Asymptotic Inference for Partially Observed Branching Processes

J 2011

Asymptotic Inference for Partially Observed Branching Processes

KVITKOVIČOVÁ, Andrea and VM PANARETOS

Basic information

Original name

Asymptotic Inference for Partially Observed Branching Processes

Authors

KVITKOVIČOVÁ, Andrea and VM PANARETOS

Edition

Advances in Applied Probability, Sheffield, Applied Probability Trust, 2011, 0001-8678

Other information

Language

English

Type of outcome

Article in a journal

Confidentiality degree

is not subject to a state or trade secret

Impact factor

Impact factor: 0.679

UT WoS

000298713900012

Keywords in English

Epidemic model; Galton-Watson branching process; partial observation; consistency; asymptotic distribution; martingale; stable convergence

Abstract

V originále

We consider the problem of estimation in a partially observed discrete-time Galton-Watson branching process, focusing on the first two moments of the offspring distribution. Our study is motivated by modelling the counts of new cases at the onset of a stochastic epidemic, allowing for the facts that only a part of the cases is detected, and that the detection mechanism may affect the evolution of the epidemic. In this setting, the offspring mean is closely related to the spreading potential of the disease, while the second moment is connected to the variability of the mean estimators. Inference for branching processes is known for its nonstandard characteristics, as compared with classical inference. When, in addition, the true process cannot be directly observed, the problem of inference suffers significant further perturbations. We propose nonparametric estimators related to those used when the underlying process is fully observed, but suitably modified to take into account the intricate dependence structure induced by the partial observation and the interaction scheme. We show consistency, derive the limiting laws of the estimators, and construct asymptotic confidence intervals, all valid conditionally on the explosion set.

Cite

KVITKOVIČOVÁ, Andrea and VM PANARETOS. Asymptotic Inference for Partially Observed Branching Processes. Advances in Applied Probability. Sheffield: Applied Probability Trust, 2011, vol. 43, No 4, p. 1166-1190. ISSN 0001-8678.

@article{1324047,
   author = {Kvitkovičová, Andrea and Panaretos, VM},
   article_location = {Sheffield},
   article_number = {4},
   keywords = {Epidemic model; Galton-Watson branching process; partial observation; consistency; asymptotic distribution; martingale; stable convergence},
   language = {eng},
   issn = {0001-8678},
   journal = {Advances in Applied Probability},
   title = {Asymptotic Inference for Partially Observed Branching Processes},
   volume = {43},
   year = {2011}
}

TY  - JOUR
ID  - 1324047
AU  - Kvitkovičová, Andrea - Panaretos, VM
PY  - 2011
TI  - Asymptotic Inference for Partially Observed Branching Processes
JF  - Advances in Applied Probability
VL  - 43
IS  - 4
SP  - 1166-1190
EP  - 1166-1190
PB  - Applied Probability Trust
SN  - 00018678
KW  - Epidemic model
KW  - Galton-Watson branching process
KW  - partial observation
KW  - consistency
KW  - asymptotic distribution
KW  - martingale
KW  - stable convergence
N2  - We consider the problem of estimation in a partially observed discrete-time Galton-Watson branching process, focusing on the first two moments of the offspring distribution. Our study is motivated by modelling the counts of new cases at the onset of a stochastic epidemic, allowing for the facts that only a part of the cases is detected, and that the detection mechanism may affect the evolution of the epidemic. In this setting, the offspring mean is closely related to the spreading potential of the disease, while the second moment is connected to the variability of the mean estimators. Inference for branching processes is known for its nonstandard characteristics, as compared with classical inference. When, in addition, the true process cannot be directly observed, the problem of inference suffers significant further perturbations. We propose nonparametric estimators related to those used when the underlying process is fully observed, but suitably modified to take into account the intricate dependence structure induced by the partial observation and the interaction scheme. We show consistency, derive the limiting laws of the estimators, and construct asymptotic confidence intervals, all valid conditionally on the explosion set.
ER  -

KVITKOVIČOVÁ, Andrea and VM PANARETOS. Asymptotic Inference for Partially Observed Branching Processes. \textit{Advances in Applied Probability}. Sheffield: Applied Probability Trust, 2011, vol.~43, No~4, p.~1166-1190. ISSN~0001-8678.

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