# Nonparametric Statistical Inference for Ergodic Processes

@article{Ryabko2010NonparametricSI, title={Nonparametric Statistical Inference for Ergodic Processes}, author={Daniil Ryabko and B. Ya. Ryabko}, journal={IEEE Transactions on Information Theory}, year={2010}, volume={56}, pages={1430-1435} }

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…

## 31 Citations

### ASYMPTOTIC STATISTICAL ANALYSIS OF STATIONARY ERGODIC TIME SERIES

- Mathematics, Computer Science
- 2012

It is shown how to construct asymptotically consistent efficient algorithms for various statistical problems concerning stationary ergodic time series based on empirical estimates of the distributional distance.

### Asymptotic Nonparametric Statistical Analysis of Stationary Time Series

- Computer Science, MathematicsSpringerBriefs in Computer Science
- 2019

The main objective in this area of research, the objective which is only partially attained, is to understand what is possible and what is not possible to do for stationary time series.

### Clustering processes

- Computer Science, MathematicsICML
- 2010

A very natural asymptotic notion of consistency is proposed, and simple consistent algorithms exist, under most general non-parametric assumptions, which generalizes such classical statistical problems as homogeneity testing and process classification.

### Clustering piecewise stationary processes

- Computer Science2020 IEEE International Symposium on Information Theory (ISIT)
- 2020

Efficient algorithms are proposed which are shown to be asymptotically consistent without any additional assumptions beyond piecewise stationarity in the context of clustering.

### Asymptotically consistent estimation of the number of change points in highly dependent time series

- Computer Science, MathematicsICML
- 2014

It turns out that in this formulation change point estimation can be reduced to time series clustering and an algorithm is proposed that finds the number of change points and locates the changes and is shown to be asymptotically consistent.

### Nonparametric multiple change point estimation in highly dependent time series

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 2013

### Confidence sets in time-series filtering

- Computer Science, Mathematics2011 IEEE International Symposium on Information Theory Proceedings
- 2011

The problem of filtering of finite-alphabet stationary ergodic time series is considered. A method for constructing a confidence set for the (unknown) signal is proposed, such that the resulting set…

### Inferring the residual waiting time for binary stationary time series

- MathematicsKybernetika
- 2014

A sequence of stopping times and universal estimators for these quantities which are pointwise consistent for all ergodic binary stationary processes are presented.

### A consistent clustering-based approach to estimating the number of change-points in highly dependent time-series

- Computer Science, MathematicsArXiv
- 2013

It is shown that a consistent clustering method may be used to estimate the number of change points, under the additional constraint that the correct number of process distributions that generate the data is provided.

### Consistent Algorithms for Clustering Time Series

- Computer ScienceJ. Mach. Learn. Res.
- 2016

A natural notion of consistency is proposed for the problem of clustering, and it is shown that there are simple, computationally efficient algorithms that are asymptotically consistent under extremely weak assumptions on the distributions that generate the data.

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