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We prove Fuk-Nagaev and Rosenthal-type inequalities for the sums of independent random matrices, focusing on the situation when the norms of the matrices possess finite moments of only low orders. Our bounds depend on the "intrinsic" dimensional char
Externí odkaz:
http://arxiv.org/abs/2407.12948
Autor:
Jirak, Moritz, Köstenberger, Georg
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 asymptotic efficiency and showed that both AIC and FPE are optimal, setti
Externí odkaz:
http://arxiv.org/abs/2406.13513
Autor:
Jirak, Moritz, Wahl, Martin
Given finite i.i.d.~samples in a Hilbert space with zero mean and trace-class covariance operator $\Sigma$, the problem of recovering the spectral projectors of $\Sigma$ naturally arises in many applications. In this paper, we consider the problem of
Externí odkaz:
http://arxiv.org/abs/2208.12871
Autor:
Gruber, Hanna, Jirak, Moritz
We consider a time-varying first-order autoregressive model with irregular innovations, where we assume that the coefficient function is H\"{o}lder continuous. To estimate this function, we use a quasi-maximum likelihood based approach. A precise con
Externí odkaz:
http://arxiv.org/abs/2201.09346
Autor:
Jirak, Moritz
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 volatility models and their possible transformations. This includes, among o
Externí odkaz:
http://arxiv.org/abs/2111.00529
Autor:
Jirak, Moritz
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 of $n^{-1/2}$ in the uniform metric, in other words, when do we have
Externí odkaz:
http://arxiv.org/abs/2008.07332
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 characteristic. This characteristic is sharp: We show that Edgeworth expansions a
Externí odkaz:
http://arxiv.org/abs/2007.05717
Akademický článek
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Autor:
Jirak, Moritz, Wahl, Martin
Publikováno v:
In Advances in Mathematics 1 January 2023 412
Autor:
Jirak, Moritz, Wahl, Martin
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 subspace distance, taylored for structured random perturbations. As a
Externí odkaz:
http://arxiv.org/abs/1803.03868