Transform, martingale estimating functions

• 成果类型: Article
• 署名作者: Merkouris, T.
• 署名单位: Statistics Canada
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053607000000299
• 发表日期: 2007
• 页码: 1975-2000
• 关键词: EMPIRICAL CHARACTERISTIC FUNCTION; quasi-likelihood estimation; models; distributions; SEMIMARTINGALES; parameters; EFFICIENCY; inference

摘要

An estimation method is proposed for a wide variety of discrete time stochastic processes that have an intractable likelihood function but are otherwise conveniently specified by an integral transform such as the characteristic function, the Laplace transform or the probability generating function. This method involves the construction of classes of transform-based martingale estimating functions that fit into the general framework of quasi-likelihood. In the parametric setting of a discrete time stochastic process, we obtain transform quasi-score functions by projecting the unavailable score function onto the special linear spaces formed by these classes. The specification of the process by any of the main integral transforms makes possible an arbitrarily close approximation of the score function in an infinite-dimensional Hilbert space by optimally combining transform martingale quasi-score functions. It also allows an extension of the domain of application of quasi-likelihood methodology to processes with infinite conditional second moment.