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 language | English |
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Pages (from-to) | 1073-1099 |
Number of pages | 27 |
Journal | Alea |
Volume | 21 |
Issue number | 2 |
DOIs | |
State | Published - 2024 |
Bibliographical note
Publisher Copyright:© (2023), (Instituto Nacional de Matematica Pura e Aplicada). All Rights Reserved.
Keywords
- nonparametric estimation
- stationary processes