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The theoretical properties of the Whittle likelihood have been studied extensively for many different types of process. In applications however, the utility of the approach is limited by the fact that the asymptotic sampling distribution of the estimator typically depends on third-order and fourth-order properties of the process that may be difficult to obtain. In this article, we show how the methodology can be embedded in the standard framework of estimating functions, which allows the asymptotic distribution to be estimated empirically without calculating higher-order spectra. We also demonstrate that some aspects of the inference, such as the calculation of confidence regions for the entire parameter vector, can be inaccurate but that a small adjustment, designed for application in situations where a mis-specified likelihood is used for inference, can lead to marked improvements. [ABSTRACT FROM AUTHOR]

With a slight modification of a previous argument due to Schechter, we show that the Axiom of Choice is equivalent to the following topological statement: 'If a product of a non-empty family of sets is closed in a topological (Tychonoff) product, then at least one of the factors is closed'. We also discuss the case on which one adds the hypothesis that the closed product of sets is a non-empty set. [ABSTRACT FROM AUTHOR]