title: Under-reported data analysis with INAR-hidden Markov chains.
abstract: 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.
authors.affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, Spain. amanda@mat.uab.cat.
authors.forename: Amanda
authors.initials: A
authors.lastname: Fernández-Fontelo
authors.affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, Spain.
authors.forename: Alejandra
authors.initials: A
authors.lastname: Cabaña
authors.affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, Spain.
authors.forename: Pedro
authors.initials: P
authors.lastname: Puig
authors.affiliation: Unit of Infections and Cancer (UNIC), Cancer Epidemiology Research Program (CERP), Catalan Institute of Oncology (ICO)-IDIBELL, L'Hospitalet de Llobregat, Barcelona, Spain.|rups de Recerca d'Àfrica i Amèrica Llatines (GRAAL), Unitat de Bioestadística, Facultat de Medicina, Universitat Autònoma de Barcelona, Bellaterra, Spain.
authors.forename: David
authors.initials: D
authors.lastname: Moriña
mesh_terms: D000465:Algorithms; D006801:Humans; D016013:Likelihood Functions; D008390:Markov Chains
keywords: discrete time series; emission probabilities; integer-autoregressive models; thinning operator; under-recorded data