138 citations · 205 across the 17 of their papers we have counts for
21 papers
Asset-specific limit order microstructure noise: Parameter estimation and empirical evidence
Markus Bibinger, Adrian Grüber, Moritz Jirak
The one-sided microstructure noise model for high-frequency quotes from a limit order book is generalized to capture asset-specific noise tail behaviour. Estimation of a noise tail…
Asymptotic equivalence for nonparametric additive regression
Moritz Jirak, Alexander Meister, Angelika Rohde
We prove asymptotic equivalence of nonparametric additive regression and an appropriate Gaussian white noise experiment in which a multidimensional shifted Wiener process is observ…
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…
Nonparametric local polynomial regression for functional covariates
Moritz Jirak, Alois Kneip, Alexander Meister +1
We consider nonparametric regression with functional covariates, that is, they are elements of an infinite-dimensional Hilbert space. A locally polynomial estimator is constructed,…
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…
Sharp oracle inequalities and universality of the AIC and FPE
Moritz Jirak, Georg Köstenberger
In two landmark papers, Akaike introduced the AIC and FPE, demonstrating their significant usefulness for prediction. In subsequent seminal works, Shibata developed a notion of asy…
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…
Time-varying first-order autoregressive processes with irregular innovations
Hanna Gruber, Moritz Jirak
We consider a time-varying first-order autoregressive model with irregular innovations, where we assume that the coefficient function is Hölder continuous. To estimate this functio…
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…
Uniform change point tests in high dimension
Moritz Jirak
Consider dependent change point tests, each based on a CUSUM-statistic. We provide an asymptotic theory that allows us to deal with the maximum over all test statistics as both…
Nonparametric change-point analysis of volatility
Markus Bibinger, Moritz Jirak, Mathias Vetter
This work develops change-point methods for statistics of high-frequency data. The main interest is in the volatility of an Itô semi-martingale, the latter being discretely observe…
Optimal eigen expansions and uniform bounds
Moritz Jirak
Let be a stationary process with associated lag operators . Uniform asymptotic expansi…
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…
Adaptive function estimation in nonparametric regression with one-sided errors
Moritz Jirak, Alexander Meister, Markus Reiß
We consider the model of nonregular nonparametric regression where smoothness constraints are imposed on the regression function and the regression errors are assumed to decay…
Simultaneous confidence bands for Yule-Walker estimators and order selection
Moritz Jirak
Let be an autoregressive process of order . Various estimators for the order and the parameters ${\bolds Θ}_q=(θ_1,...,θ_q)^T$ are known; the orde…