Nonparametric Statistical Inference for
Daniil Ryabko, Boris Ya. Ryabko · 2010
In this work, a method for statistical analysis of time series is proposed, which is used to obtain solutions to some classical problems of mathematical statistics under the only assumption that the process generating the data is stationary ergodic. Namely, three problems are considered: goodness-of-fit (or identity) testing, process classification, and the change point problem. For each of the problems a test is constructed that is asymptotically accurate for the case when the data is generated by stationary ergodic processes. The tests are based on empirical estimates of distributional distance. All the algorithms are based on empirical estimates of distribu- tional distance, which is in the core of the suggested approach. We suggest that the proposed approach can be applied to other problems of statistical analysis of time series, with the view of establishing principled positive results, leaving the task of findingoptimalalgorithmsforeachparticularproblemasatopic