Efficient estimation of auto-regression parameters and innovation distributions for semiparametric integer-valued AR(p) models

• 成果类型: Article
• 署名作者: Drost, Feike C.; van den Akker, Ramon; Werker, Bas J. M.
• 署名单位: Tilburg University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2008.00687.x
• 发表日期: 2009
• 页码: 467-485
• 关键词: Adaptive Estimation; entry; QUEUE

摘要

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.