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极值指数的估计AI 解读

SUMMARY The extremal index is an important parameter measuring the degree of clustering of extremes in a stationary process. If we consider the point process of exceedance times over a high threshold, then this can be shown to converge asymptotically to a clustered Poisson process. The extremal index, a parameter in the interval [0, 1], is the reciprocal of the mean cluster size. Apart from being of interest in its own right, it is a crucial parameter for determining the…

利用最大似然预测纪录AI 解读

A maximum likelihood method of fitting a model to a series of records is proposed, using ideas from the analysis of censored data to construct a likelihood function based on observed records. This method is tried out by fitting several models to series of athletics records for mile and marathon races. A form of residual analysis is proposed for testing the models. Forecasting consequences are also considered. In the case of mile records, a steady linear improvement since…

用最大似然法预测纪录AI 解读

A maximum likelihood method of fitting a model to a series of records is proposed, using ideas from the analysis of censored data to construct a likelihood function based on observed records. This method is tried out by fitting several models to series of athletics records for mile and marathon races. A form of residual analysis is proposed for testing the models. Forecasting consequences are also considered. In the case of mile records, a steady linear improvement since…

NEAR(2) 模型的最大似然估计AI 解读

SUMMARY The NEAR(2) model is a model for nonlinear time series with exponential marginals. It formed the subject of a recent discussion paper by Lawrance and Lewis. We explore the possibility of maximum likelihood estimation with particular reference to the difficulties created by discontinuities in the likelihood function. Two exploratory techniques are proposed for resolving those difficulties. This note is an expanded version of a contribution presented orrally at the…