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 Name: Maud Thomas

Talk Title: Non-asymptotic bounds for probability weighted moment estimators

Abstract: In hydrology and other applied fields, Probability weighted moments (PWM) have been frequently used to estimate the parameters of classical  extreme value distributions (see de Haan and Ferreira, 2006)). This method-of-moment technique can be applied  when second moments are finite, a reasonable assumption in hydrology. Two advantages of PWM estimators are their ease of implementation and their close connection to the well-studied class of  U-statistics. Consequently, precise asymptotic properties can be deduced. In practice,  sample sizes  are always finite and, depending on the application at hand, the sample length can be small, e.g. a sample of only 30 years of  maxima of daily precipitation is quiet common in some regions of the globe.  In such a context, asymptotic theory is on a shaky ground and it is desirable to get non-asymptotic bounds.

Deriving such bounds from off-the-shelf techniques (Chernoff method) requires exponential moment assumptions, which are unrealistic in many settings. To bypass this hurdle, we propose a new estimator for PWM, inspired by the median-of-means framework of Devroye, Lerasle, Lugosi and Oliveira, 2016. This estimator is then shown to satisfy a sub- Gaussian inequality, with only second moment assumptions. This allows us to derive non-asymptotic bounds for the estimation of the parameters of extreme value distributions, and of extreme quantiles.

This talk is a contributed talk at EVA 2021.