Central Limit Theorems for Conditional Markov Chains

Mathieu Sinn, Bei Chen
Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics, PMLR 31:554-562, 2013.

Abstract

This paper studies Central Limit Theorems for real-valued functionals of Conditional Markov Chains. Using a classical result by Dobrushin (1956) for non-stationary Markov chains, a conditional Central Limit Theorem for fixed sequences of observations is established. The asymptotic variance can be estimated by resampling the latent states conditional on the observations. If the conditional means themselves are asymptotically normally distributed, an unconditional Central Limit Theorem can be obtained. The methodology is used to construct a statistical hypothesis test which is applied to synthetically generated environmental data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v31-sinn13a, title = {Central Limit Theorems for Conditional Markov Chains}, author = {Sinn, Mathieu and Chen, Bei}, booktitle = {Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics}, pages = {554--562}, year = {2013}, editor = {Carvalho, Carlos M. and Ravikumar, Pradeep}, volume = {31}, series = {Proceedings of Machine Learning Research}, address = {Scottsdale, Arizona, USA}, month = {29 Apr--01 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v31/sinn13a.pdf}, url = {https://proceedings.mlr.press/v31/sinn13a.html}, abstract = {This paper studies Central Limit Theorems for real-valued functionals of Conditional Markov Chains. Using a classical result by Dobrushin (1956) for non-stationary Markov chains, a conditional Central Limit Theorem for fixed sequences of observations is established. The asymptotic variance can be estimated by resampling the latent states conditional on the observations. If the conditional means themselves are asymptotically normally distributed, an unconditional Central Limit Theorem can be obtained. The methodology is used to construct a statistical hypothesis test which is applied to synthetically generated environmental data.} }
Endnote
%0 Conference Paper %T Central Limit Theorems for Conditional Markov Chains %A Mathieu Sinn %A Bei Chen %B Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2013 %E Carlos M. Carvalho %E Pradeep Ravikumar %F pmlr-v31-sinn13a %I PMLR %P 554--562 %U https://proceedings.mlr.press/v31/sinn13a.html %V 31 %X This paper studies Central Limit Theorems for real-valued functionals of Conditional Markov Chains. Using a classical result by Dobrushin (1956) for non-stationary Markov chains, a conditional Central Limit Theorem for fixed sequences of observations is established. The asymptotic variance can be estimated by resampling the latent states conditional on the observations. If the conditional means themselves are asymptotically normally distributed, an unconditional Central Limit Theorem can be obtained. The methodology is used to construct a statistical hypothesis test which is applied to synthetically generated environmental data.
RIS
TY - CPAPER TI - Central Limit Theorems for Conditional Markov Chains AU - Mathieu Sinn AU - Bei Chen BT - Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics DA - 2013/04/29 ED - Carlos M. Carvalho ED - Pradeep Ravikumar ID - pmlr-v31-sinn13a PB - PMLR DP - Proceedings of Machine Learning Research VL - 31 SP - 554 EP - 562 L1 - http://proceedings.mlr.press/v31/sinn13a.pdf UR - https://proceedings.mlr.press/v31/sinn13a.html AB - This paper studies Central Limit Theorems for real-valued functionals of Conditional Markov Chains. Using a classical result by Dobrushin (1956) for non-stationary Markov chains, a conditional Central Limit Theorem for fixed sequences of observations is established. The asymptotic variance can be estimated by resampling the latent states conditional on the observations. If the conditional means themselves are asymptotically normally distributed, an unconditional Central Limit Theorem can be obtained. The methodology is used to construct a statistical hypothesis test which is applied to synthetically generated environmental data. ER -
APA
Sinn, M. & Chen, B.. (2013). Central Limit Theorems for Conditional Markov Chains. Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 31:554-562 Available from https://proceedings.mlr.press/v31/sinn13a.html.

Related Material