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2015 Nonparametric statistical inference for the context tree of a stationary ergodic process
Sandro Gallo, Florencia Leonardi
Electron. J. Statist. 9(2): 2076-2098 (2015). DOI: 10.1214/15-EJS1065

Abstract

We consider the problem of estimating the context tree of a stationary ergodic process with finite alphabet without imposing additional conditions on the process. As a starting point we introduce a Hamming metric in the space of irreducible context trees and we use the properties of the weak topology in the space of ergodic stationary processes to prove that if the Hamming metric is unbounded, there exist no consistent estimators for the context tree. Even in the bounded case we show that there exist no two-sided confidence bounds. However we prove that one-sided inference is possible in this general setting and we construct a consistent estimator that is a lower bound for the context tree of the process with an explicit formula for the coverage probability. We develop an efficient algorithm to compute the lower bound and we apply the method to test a linguistic hypothesis about the context tree of codified written texts in European Portuguese.

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Sandro Gallo. Florencia Leonardi. "Nonparametric statistical inference for the context tree of a stationary ergodic process." Electron. J. Statist. 9 (2) 2076 - 2098, 2015. https://doi.org/10.1214/15-EJS1065

Information

Received: 1 September 2014; Published: 2015
First available in Project Euclid: 17 September 2015

zbMATH: 1327.62457
MathSciNet: MR3397402
Digital Object Identifier: 10.1214/15-EJS1065

Subjects:
Primary: 62G15 , 62G20 , 62M09
Secondary: 60G10 , 60J10

Keywords: Confidence bounds , consistent estimation , Context tree , nonparametric inference , Variable length markov chain

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.9 • No. 2 • 2015
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