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Under‐reported data analysis with INAR‐hidden Markov chains
Author(s) -
FernándezFontelo Amanda,
Cabaña Alejandra,
Puig Pedro,
Moriña David
Publication year - 2016
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.7026
Subject(s) - viterbi algorithm , autocorrelation , computer science , markov chain , hidden markov model , markov model , hidden semi markov model , likelihood function , maximum likelihood , series (stratigraphy) , variable order markov model , forward algorithm , expectation–maximization algorithm , estimation theory , simple (philosophy) , algorithm , artificial intelligence , statistics , machine learning , mathematics , paleontology , philosophy , epistemology , biology
In this work, we deal with correlated under‐reported data through INAR(1)‐hidden Markov chain models. These models are very flexible and can be identified through its autocorrelation function, which has a very simple form. A naïve method of parameter estimation is proposed, jointly with the maximum likelihood method based on a revised version of the forward algorithm. The most‐probable unobserved time series is reconstructed by means of the Viterbi algorithm. Several examples of application in the field of public health are discussed illustrating the utility of the models. Copyright © 2016 John Wiley & Sons, Ltd.