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On Statistical Models for d ‐Dimensional Stable Processes, and Some Generalizations
Author(s) -
Hopfner Reinhard
Publication year - 1999
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00171
Subject(s) - mathematics , measure (data warehouse) , estimator , lévy process , jump , poisson distribution , neighbourhood (mathematics) , type (biology) , point process , combinatorics , statistical physics , statistics , mathematical analysis , ecology , physics , quantum mechanics , database , computer science , biology
In statistical models where jumps of a d ‐dimensional stable process ( S t ) t ≥0 are observed in windows with certain asymptotic properties, and where parameters appearing in the Levy measure of S are to be estimated, we have asymptotically efficient estimators. If Poisson random measure μ on (0, ∞) × ( R d \{0}) with intensity dt Λ( dx ) replaces the jump measure of S , where Λ is a ε‐finite measure on R d \{0} admitting tail parameters in a suitable sense, we specify a notion of neighbourhood which allows to treat efficiency in statistical experiments of the second type by switching to accompanying sequences of the stable process type considered first.