138 citations · 205 across the 17 of their papers we have counts for
11 papers · 1 filter
Weak dependence and optimal quantitative self-normalized central limit theorems
Moritz Jirak
Consider a stationary, weakly dependent sequence of random variables. Given only mild conditions, allowing for polynomial decay of the autocovariance function, we show a Berry-Esse…
Concentration and moment inequalities for sums of independent heavy-tailed random matrices
Moritz Jirak, Stanislav Minsker, Yiqiu Shen +1
We prove Fuk-Nagaev and Rosenthal-type inequalities for sums of independent random matrices, focusing on the situation when the norms of the matrices possess finite moments of only…
Quantitative limit theorems and bootstrap approximations for empirical spectral projectors
Moritz Jirak, Martin Wahl
Given finite i.i.d.~samples in a Hilbert space with zero mean and trace-class covariance operator , the problem of recovering the spectral projectors of naturally arises in…
Edgeworth expansions for volatility models
Moritz Jirak
Motivated from option and derivative pricing, this note develops Edgeworth expansions both in the Kolmogorov and Wasserstein metric for many different types of discrete time volati…
A Berry-Esseen bound with (almost) sharp dependence conditions
Moritz Jirak
Suppose that the (normalised) partial sum of a stationary sequence converges to a standard normal random variable. Given sufficiently moments, when do we have a rate of convergence…
Sharp connections between Berry-Esseen characteristics and Edgeworth expansions for stationary processes
Moritz Jirak, Wei Biao Wu, Ou Zhao
Given a weakly dependent stationary process, we describe the transition between a Berry-Esseen bound and a second order Edgeworth expansion in terms of the Berry-Esseen characteris…
Perturbation bounds for eigenspaces under a relative gap condition
Moritz Jirak, Martin Wahl
A basic problem in operator theory is to estimate how a small perturbation effects the eigenspaces of a self-adjoint compact operator. In this paper, we prove upper bounds for the…
Relative perturbation bounds with applications to empirical covariance operators
Moritz Jirak, Martin Wahl
The goal of this paper is to establish relative perturbation bounds, tailored for empirical covariance operators. Our main results are expansions for empirical eigenvalues and spec…
Rate of convergence for Hilbert space valued processes
Moritz Jirak
Consider a stationary, linear Hilbert space valued process. We establish Berry-Essen type results with optimal convergence rates under sharp dependence conditions on the underlying…
Berry-Esseen theorems under weak dependence
Moritz Jirak
Let be a stationary sequence. Given moments and a mild weak dependence condition, we show a Berry-Esseen theorem with optimal rate $n^{p/2…
Volatility estimation under one-sided errors with applications to limit order books
Markus Bibinger, Moritz Jirak, Markus Reiß
For a semi-martingale , which forms a stochastic boundary, a rate-optimal estimator for its quadratic variation is constructed based on observations i…