Gold standard process Markovian poisoning
Abstract
In this paper, we consider a stochastic process that mixes two separate sources of randomness over time, governed by an unobserved stationary Markov selection process: (i) a stationary process whose distribution is known (the gold standard), and (ii) a pure i.i.d. sequence whose distribution is unknown (the poisoning process). Within this framework, we propose two distinct approaches to estimate the transition probabilities of the hidden Markov selection process, as well as the distribution of the unknown i.i.d. sequence, which is not assumed to belong to any parametric family. These estimations are performed under minimal conditions regarding identifiability, stationarity, and time dependence. We show that both estimators consistently estimate the Euclidean transition parameter. Furthermore, we prove that one of them is square-root-of-n consistent, enabling the establishment of a functional central limit theorem for the cumulative distribution function of the unknown poisoning sequence. Finally, the numerical performance of our estimators is illustrated through various challenging examples.theorem about the unknown poisoning sequence cumulative distribution function. The numerical performances of our estimators are illustrated through various challenging examples.
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BibTeX
@misc{lacour2026gold,
title = {{Gold standard process Markovian poisoning}},
author = {Claire Lacour and Pierre Vandekerkhove},
howpublished = {HAL},
year = {2026},
month = sep,
eprint = {2601.07503},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05453397v2},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Gold standard process Markovian poisoning
AU - Claire Lacour
AU - Pierre Vandekerkhove
PY - 2026
DA - 2026/09/11
PB - HAL
UR - https://hal.science/hal-05453397v2
AB - In this paper, we consider a stochastic process that mixes two separate sources of randomness over time, governed by an unobserved stationary Markov selection process: (i) a stationary process whose distribution is known (the gold standard), and (ii) a pure i.i.d. sequence whose distribution is unknown (the poisoning process). Within this framework, we propose two distinct approaches to estimate the transition probabilities of the hidden Markov selection process, as well as the distribution of the unknown i.i.d. sequence, which is not assumed to belong to any parametric family. These estimations are performed under minimal conditions regarding identifiability, stationarity, and time dependence. We show that both estimators consistently estimate the Euclidean transition parameter. Furthermore, we prove that one of them is square-root-of-n consistent, enabling the establishment of a functional central limit theorem for the cumulative distribution function of the unknown poisoning sequence. Finally, the numerical performance of our estimators is illustrated through various challenging examples.theorem about the unknown poisoning sequence cumulative distribution function. The numerical performances of our estimators are illustrated through various challenging examples.
ER -