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Parameter estimation for uniform maximum process. (English) Zbl 1084.62085

The authors give some properties for the uniform maximum process introduced by P.A.W. Lewis and Ed McKenzie [see J. Appl. Probab. 28, 45–57 (1991; Zbl 0729.60028)]. Some estimation methods concerning the parameters of the process are given, and it is shown that the conditional least squares estimator is strongly consistent and has an asymptotically normal distribution.

MSC:

62M09 Non-Markovian processes: estimation
62F12 Asymptotic properties of parametric estimators
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)

Citations:

Zbl 0729.60028
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