Nonparametric quasi-maximum likelihood estimation for Gaussian locally stationary processes

Dahlhaus, Rainer; Polonik, Wolfgang

Ann. Statist., Tome 34 (2006) no. 1, p. 2790-2824 / Harvested from Project Euclid

Résumé

This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior of the resulting estimator is studied. The results depend on the richness of the class of functions. Both sieve estimation and global estimation are considered. ¶ Our results apply, in particular, to estimation under shape constraints. As an example, autoregressive model fitting with a monotonic variance function is discussed in detail, including algorithmic considerations. ¶ A key technical tool is the time-varying empirical spectral process indexed by functions. For this process, a Bernstein-type exponential inequality and a central limit theorem are derived. These results for empirical spectral processes are of independent interest.

Publié le : 2006-12-15
Classification: Empirical spectral process, exponential inequalities for quadratic forms, nonparametric maximum likelihood estimation, locally stationary processes, sieve estimation, 62M10, 62F30

@article{1179935065,
     author = {Dahlhaus, Rainer and Polonik, Wolfgang},
     title = {Nonparametric quasi-maximum likelihood estimation for Gaussian locally stationary processes},
     journal = {Ann. Statist.},
     volume = {34},
     number = {1},
     year = {2006},
     pages = { 2790-2824},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1179935065}
}

Dahlhaus, Rainer; Polonik, Wolfgang. Nonparametric quasi-maximum likelihood estimation for Gaussian locally stationary processes. Ann. Statist., Tome 34 (2006) no. 1, pp.  2790-2824. http://gdmltest.u-ga.fr/item/1179935065/