Prof. Dr. Markus Reiß
Profil
Forschungsthemen21
DYNSTOCH 2009 (Veranstaltung: 08.10.- 10.10.09, Berlin)
Quelle ↗Förderer: DFG sonstige Programme Zeitraum: 05/2009 - 10/2009 Projektleitung: Prof. Dr. Markus Reiß
FG 1735/1: Efficient nonparametric regression when the support is bounded in DFG-FOR 1735; (TP 03)
Quelle ↗Förderer: DFG Forschungsgruppe Zeitraum: 04/2012 - 06/2015 Projektleitung: Prof. Dr. Markus Reiß
FG 1735/1: Identifiability and structural inference for high-dimensional diffusion matrices in DFG FG 1735
Quelle ↗Förderer: DFG Forschungsgruppe Zeitraum: 04/2012 - 03/2015 Projektleitung: Prof. Dr. Markus Reiß
FG 1735/1: Multiple testing under unspecified dependency structure in DFG-FOR 1735 (TP01)
Quelle ↗Förderer: DFG Forschungsgruppe Zeitraum: 04/2012 - 08/2015 Projektleitung: Prof. Dr. Markus Reiß
FOR 1735/2: Efficient Nonparametric Regression When the Support Is Bounded (TP 03)
Quelle ↗Förderer: DFG Forschungsgruppe Zeitraum: 07/2015 - 06/2019 Projektleitung: Prof. Dr. Markus Reiß
FOR 1735/2: Zentralprojekt: Strukturelle Inferenz in der Statistik: Adaption und Effizienz
Quelle ↗Förderer: DFG Forschungsgruppe Zeitraum: 09/2015 - 12/2019 Projektleitung: Prof. Dr. Markus Reiß
FOR 5381/2: Optimale Aktionen und Stoppen im sequentiellen Lernen (TP 02)
Quelle ↗Förderer: DFG Forschungsgruppe Zeitraum: 04/2026 - 03/2030 Projektleitung: Prof. Dr. Markus Reiß
GRK 1792: Hochdimensionale nicht stationäre Zeitreihen
Quelle ↗Förderer: DFG Graduiertenkolleg Zeitraum: 01/2013 - 06/2023 Projektleitung: Prof. Dr. Wolfgang Karl Härdle
IGRK 1792/2: Hochdimensionale nicht stationäre Zeitreihen
Quelle ↗Förderer: DFG Graduiertenkolleg Zeitraum: 04/2018 - 06/2023 Projektleitung: Prof. Dr. Wolfgang Härdle
IGRK 2544/1: Stochastische Analysis in Interaktion
Quelle ↗Förderer: DFG Graduiertenkolleg Zeitraum: 04/2020 - 09/2024 Projektleitung: Prof. Dr. Ulrich Horst, Prof. Dr. Markus Reiß, Prof. Dr. Dirk Becherer, Prof. Dr. Dörte Kreher
IGRK 2544: Stochastische Analysis in Interaktion
Quelle ↗Förderer: DFG Graduiertenkolleg Zeitraum: 04/2020 - 03/2029 Projektleitung: Prof. Dr. Peter Bank, Terry Lyons Ph.D.
SFB 1294/1: Datenassimilation – Die nahtlose Verschmelzung von Daten und Modellen
Quelle ↗Förderer: DFG Sonderforschungsbereich Zeitraum: 07/2017 - 06/2021 Projektleitung: Prof. Dr. Markus Reiß
SFB 1294/1: Nichtlineare statistische inverse Probleme mit zufälligen Beobachtungen (TP A04)
Quelle ↗Förderer: DFG Sonderforschungsbereich Zeitraum: 07/2017 - 06/2021 Projektleitung: Prof. Dr. Markus Reiß
SFB 1294/1: Statistik von stochastischen partiellen Differentialgleichungen (SPDEs) (TP A01)
Quelle ↗Förderer: DFG Sonderforschungsbereich Zeitraum: 07/2017 - 06/2021 Projektleitung: Prof. Dr. Markus Reiß
SFB 1294/2: Nichtlineare statistische inverse Probleme mit zufälligen Beobachtungen (TP A04)
Quelle ↗Förderer: DFG Sonderforschungsbereich Zeitraum: 07/2021 - 12/2025 Projektleitung: Prof. Dr. Markus Reiß
SFB 1294/2: Statistik von stochastischen partiellen Differentialgleichungen (SPDEs) (TP A01)
Quelle ↗Förderer: DFG Sonderforschungsbereich Zeitraum: 07/2021 - 12/2025 Projektleitung: Prof. Dr. Markus Reiß
SFB 1294/3: Nichtlineare statistische inverse Probleme mit zufälligen Beoachtungen (TP A04)
Quelle ↗Förderer: DFG Sonderforschungsbereich Zeitraum: 01/2026 - 06/2029 Projektleitung: Prof. Dr. Markus Reiß, Prof. Dr. Melina Freitag
SFB 1294/3: Statistik von stochastischen partiellen Differentialgleichungen (SPDEs) (TP A01)
Quelle ↗Förderer: DFG Sonderforschungsbereich Zeitraum: 01/2026 - 06/2029 Projektleitung: Prof. Dr. Markus Reiß
SFB 649/2: Inference for Jump Models and Nonlinear Inverse Problems (TP C 12)
Quelle ↗Förderer: DFG Sonderforschungsbereich Zeitraum: 10/2010 - 12/2016 Projektleitung: Prof. Dr. Markus Reiß
SFB/TRR 388/1: „Statistik für Bevölkerungsmodelle mit stochastischen (partiellen) Verzögerungsdifferentialgleichungen“ (TP B07)
Quelle ↗Förderer: DFG Sonderforschungsbereich Zeitraum: 10/2024 - 06/2028 Projektleitung: Prof. Dr. Markus Reiß, Prof. Dr. Maite Wilke Berenguer
SFB/TRR 388/1: Statistisches Lernen aus Pfadbeobachtungen (B01)
Quelle ↗Förderer: DFG Sonderforschungsbereich Zeitraum: 10/2024 - 06/2028 Projektleitung: Prof. Dr. Markus Reiß, Dr. Christian Bayer
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Publikationen25
Top 25 nach Zitationen — Quelle: OpenAlex (BAAI/bge-m3 embedded für Matching).
Bernoulli · 119 Zitationen · DOI
We suppose that a Lévy process is observed at discrete time points. A rather general construction of minimum-distance estimators is shown to give consistent estimators of the Lévy–Khinchine characteristics as the number of observations tends to infinity, keeping the observation distance fixed. For a specific $C^2$-criterion this estimator is rate-optimal. The connection with deconvolution and inverse problems is explained. A key step in the proof is a uniform control on the deviations of the empirical characteristic function on the whole real line.
SIAM Journal on Numerical Analysis · 105 Zitationen · DOI
We introduce and analyze numerical methods for the treatment of inverse problems, based on an adaptive wavelet Galerkin discretization. These methods combine the theoretical advantages of the wavelet-vaguelette decomposition (WVD) in terms of optimally adapting to the unknown smoothness of the solution, together with the numerical simplicity of Galerkin methods. In a first step, we simply combine a thresholding algorithm on the data with a Galerkin inversion on a fixed linear space. In a second step, a more elaborate method performs the inversion by an adaptive procedure in which a smaller space adapted to the solution is iteratively constructed; this leads to a significant reduction of the computational cost.
Open MIND · 95 Zitationen
We study two nonlinear methods for statistical linear inverse problems when the operator is not known. The two constructions combine Galerkin regularization and wavelet thresholding. Their performances depend on the underlying structure of the operator, quantified by an index of sparsity. We prove their rate-optimality and adaptivity properties over Besov classes. 1. Introduction. Linear inverse problems with error in the operator. We want to recover f ∈ L 2 (D), where D is a domain in R d, from data (1.1) gε = Kf + ε ˙ W,
The Annals of Statistics · 91 Zitationen · DOI
We consider discrete-time observations of a continuous martingale under measurement error. This serves as a fundamental model for high-frequency data in finance, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam’s sense asymptotically equivalent to a Gaussian shift experiment in terms of the square root of the volatility function σ and a nonstandard noise level. As an application, new rate-optimal estimators of the volatility function and simple efficient estimators of the integrated volatility are constructed.
The Annals of Statistics · 85 Zitationen · DOI
We show that nonparametric regression is asymptotically equivalent, in Le Cam’s sense, to a sequence of Gaussian white noise experiments as the number of observations tends to infinity. We propose a general constructive framework, based on approximation spaces, which allows asymptotic equivalence to be achieved, even in the cases of multivariate and random design.
Finance and Stochastics · 77 Zitationen · DOI
Probability Theory and Related Fields · 63 Zitationen · DOI
Journal of Functional Analysis · 62 Zitationen · DOI
A remark on the rates of convergence for integrated volatility estimation in the presence of jumps
2014The Annals of Statistics · 50 Zitationen · DOI
The optimal rate of convergence of estimators of the integrated volatility, for a discontinuous Itô semimartingale sampled at regularly spaced times and over a fixed time interval, has been a long-standing problem, at least when the jumps are not summable. In this paper, we study this optimal rate, in the minimax sense and for appropriate “bounded” nonparametric classes of semimartingales. We show that, if the $r$th powers of the jumps are summable for some $r\in[0,2)$, the minimax rate is equal to $\min(\sqrt{n},(n\log n)^{(2-r)/2})$, where $n$ is the number of observations.
Statistica Neerlandica · 45 Zitationen · DOI
A Lévy process is observed at time points of distance Δ until time T . We construct an estimator of the Lévy–Khinchine characteristics of the process and derive optimal rates of convergence simultaneously in T and Δ. Thereby, we encompass the usual low‐ and high‐frequency assumptions and also obtain asymptotics in the mid‐frequency regime.
Nonparametric test for a constant beta between Itô semi-martingales based on high-frequency data
2015Stochastic Processes and their Applications · 41 Zitationen · DOI
SSRN Electronic Journal · 38 Zitationen · DOI
TU/e Research Portal (Eindhoven University of Technology) · 35 Zitationen
Quantile estimation in deconvolution problems is studied comprehensively. In particular, the more realistic setup of unknown error distributions is covered. Our plug-in method is based on a deconvolution density estimator and is minimax optimal under minimal and natural conditions. This closes an important gap in the literature. Optimal adaptive estimation is obtained by a data-driven bandwidth choice. As a side result we obtain optimal rates for the plug-in estimation of distribution functions with unknown error distributions. The method is applied to a real data example.
Cancers · 34 Zitationen · DOI
Primary neuroendocrine carcinoma of the breast (NECB) as defined by the World Health Organization (WHO) in 2012 is a rare, but possibly under-diagnosed entity. It is heterogeneous as it entails a wide spectrum of diseases comprising both well-differentiated neuroendocrine tumors of the breast as well as highly aggressive small cell carcinomas. Retrospective screening of hospital charts of 612 patients (2008-2019) from our specialized outpatient unit for neuroendocrine neoplasia revealed five patients diagnosed with NECB. Given the low prevalence of these malignancies, correct diagnosis remains a challenge that requires an interdisciplinary approach. Specifically, NECB may be misclassified as carcinoma of the breast with neuroendocrine differentiation, carcinomas of the breast of no special type/invasive ductal carcinoma, or a metastasis to the breast. Therefore, this study presents multifaceted characteristics as well as the clinical course of these patients and discusses the five cases from our institution in the context of available literature.
Scandinavian Journal of Statistics · 34 Zitationen · DOI
ABSTRACT We propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes, which are observed discretely with additive observation noise. The appropriate estimation for time‐varying volatilities is based on an asymptotic equivalence of the underlying statistical model to a white‐noise model with correlation and volatility processes being constant over small time intervals. The asymptotic equivalence of the continuous‐time and discrete‐time experiments is proved by a construction with linear interpolation in one direction and local means for the other. The new estimator outperforms earlier non‐parametric methods in the literature for the considered model. We investigate its finite sample size characteristics in simulations and draw a comparison between various proposed methods.
SIAM/ASA Journal on Uncertainty Quantification · 29 Zitationen · DOI
Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 13 October 2020Accepted: 14 September 2021Published online: 07 February 2022Keywordslocal measurements, stochastic partial differential equation, pattern formation, Meinhardt model, stochastic reaction-diffusion equation, drift estimation, augmented MLEAMS Subject HeadingsPrimary, 60H15, 92C37, 62M05; Secondary, 60J60Publication DataISSN (online): 2166-2525Publisher: Society for Industrial and Applied MathematicsCODEN: sjuqa3
Probability Theory and Related Fields · 29 Zitationen · DOI
Econstor (Econstor) · 27 Zitationen · DOI
The basic model for high-frequency data in finance is considered, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam's sense asymptotically equivalent to a Gaussian shift experiment in terms of the square root of the volatility function σ. As an application, simple rateoptimal estimators of the volatility and efficient estimators of the integrated volatility are constructed.
Econometric Theory · 24 Zitationen · DOI
In this paper we clarify the relations between the existing sets of regularity conditions for convergence rates of nonparametric indirect regression (NPIR) and nonparametric instrumental variables (NPIV) regression models. We establish minimax risk lower bounds in mean integrated squared error loss for the NPIR and NPIV models under two basic regularity conditions: the approximation number and the link condition. We show that both a simple projection estimator for the NPIR model and a sieve minimum distance estimator for the NPIV model can achieve the minimax risk lower bounds and are rate optimal uniformly over a large class of structure functions, allowing for mildly ill-posed and severely ill-posed cases.
SSRN Electronic Journal · 23 Zitationen · DOI
Stochastic Analysis and Applications · 21 Zitationen · DOI
Abstract A generalization of Émery's inequality for stochastic integrals is shown for convolution integrals of the form , where Z is a semimartingale, Y an adapted càdlàg process, and g a deterministic function. An even more general inequality for processes with two parameters is proved. The inequality is used to prove existence and uniqueness of solutions of equations of variation-of-constants type. As a consequence, it is shown that the solution of a semilinear delay differential equation with functional Lipschitz diffusion coefficient and driven by a general semimartingale satisfies a variation-of-constants formula.
Cemmap working papers · 21 Zitationen · DOI
In this paper, we clarify the relations between the existing sets of regularity conditions for convergence rates of nonparametric indirect regression (NPIR) and nonparametric instrumental variables (NPIV) regression models.We establish minimax risk lower bounds in mean integrated squared error loss for the NPIR and the NPIV models under two basic regularity conditions that allow for both mildly ill-posed and severely ill-posed cases.We show that both a simple projection estimator for the NPIR model, and a sieve minimum distance estimator for the NPIV model, can achieve the minimax risk lower bounds, and are rate-optimal uniformly over a large class of structure functions, allowing for mildly ill-posed and severely ill-posed cases.
Lévy Matters IV
2014Lecture notes in mathematics · 20 Zitationen · DOI
arXiv (Cornell University) · 19 Zitationen · DOI
We consider truncated SVD (or spectral cut-off, projection) estimators for a\nprototypical statistical inverse problem in dimension $D$. Since calculating\nthe singular value decomposition (SVD) only for the largest singular values is\nmuch less costly than the full SVD, our aim is to select a data-driven\ntruncation level $\\widehat m\\in\\{1,\\ldots,D\\}$ only based on the knowledge of\nthe first $\\widehat m$ singular values and vectors. We analyse in detail\nwhether sequential {\\it early stopping} rules of this type can preserve\nstatistical optimality. Information-constrained lower bounds and matching upper\nbounds for a residual based stopping rule are provided, which give a clear\npicture in which situation optimal sequential adaptation is feasible. Finally,\na hybrid two-step approach is proposed which allows for classical oracle\ninequalities while considerably reducing numerical complexity.\n
edoc Publication server (Humboldt University of Berlin) · 19 Zitationen · DOI
Sei (X(t), t>= -r) ein stationärer stochastischer Prozess, der die affine stochastische Differentialgleichung mit Gedächtnis dX(t)=L(X(t+s))dt+sigma dW(t), t>= 0, löst, wobei sigma>0, (W(t), t>=0) eine Standard-Brownsche Bewegung und L ein stetiges lineares Funktional auf dem Raum der stetigen Funktionen auf [-r,0], dargestellt durch ein endliches signiertes Maß a, bezeichnet. Wir nehmen an, dass eine Trajektorie (X(t), -r 0, konvergiert. Diese Rate ist schlechter als in vielen klassischen Fällen. Wir beweisen jedoch eine untere Schranke, die zeigt, dass keine Schätzung eine bessere Rate im Minimax-Sinn aufweisen kann. Für zeit-diskrete Beobachtungen von maximalem Abstand Delta konvergiert die Galerkin-Schätzung immer noch mit obiger Rate, sofern Delta is in etwa von der Ordnung T^(-1/2). Hingegen wird bewiesen, dass für festes Delta unabhängig von T die Rate sich signifikant verschlechtern muss, indem eine untere Schranke von T^(-s/(2s+6)) gezeigt wird. Außerdem wird eine adaptive Schätzung basierend auf Wavelet-Thresholding-Techniken für das assoziierte schlechtgestellte Problem konstruiert. Diese nichtlineare Schätzung erreicht die obige Minimax-Rate sogar für die allgemeinere Klasse der Besovräume B^s_(p,infinity) mit p>max(6/(2s+3),1). Die Restriktion p>=max(6/(2s+3),1) muss für jede Schätzung gelten und ist damit inhärent mit dem Schätzproblem verknüpft. Schließlich wird ein Hypothesentest mit nichtparametrischer Alternative vorgestellt, der zum Beispiel für das Testen auf Gedächtnis verwendet werden kann. Dieser Test ist anwendbar für eine L^2-Trennungsrate zwischen Hypothese und Alternative der Ordnung T^(-s/(2s+2.5)). Diese Rate ist wiederum beweisbar optimal für jede mögliche Teststatistik. Für die Beweise müssen die Parameterabhängigkeit der stationären Lösungen sowie die Abbildungseigenschaften der assoziierten Kovarianzoperatoren detailliert bestimmt werden. Weitere Resultate von allgemeinem Interessen beziehen sich auf die Mischungseigenschaft der stationären Lösung, eine Fallstudie zu exponentiellen Gewichtsfunktionen sowie der Approximation des stationären Prozesses durch autoregressive Prozesse in diskreter Zeit.
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FOR 5381/2: Optimale Aktionen und Stoppen im sequentiellen Lernen (TP 02)
university
IGRK 2544/1: Stochastische Analysis in Interaktion
university
SFB 1294/1: Datenassimilation – Die nahtlose Verschmelzung von Daten und Modellen
other
SFB 1294/3: Statistik von stochastischen partiellen Differentialgleichungen (SPDEs) (TP A01)
university
IGRK 2544: Stochastische Analysis in Interaktion
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FOR 5381/2: Optimale Aktionen und Stoppen im sequentiellen Lernen (TP 02)
university
SFB/TRR 388/1: Statistisches Lernen aus Pfadbeobachtungen (B01)
other
IGRK 1792/2: Hochdimensionale nicht stationäre Zeitreihen
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Stammdaten
Identität, Organisation und Kontakt aus HU-FIS.
- Name
- Prof. Dr. Markus Reiß
- Titel
- Prof. Dr.
- Fakultät
- Mathematisch-Naturwissenschaftliche Fakultät
- Institut
- Institut für Mathematik
- Arbeitsgruppe
- Mathematische Statistik
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- +49 30 2093-45466
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- 26.4.2026, 01:10:53