7 papers
Multifractional Stable Motion with Random Hurst Exponent
Fabian Mies, Duuk Sikkens
The fractional stable motion is a prototypical stochastic process exhibiting both heavy tails and long-range dependence, parameterized via a stability index and a Hurst expone…
Besov-Orlicz moduli of Brownian motion and polygonal partial sum processes
Fabian Mies
The sample paths of Brownian motion are known to admit the exact Besov-type smoothness exponent 1/2 when measured in the sub-Gaussian Orlicz norm. We extend these regularity result…
Empirical Orlicz norms
Fabian Mies
The empirical Orlicz norm based on a random sample is defined as a natural estimator of the Orlicz norm of a univariate probability distribution. A law of large numbers is derived…
Rough Hurst function estimation
Fabian Mies, Benedikt Wilkens
The fractional Brownian motion (fBm) is parameterized by the Hurst exponent , which determines the dependence structure and regularity of sample paths. Empirical finding…
Likelihood asymptotics of stationary Gaussian arrays
Carsten H. Chong, Fabian Mies
This paper develops an asymptotic likelihood theory for triangular arrays of stationary Gaussian time series depending on a multidimensional unknown parameter. We give sufficient c…
At the edge of Donsker's Theorem: Asymptotics of multiscale scan statistics
Johann Köhne, Fabian Mies
For nonparametric inference about a function, multiscale testing procedures resolve the need for bandwidth selection and achieve asymptotically optimal detection performance agains…