Improved interexceedance-times-based estimator of the extremal index using truncated distribution. (English) Zbl 07613179
Summary: The extremal index is an important parameter in the characterization of extreme values of a stationary sequence. This paper presents a novel approach to estimation of the extremal index based on truncation of interexceedance times. The truncated estimator based on the maximum likelihood method is derived together with its first-order bias. The estimator is further improved using penultimate approximation to the limiting mixture distribution. In order to assess the performance of the proposed estimator, a simulation study is carried out for various stationary processes satisfying the local dependence condition \(D^{(k)}(u_n)\). An application to daily maximum temperatures at Uccle, Belgium, is also presented.
MSC:
| 62G32 | Statistics of extreme values; tail inference |
| 62M09 | Non-Markovian processes: estimation |
| 62N01 | Censored data models |
| 62N02 | Estimation in survival analysis and censored data |
| 62P12 | Applications of statistics to environmental and related topics |
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