## Report in Wirtschaftsmathematik (WIMA Report)

### Refine

#### Year of publication

- 2009 (4) (remove)

#### Document Type

- Preprint (4) (remove)

#### Keywords

- hidden variables (2)
- mixture (2)
- nonparametric regression (2)
- AR-ARCH (1)
- EM algorith (1)
- EM algorithm (1)
- Markov switching (1)
- consistency (1)
- geometric ergodicity (1)
- inverse optimization (1)

- 124
- Maximum Likelihood Estimators for Markov Switching Autoregressive Processes with ARCH Component (2009)
- We consider a mixture of AR-ARCH models where the switching between the basic states of the observed time series is controlled by a hidden Markov chain. Under simple conditions, we prove consistency and asymptotic normality of the maximum likelihood parameter estimates combining general results on asymptotics of Douc et al (2004) and of geometric ergodicity of Franke et al (2007).

- 121
- Mixtures of Nonparametric Autoregression, revised (2009)
- We consider data generating mechanisms which can be represented as mixtures of finitely many regression or autoregression models. We propose nonparametric estimators for the functions characterizing the various mixture components based on a local quasi maximum likelihood approach and prove their consistency. We present an EM algorithm for calculating the estimates numerically which is mainly based on iteratively applying common local smoothers and discuss its convergence properties.

- 120
- Mixtures of Nonparametric Autoregressions (2009)
- We consider data generating mechanisms which can be represented as mixtures of finitely many regression or autoregression models. We propose nonparametric estimators for the functions characterizing the various mixture components based on a local quasi maximum likelihood approach and prove their consistency. We present an EM algorithm for calculating the estimates numerically which is mainly based on iteratively applying common local smoothers and discuss its convergence properties.

- 118
- A Note On Inverse Max Flow Problem Under Chebyshev Norm (2009)
- In this paper, we study the inverse maximum flow problem under \(\ell_\infty\)-norm and show that this problem can be solved by finding a maximum capacity path on a modified graph. Moreover, we consider an extension of the problem where we minimize the number of perturbations among all the optimal solutions of Chebyshev norm. This bicriteria version of the inverse maximum flow problem can also be solved in strongly polynomial time by finding a minimum \(s - t\) cut on the modified graph with a new capacity function.