41 citations · 175 across the 27 of their papers we have counts for
34 papers
Convergence of Stochastic Gradient Descent with mini-batching and infinite variance
Bartosz Glowacki, Rafal Kulik, Philippe Soulier
Stochastic gradient descent (SGD) with mini-batching is a standard tool in large-scale optimization, yet its theoretical properties under heavy-tailed gradient noise remain largely…
A remarkable example on clustering of extremes for regularly-varying stochastic processes
Shuyang Bai, Rafał Kulik, Yizao Wang
The stable-regenerative multiple-stable model has been shown recently to have distinct candidate extremal index and extremal index. To understand further this rare phenomenon, two…
Asymptotic expansions for blocks estimators: PoT framework
Zaoli Chen, Rafał Kulik
We consider disjoint and sliding blocks estimators of cluster indices for multivariate, regularly varying time series in the Peak-over-Threshold framework. We aim to provide a comp…
Limit theorems for unbounded cluster functionals of regularly varying time series
Zaoli Chen, Rafal Kulik
A blocks method is used to define clusters of extreme values in stationary time series. The cluster starts at the first large value in the block and ends at the last one. The block…
Estimation of cluster functionals for regularly varying time series: runs estimators
Youssouph Cissokho, Rafal Kulik
Cluster indices describe extremal behaviour of stationary time series. We consider runs estimators of cluster indices. Using a modern theory of multivariate, regularly varying time…
Change-point tests for the tail parameter of Long Memory Stochastic Volatility time series
Annika Betken, Davide Giraudo, Rafał Kulik
We consider a change-point test based on the Hill estimator to test for structural changes in the tail index of Long Memory Stochastic Volatility time series. In order to determine…