[Statistics & Probability Seminar]
The block maxima method in extremum estimation
Over the last decade there has been an astonishing growth in the statistical techniques to analyse extreme values. As typified by the classical maximum likelihood (ML) inference on block maxima, the Generalised Extreme Value distribution is the appropriate probabilistic instrument when fitting a sample of maxima. The recent maximum Lq-likelihood method has a notable advantage to the usual ML estimation: with small up to moderate sample sizes, a proper choice for the distortion parameter q > 0 can deploy the variance in mitigating the mean squared error, thus eroding the role of bias. In this framework, an alternative class of parametric estimators stems from the maximum product of spacings (MSP) method through its obvious extension to the MSPq class. In this talk, we will assess the current state of development and usage of these two classes of estimators and outline a semi-parametric approach to both methods by assuming that the distortion parameter q = q_m depends on the size of blocks m rather than the sample size n. We will proceed via simulation, addressing how the choice of q crosses over to the estimation of high quantiles, including the finite upper endpoint. The simulation study will be partially mirrored in the practical application to the annual maxima of Lowestoft sea levels.
This is joint work with Christopher Jeffree, University of Reading.
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