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Robust estimation of extremes
Author(s) -
Dupuis D. J.,
Field C. A.
Publication year - 1998
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315505
Subject(s) - quantile , extreme value theory , moment (physics) , statistics , generalized extreme value distribution , data point , distribution (mathematics) , point estimation , mathematics , computer science , physics , mathematical analysis , classical mechanics
We consider the problem of making inferences about extreme values from a sample. The underlying model distribution is the generalized extreme‐value (GEV) distribution, and our interest is in estimating the parameters and quantiles of the distribution robustly. In doing this we find estimates for the GEV parameters based on that part of the data which is well fitted by a GEV distribution. The robust procedure will assign weights between 0 and 1 to each data point. A weight near 0 indicates that the data point is not well modelled by the GEV distribution which fits the points with weights at or near 1. On the basis of these weights we are able to assess the validity of a GEV model for our data. It is important that the observations with low weights be carefully assessed to determine whether diey are valid observations or not. If they are, we must examine whether our data could be generated by a mixture of GEV distributions or whether some other process is involved in generating the data. This process will require careful consideration of die subject matter area which led to the data. The robust estimation techniques are based on optimal B‐robust estimates. Their performance is compared to the probability‐weighted moment estimates of Hosking et al. (1985) in both simulated and real data.