent mixtures” we analyze the dependence structure of hidden Markov models with state-dependent finite mixtures. Our results have applications to model selection as well as to model-based clustering. We propose algorithms for both purposes. In the paper “Peaks vs Components” we analyze welfare groups of countries all over the world by applying finite mixture models to the GDP per capita of 190 countries from 1970 to 2009.

Bibliographie / References

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11. Peaks vs Components
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14. Table 4: Estimated means (based on the log GDP data, but displayed on the original scale) of the three or respectively two distinct groups. Peaks vs Components low middle high 1970 0.50 0.33 0.17 1971 0.48 0.35 0.17 1972 0.43 0.40 0.17 1973 0.40 0.44 0.17 1974 0.39 0.44 0.17 1975 0.35 0.49 0.15 1976 0.30 0.56 0.14 1977 0.29 0.56 0.15 1978 0.31 0.54 0.16 1979 0.23 0.62 0.15 1980 0.33 0.51 0.16 1981 0.35 0.47 0.17 1982 0.37 0.46 0.17 1983 0.33 0.51 0.17 1984 0.33 0.49 0.18 1985 0.33 0.49 0.18 1986 0.32 0.50 0.18 1987 0.34 0.48 0.18 1988 0.30 0.51 0.18 1989 0.31 0.52 0.17 1990 0.31 0.50 0.19 1991 0.25 0.57 0.18 1992 0.42 0.36 0.22 1993 0.49 0.27 0.24 1994 0.50 0.25 0.24 1995 0.53 0.23 0.24 (a) Component weights for the years 1970 to 1995 (balanced dataset). low high 1996 0.81 0.19 1997 0.81 0.19 1998 0.81 0.19 1999 0.81 0.19 2000 0.82 0.18 2001 0.81 0.19 2002 0.81 0.19 2003 0.82 0.18 2004 0.83 0.17 2005 0.82 0.18 2006 0.82 0.18 2007 0.83 0.17 2008 0.83 0.17 2009 0.83 0.17
15. (a) Component means for the years 1970 to 1995 (balanced dataset). low high 1996 2752 25910
16. (b) Component weights for the years 1996 to 2009 (balanced dataset).
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