Estimating the transition matrix of a Markov chain observed at random times

Flavia Barsotti; Yohann De Castro; Thibault Espinasse; Paul Rochet

doi:10.1016/j.spl.2014.07.009

Estimating the transition matrix of a Markov chain observed at random times

Flavia Barsotti
, Yohann De Castro
, Thibault Espinasse
, Paul Rochet

UniCredit S.p.A
Université Paris-Saclay
Institut Camille Jordan
Laboratoire de Mathématiques Jean Leray

Research output: Contribution to journal › Article › peer-review

Abstract

We want to recover the transition kernel P of a Markov chain X when only a sub-sequence of X is available. The time gaps between the observations are iid with unknown distribution. We propose a method to build an estimator of P under the assumption that it has some zero entries. Its asymptotic performance is discussed in theory and through numerical simulations.

Original language	English
Pages (from-to)	98-105
Number of pages	8
Journal	Statistics and Probability Letters
Volume	94
DOIs	https://doi.org/10.1016/j.spl.2014.07.009
Publication status	Published - 1 Jan 2014
Externally published	Yes

Keywords

Asymptotic normality
Identifiability
Lie bracket
Parametric estimation
Sparse transition matrix
Time varying Markov process

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10.1016/j.spl.2014.07.009

Cite this

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title = "Estimating the transition matrix of a Markov chain observed at random times",

abstract = "We want to recover the transition kernel P of a Markov chain X when only a sub-sequence of X is available. The time gaps between the observations are iid with unknown distribution. We propose a method to build an estimator of P under the assumption that it has some zero entries. Its asymptotic performance is discussed in theory and through numerical simulations.",

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author = "Flavia Barsotti and \{De Castro\}, Yohann and Thibault Espinasse and Paul Rochet",

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AU - De Castro, Yohann

AU - Espinasse, Thibault

AU - Rochet, Paul

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Y1 - 2014/1/1

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AB - We want to recover the transition kernel P of a Markov chain X when only a sub-sequence of X is available. The time gaps between the observations are iid with unknown distribution. We propose a method to build an estimator of P under the assumption that it has some zero entries. Its asymptotic performance is discussed in theory and through numerical simulations.

KW - Asymptotic normality

KW - Identifiability

KW - Lie bracket

KW - Parametric estimation

KW - Sparse transition matrix

KW - Time varying Markov process

UR - https://www.scopus.com/pages/publications/84904910800

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DO - 10.1016/j.spl.2014.07.009

M3 - Article

AN - SCOPUS:84904910800

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VL - 94

SP - 98

EP - 105

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

Estimating the transition matrix of a Markov chain observed at random times

Abstract

Keywords

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