Efficient estimation of auto-regression parameters and innovation distributions for semiparametric integer-valued AR(p) models |
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Authors: | Feike C Drost Ramon van den Akker Bas J M Werker |
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Institution: | Tilburg University, The Netherlands |
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Abstract: | Summary. Integer-valued auto-regressive (INAR) processes have been introduced to model non-negative integer-valued phenomena that evolve over time. The distribution of an INAR( p ) process is essentially described by two parameters: a vector of auto-regression coefficients and a probability distribution on the non-negative integers, called an immigration or innovation distribution. Traditionally, parametric models are considered where the innovation distribution is assumed to belong to a parametric family. The paper instead considers a more realistic semiparametric INAR( p ) model where there are essentially no restrictions on the innovation distribution. We provide an (semiparametrically) efficient estimator of both the auto-regression parameters and the innovation distribution. |
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Keywords: | Count data Infinite dimensional Z-estimator Non-parametric maximum likelihood Semiparametric efficiency |
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