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Chain Binomial Models and Binomial Autoregressive Processes
Author(s) -
Weiß Christian H.,
Pollett Philip K.
Publication year - 2012
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2011.01716.x
Subject(s) - negative binomial distribution , binomial distribution , autoregressive model , estimator , mathematics , negative multinomial distribution , binomial (polynomial) , statistics , multinomial distribution , econometrics , count data , continuity correction , beta binomial distribution , poisson distribution
Summary We establish a connection between a class of chain‐binomial models of use in ecology and epidemiology and binomial autoregressive (AR) processes. New results are obtained for the latter, including expressions for the lag‐ conditional distribution and related quantities. We focus on two types of chain‐binomial model, extinction–colonization and colonization–extinction models, and present two approaches to parameter estimation. The asymptotic distributions of the resulting estimators are studied, as well as their finite‐sample performance, and we give an application to real data. A connection is made with standard AR models, which also has implications for parameter estimation.