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        Department of Systems Engineering and Engineering Management

                            The Chinese University of Hong Kong

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Date: 4:30pm - 5:30pm on 17 October (Friday)

Venue: ERB 513, The Chinese University of Hong Kong

Title: On the smoothed empirical distribution function

Speaker: Henryk Zaehle, Department of Mathematics, Saarland University





Abstract:

Since Glivenko and Cantelli proved the fundamental theorem of statistics in 1933, the empirical distribution function has been one of the most widely used objects in mathematical statistics. It is undoubtedly the standard non-parametric estimator of the distribution function. However, even after nearly a hundred years, there is still scope for simple yet effective improvements.



In this talk, I will discuss the extent to which sophisticated kernel smoothing of this step function can improve estimation. First, I will address the theoretically optimal bandwidth and explain why the choice of smoothing kernel is less important here than in kernel-based density estimation. Next, I will present two novel, data-adaptive bandwidth selectors and investigate their performance. Finally, I will discuss some theoretical properties of the smoothed empirical distribution function (strong consistency, asymptotic distribution, exponential concentration inequalities) and explain how it can be used for the re-sampling in Efron's bootstrap method.





Bio:

Henryk Zaehle received his M.Sc. in Mathematics from the University of Goettingen, Germany, in 2000 and his Ph.D. in Mathematics from the Technical University Berlin in 2004. During his doctoral studies, he spent eight months as a Marie Curie Fellow at the University of Warwick, UK. After holding postdoctoral research positions in Berlin and at the RWTH Aachen University, he was appointed Junior Professor at the Technical University Dortmund, Germany, in 2008. He was appointed Professor of Applied Mathematics at Saarland University, Germany, in 2010, becoming a Full Professor in 2014. His research interests include mathematical statistics, monetary risk measurement, copulas, and stochastic processes. From 2021 to 2023 he was Chairman of the Board of the German Association for Insurance and Financial Mathematics (DGVFM). He also held a senior position at the German Actuarial Association (DAV) for more than ten years.