Abstract:

Goodness-of-fit tests for stationary distributions of dependent data are considered, based on $f$-divergences of observed and theoretical cell frequencies. Pearson's $X^2_n$ is a special version. A methodology is presented leading to asymptotically $\alpha$-level variants of these tests, and also to the selection of most powerful versions. This methodology is illustrated on binary Markov data. Similar procedures have been previously established for independent data. The possibility to extend these procedures to dependent data is a new argument in favour of the $f$-divergence alternatives to the classical Pearson's $X^2_n$.