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Guenther WALTHER (Stanford University) – “Constructing an optimal confidence set for a distribution function with applications to visualizing data”
November 20, 2018, 2:00 pm - 3:15 pm
The Statistical Seminar: Every Monday at 2:00 pm.
Time: 2:00 pm – 3:15 pm
Date: 20th of November 2018 exceptionally Tuesday
Place: Room 3001.
Guenther WALTHER (Stanford University) – “Constructing an optimal confidence set for a distribution function with applications to visualizing data“
We show how to construct a confidence set of distribution functions that have the same optimal estimation performance as the empirical distribution function, but which may be much simpler, that is the distribution functions may have many fewer jumps.
We show how an accelerated dynamic program can be applied to a relaxed optimization problem in order to find the distribution function in the confidence set that has the fewest jumps.
We propose to use this distribution function for summarizing and visualizing the data via a histogram, as this distribution function is the simplest function that optimally addresses the two main tasks of the histogram: estimating probabilities and detecting features such as increases and (anti)modes in the distribution. We will illustrate our methodology with examples.
This is joint work with Housen Li, Axel Munk, and Hannes Sieling.
Cristina BUTUCEA, Alexandre TSYBAKOV, Julie JOSSE, Eric MOULINES, Mathieu ROSENBAUM