Prof. Dr. Axel Bücher

• Extreme value statistics
• Nonparametric statistics, copulas
• Empirical processes
• Time series
• Change point analysis
• Statistics for stochastic processes

Submitted for publication:

1. Bücher, A. and Pakzad, C. (2024+):
   The empirical copula process in high dimensions: Stute's representation and applications.
   https://arxiv.org/abs/2405.05597
2. Bücher, A. and Staud, T. (2023+):
   Limit theorems for non-degenerate U-statistics of block maxima for time series.
   https://arxiv.org/abs/2308.13761

In peer-reviewed journals:

1. Bücher, A. and Rosenstock, A. (2024+):
   Combined modelling of micro-leveloutstanding claim counts and individualclaim frequencies in general insurance.
   To appear in: European Actuarial Journal.
   https://doi.org/10.1007/s13385-024-00383-7
2. Bücher, A. and Jennessen T. (2023+):
   Statistics for Heteroscedastic Time Series Extremes.
   To appear in: Bernoulli.
   https://arxiv.org/abs/2204.09534
3. Bücher, A. and Pakzad, C. (2024):
   Testing for independence in high dimensions based on empirical copulas.
   Annals of Statistics, Vol. 52(1): 311-334.
   https://doi.org/10.1214/23-AOS2348
4. Zanger, L., Bücher, A., Kreienkamp, F., Lorenz, P. and Tradowsky, J. (2024):
   Regional Pooling in Extreme Event Attribution Studies: an Approach Based on Multiple Statistical Testing.
   Extremes, Vol. 27, 1–32.
   https://doi.org/10.1007/s10687-023-00480-y
5. Bücher, A. and Jennessen T. (2024):
   Weighted weak convergence of the sequential tail empirical process for heteroscedastic time series with an application to tail index estimation.
   Extremes, Vol. 27, 163–184.
   https://doi.org/10.1007/s10687-023-00476-8
6. Bücher, A. and Zanger, L. (2023):
   On the Disjoint and Sliding Block Maxima method for piecewise stationary time series.
   Annals of Statistics, Vol. 51(2), 573-598
   https://doi.org/10.1214/23-AOS2260
7. Bücher, A., Dette, H. and Heinrichs, F. (2023):
   A Portmanteau-type test for detecting serial correlation in locally stationary functional time series.
   Statistical Inference for Stochastic Processes, Vol. 26, 255–278
   https://doi.org/10.1007/s11203-022-09285-5
8. Bücher, A., Genest, C., Lockhart, R., and Nešlehová, J. (2023):
   Asymptotic behavior of an intrinsic rank-based estimator of the Pickands dependence function constructed from B-splines.
   Extremes, Vol. 26, 101–138
   https://doi.org/10.1007/s10687-022-00451-9
9. Lilienthal, J., Zanger, L., Bücher, A. and Fried, R. (2022):
   A note on statistical tests for homogeneities in multivariate extreme value models for block maxima.
   Environmetrics, e2746.
   https://doi.org/10.1002/env.2746
10. Bücher, A. and Rosenstock, A. (2023):
    Micro-level Prediction of Outstanding Claim Counts using Neural Networks.
    European Actuarial Journal, Vol. 13, 55–90
    https://doi.org/10.1007/s13385-022-00314-4
11. Bücher, A. and Jennessen T. (2022):
    Statistical analysis for stationary time series at extreme levels: new estimators for the limiting cluster size distribution.
    Stochastic Processes and their Applications, Vol. 149, 75-106.
    https://doi.org/10.1016/j.spa.2022.03.004
12. Bücher, A., Dette, H. and Heinrichs, F. (2021):
    Are deviations in a gradually varying mean relevant? A testing approach based on sup-norm estimators.
    Annals of Statistics, Vol. 49, No. 6, 3583-3617.
    http://dx.doi.org/10.1214/21-AOS2098
13. Bücher A. Jaser, M. and Min, A. (2021):
    Detecting departures from meta-ellipticity for multivariate stationary time series.
    Dependence Modeling, Vol. 9, No. 1, 121-140.
    https://doi.org/10.1515/demo-2021-0105
14. Bücher, A. and Zhou, C. (2021):
    A horse race between the block maxima method and the peak-over-threshold approach.
    Statistical Science, Vol. 36, No. 3, 360-378.
    https://doi.org/10.1214/20-STS795
15. Bücher, A., Fried, R., Kinsvater, P. and Lilienthal, J. (2021):
    Penalized Quasi-Maximum-Likelihood Estimation for Extreme Value Models with Application to Flood Frequency Analysis. Extremes, Vol. 24, 325–348.
    http://dx.doi.org/10.1007/s10687-020-00379-y
16. Bücher, A., Volgushev, S. and Zou, N. (2021):
    Multiple block sizes and overlapping blocks for multivariate time series extremes.
    Annals of Statistics, Vol. 49, No. 1, 295-320.
    http://dx.doi.org/10.1214/20-AOS1957
17. Bücher, A. and Jennessen T. (2020):
    Method of moments estimators for the extremal index of a stationary time series.
    Electronic Journal Of Statistics, Vol. 14, No. 2, 3103-3156.
    https://doi.org/10.1214/20-EJS1734
18. Bücher, A., Dette, H. and Heinrichs, F. (2020):
    Detecting deviations from second-order stationarity in locally stationary functional time series.
    Annals of the Institute of Statistical Mathematics, Vol. 72(4), 1055-1094.
    https://doi.org/10.1007/s10463-019-00721-7
19. Bücher, A., Posch, P. N. and Schmidtke, P. (2020):
    Using the Extremal Index for Value-at-Risk Backtesting.
    Journal of Financial Econometrics, Vol. 18 (3), 556–584.
    https://doi.org/10.1093/jjfinec/nbaa011
20. Bücher, A., Volgushev, S. and Zou, N. (2019):
    On second order conditions in the multivariate block maxima and peak over threshold method.
    Journal of Multivariate Analysis, Vol. 173, 604-619.
    https://doi.org/10.1016/j.jmva.2019.04.011
21. Bücher, A., Fermanian, J.-D. and Kojadinovic, I. (2019):
    Combining cumulative sum change-point detection tests for assessing the stationarity of univariate time series.
    Journal of Time Series Analysis, Vol. 40, 124-150.
    https://doi.org/10.1111/jtsa.12431
22. Bücher, A. and Kojadinovic, I. (2019):
    A note on conditional versus joint unconditional weak convergence in bootstrap consistency results.
    Journal of Theoretical Probability, Vol. 32(3), 1145-1165.
    https://doi.org/10.1007/s10959-018-0823-3
23. Berghaus, B. and Bücher, A. (2018):
    Weak Convergence of a Pseudo Maximum Likelihood Estimator for the Extremal Index.
    Annals of Statistics, Vol. 46(5), 2307-2335.
    https://doi.org/10.1214/17-AOS1621
24. Bücher, A. and Segers, J. (2018):
    Inference for heavy tailed stationary time series based on sliding blocks.
    Electronic Journal of Statistics, Vol. 12(1), 1098–1125.
    https://doi.org/10.1214/18-EJS1415
25. Bücher, A. and Segers, J. (2018):
    Maximum likelihood estimation for the Fréchet distribution based on block maxima extracted from a time series.
    Bernoulli Vol. 24(2), 1427–1462.
    https://doi.org/10.3150/16-BEJ903
26. Bücher, A. and Segers, J. (2017):
    On the maximum likelihood estimator for the Generalized Extreme-Value distribution.
    Extremes, Vol. 20(4), 839–872.
    https://doi.org/10.1007/s10687-017-0292-6
27. Bücher, A., Irresberger, F. and Weiß, G. (2017):
    Testing Asymmetry in Dependence with Copula-Coskewness.
    North American Actuarial Journal, Vol. 21, 267–280.
    https://doi.org/10.1080/10920277.2017.1282876
28. Bücher, A., Kinsvater, P. and Kojadinovic, I. (2017):
    Detecting breaks in the dependence of multivariate extreme-value distributions.
    Extremes, Vol. 20(1), 53-89.
    https://doi.org/10.48550/arXiv.1505.00954
29. Berghaus, B. and Bücher, A. (2017):
    Goodness-of-fit tests for multivariate copula-based time series models.
    Econometric Theory, Vol. 33(2), 292–330.
    https://doi.org/10.1017/S0266466615000419
30. Berghaus, B., Bücher, A. and Volgushev, S. (2017):
    Weak convergence of the empirical copula process with respect to weighted metrics.
    Bernoulli, Vol. 23(1), 743–772.
    https://doi.org/10.3150/15-BEJ751
31. Bücher, A., Hoffmann, M., Vetter, M. and Dette, H. (2017):
    Nonparametric tests for detecting breaks in the jump behaviour of a time-continuous process.
    Bernoulli, Vol. 23(2), 1335–1364.
    https://doi.org/10.3150/15-BEJ780
32. Bücher, A. and Kojadinovic, I. (2016):
    A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing.
    Bernoulli, Vol. 22(2), 927–968.
    https://doi.org/10.3150/14-BEJ682
33. Bücher, A., Jäschke, S. and Wied, D. (2015):
    Nonparametric tests for constant tail dependence with an application to energy and finance.
    Journal of Econometrics, Vol. 187(1), 154–168.
    https://doi.org/10.1016/j.jeconom.2015.02.002
34. Bücher, A. (2015):
    A note on weak convergence of the sequential multivariate empirical process under strong mixing.
    Journal of Theoretical Probability, Vol. 28(3), 1028–1037.
    https://doi.org/10.1007/s10959-013-0529-5
35. Bücher, A. and Kojadinovic, I. (2015):
    Dependent multiplier bootstraps for nondegenerate U-statistics under mixing conditions with applications.
    Journal of Statistical Planning and Inference, Vol. 170, 83–105.
    https://doi.org/10.1016/j.jspi.2015.09.006
36. Bücher, A., Segers, J. and Volgushev, S. (2014):
    When uniform weak convergence fails: empirical processes for dependence functions and residuals via epi- and hypographs.
    Annals of Statistics, Vol. 42, 1598–1634.
    https://doi.org/10.1214/14-AOS1237
37. Bücher, A. and Segers, J. (2014):
    Extreme value copula estimation based on block maxima of a multivariate stationary time series.
    Extremes, Vol. 13, 495–528.
    https://doi.org/10.1007/s10687-014-0195-8
38. Bücher, A. (2014):
    A note on nonparametric estimation of bivariate tail dependence.
    Statistics & Risk Modeling, Vol. 31, 151–162.
    https://doi.org/10.1515/strm-2013-1143
39. Bücher, A., Kojadinovic, I., Rohmer, T. and Segers, J. (2014):
    Detecting changes in cross-sectional dependence in multivariate time series.
    Journal of Multivariate Analysis, Vol. 132, 111–128.
    https://doi.org/10.1016/j.jmva.2014.07.012
40. Berghaus, B. and Bücher, A. (2014):
    Nonparametric tests for tail monotonicity.
    Journal of Econometrics, Vol. 180(2), 117–126.
    https://doi.org/10.1016/j.jeconom.2014.03.005
41. Bücher, A. and Vetter, M. (2013):
    Nonparametric Inference on Lévy measures and copulas.
    Annals of Statistics, Vol. 41, 1485–1515.
    https://doi.org/10.1214/13-AOS1116
42. Bücher, A. and Dette, H. (2013):
    Multiplier bootstrap of tail copulas – with applications.
    Bernoulli, Vol. 5(A), 1655–1687.
    https://doi.org/10.3150/12-BEJ425
43. Bücher, A. and Ruppert, M. (2013):
    Consistent testing for a constant copula under strong mixing based on the tapered block multiplier technique.
    Journal of Multivariate Analysis, Vol. 116, 208–229.
    https://doi.org/10.1016/j.jmva.2012.12.002
44. Bücher, A. and Volgushev, S. (2013):
    Empirical and sequential empirical copula processes under serial dependence.
    Journal of Multivariate Analysis, Vol. 119, 61–70.
    https://doi.org/10.1016/j.jmva.2013.04.003
45. Berghaus, B., Bücher, A. and Dette H. (2013):
    Minimum distance estimators of the Pickands dependence function and related tests of multivariate extreme-value dependence.
    Journal de la Societé Francaise de Statistique, Vol. 154, 116– 137.
    http://www.numdam.org/item/JSFS_2013__154_1_116_0/
46. Bücher, A., Dette, H. and Volgushev, S. (2012):
    A test for Archimedeanity in bivariate copula models.
    Journal of Multivariate Analysis, Vol. 110, 121–132.
    https://doi.org/10.1016/j.jmva.2012.01.026
47. Bücher, A., Dette, H. and Volgushev, S. (2011):
    New estimators of the Pickands dependence function and a test for extreme-value dependence.
    Annals of Statistics, Vol. 39, No. 4, 1963–2006.
    https://doi.org/10.1214/11-AOS890
48. Bücher, A., Dette, H. and Wieczorek, G. (2011):
    Testing model assumptions in functional regression models.
    Journal of Multivariate Analysis, Vol. 102, 1472– 1488.
    https://doi.org/10.1016/j.jmva.2011.05.014
49. Bücher, A. and Dette, H. (2010):
    A note on bootstrap approximations for the empirical copula process.
    Statistics and Probability Letters, Vol. 80, 1925–1932.
    https://doi.org/10.1016/j.spl.2010.08.021
50. Bücher, A. and Dette, H. (2010):
    Some comments on goodness-of-fit tests for the parametric form of the copula based on L2-distances.
    Journal of Multivariate Analysis, Vol. 101, 749–763.
    https://doi.org/10.1016/j.jmva.2009.09.014

Refereed Book Chapters:

1. Bücher, A., El Ghouch, A. and Van Keilegom, I. (2021):
   Single-index quantile regression models for censored data. In: Daouia A., Ruiz-Gazen A. (eds)Advances in Contemporary Statistics and Econometrics.
   Springer, Cham, 177–196.
   https://link.springer.com/chapter/10.1007/978-3-030-73249-3_10
2. Bücher, A. and Kojadinovic, I. (2015):
   An overview of nonparametric tests of extremevalue dependence. In: Dey, D. and Yan, J: Extreme Value Modeling and Risk Analysis: Methods and Applications.
   Crc Press Inc, 2015, 377–398.
   https://arxiv.org/abs/1410.6784

Here you can find the completed externally funded projects.

• Associate Editor for Journal of Statistical Planning and Inference (seit 2014):
  www.journals.elsevier.com/journal-of-statistical-planning-and-inference
• Associate Editor for Bernoulli Journal (seit 2019):
  https://www.bernoullisociety.org/publications/bernoulli-journal
• Associate Editor for Statistical Inference for Stochastic Processes (seit 2020):
  https://www.springer.com/journal/11203
• Elected member of the European Regional Committee from Bernoulli Society (seit 2020)
• Managing Director of the Mathematical Institute at Heinrich Heine University Düsseldorf (2021 - 2023)

• Mit Extremen rechnen (in german)
• Axel Bücher interessiert sich für Extremwerte. (in german)
• HHU Podcast Zuckerschoten. (in german)
• HHU - Forschung im Fokus. (in german)