Countable alphabet stationary processes with at least one memory word and intermittent estimation with universal rates

Gusztáv Morvai, Benjamin Weiss

Research output: Contribution to journalArticlepeer-review

Abstract

We present here a number of results that provide universal rates of convergence for certain non parametric estimation problems. For example consider the class C of all finite order Markov chains on a countable alphabet and the problem of estimating the conditional distribution of Xn+1 given the first n outputs of the process. We will give a sequence of stopping times with density one and estimators at those times such that almost surely our estimators will eventually differ from the true conditional distribution by no more than a certain fixed sequence tending to zero. Similar results are given for estimating the conditional expectation of Xn+1 given the first n outputs, but here some additional moment conditions are required. An example shows that this is not possible in general.

Original languageEnglish
Pages (from-to)1073-1099
Number of pages27
JournalAlea
Volume21
Issue number2
DOIs
StatePublished - 2024

Bibliographical note

Publisher Copyright:
© (2023), (Instituto Nacional de Matematica Pura e Aplicada). All Rights Reserved.

Keywords

  • nonparametric estimation
  • stationary processes

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