Prof. Dr. Michael Kohler
- M. Kohler. Nichtparametrische Regressionsschätzung mit Splines. Dissertation, Universität Stuttgart, 1997.
- M. Kohler. Analyse von nichtparametrischen Regressionsschätzern unter minimalen Voraussetzungen. Habilitationsschrift, Universität Stuttgart. Shaker Verlag, 2000.
- L. Györfi, M. Kohler, A. Krzyzak und H. Walk. A Distribution-Free Theory of Nonparametric Regression. Springer Series in Statistics, Springer-Verlag New York, 2002.
- J. Eckle-Kohler und M. Kohler. Eine Einführung in die Statistik und ihre Anwendungen. Springer-Verlag, Berlin, 2009.
- L. Devroye, B. Karasözen, M. Kohler und R. Korn (Eds.) Recent Developments in Applied Probability and Statistics - Dedicated to the Memory of Jürgen Lehn. Springer, 2010.
- A. Braun, M. Kohler und H. Walk.
On the rate of convergence of a neural network regression estimate
learned by gradient descent.
Herunterladbar als pdf-file.
- M. Kohler und S. Kersting.
Uncertainty quantification based on (imperfect) simulation models with estimated input distributions.
Herunterladbar als pdf-file.
- M. Kohler und A. Krzyzak.
Over-parametrized neural networks learned by gradient
descent can generalize especially well.
Herunterladbar als pdf-file.
- M. Kohler und A. Krzyzak.
Analysis of the rate of convergence of an over-parametrized deep neural network estimate learned by gradient descent.
Herunterladbar als pdf-file.
- M. Kohler und A. Krzyzak.
On the rate of convergence of an over-parametrized deep neural
network regression estimate with ReLU activation function
learned by gradient descent.
Herunterladbar als pdf-file.
- S. Drews und M. Kohler.
Analysis of the expected L_2 error of an over-parametrized deep neural
network estimate learned by gradient descent without regularization.
Herunterladbar als pdf-file.
- M. Kohler und A. Krzyzak.
On the rate of convergence of an over-parametrized
Transformer classifier
learned by gradient descent.
Herunterladbar als pdf-file.
- M. Kohler, A. Krzyzak und A. Sänger.
Learning of deep convolutional network image classifiers
via stochastic gradient descent and over-parametrization.
Herunterladbar als pdf-file.
- M. Kohler. On the universal consistency of a least squares spline regression estimator. Mathematical Methods of Statistics 6, pp. 349-364, 1997.
- L. Györfi, M. Kohler und H. Walk. Weak and strong universal consistency of semi-recursive kernel and partitioning regression estimates. Statistics & Decisions 16, pp. 1-18, 1998.
- M. Kohler. Nonparametric Regression Function Estimation Using Interaction Least Squares Splines and Complexity Regularization. Metrika 47, pp. 147-163, 1998.
- M. Kohler. Universally Consistent Regression Function Estimation Using Hierarchical B-Splines. Journal of Multivariate Analysis 67, pp. 138-164 , 1999.
- M. Kohler. Nonparametric estimation of piecewise smooth regression functions. Statistics and Probability Letters 43, pp. 49-55, 1999.
- A. Antos, L. Györfi und M. Kohler. Lower bounds on the rate of convergence of nonparametric regression estimates. Journal of Statistical Planning and Inference 83, pp. 91-100, 2000.
- M. Kohler. Inequalities for uniform deviations of averages from expectations with applications to nonparametric regression. Journal of Statistical Planning and Inference 89, pp. 1-23, 2000.
- M. Kohler und A. Krzyzak. Nonparametric regression estimation using penalized least squares. IEEE Transaction on Information Theory 47, pp. 3054-3058, 2001.
- M. Kohler, K. Máthé und M. Pintér. Prediction from randomly right censored data. Journal of Multivariate Analysis 80, pp. 73-100, 2002.
- M. Kohler, A. Krzyzak und D. Schäfer. Application of structural risk minimization to multivariate smoothing spline regression estimates. Bernoulli 8, pp. 1-15, 2002.
- J. Dippon, P. Fritz und M. Kohler. A statistical approach to case based reasoning, with application to breast cancer data. Computational Statistics and Data Analysis 40, pp. 579-602, 2002.
- M. Kohler. Nonlinear orthogonal series estimates for random design regression. Journal of Statistical Planning and Inference 115, pp. 491-520, 2003.
- M. Kohler. Universal consistency of local polynomial kernel regression estimates. Annals of the Institute of Statistical Mathematics 54, pp. 879-899, 2003.
- M. Hamers und M. Kohler. A bound on the expected maximal deviation of averages from their means. Statistics and Probability Letters 62, pp.137-144, 2003.
- M. Kohler, A. Krzyzak und H. Walk. Strong consistency of automatic kernel regression estimates. Annals of the Institute of Statistical Mathematics 55, pp. 287-308, 2003.
- M. Hamers und M. Kohler. How well can a regression function be estimated if the distribution of the (random) design is concentrated on a finite set? Journal of Statistical Planning and Inference 123, pp. 377-394, 2004.
- M. Kohler. Estimation of smooth regression functions from stationary and ergodic observations via least squares. Mathematical Methods of Statistics 13, pp. 460-471, 2004.
- M. Kohler und A. Krzyzak. Adaptive regression estimation with multilayer feedforward neural networks. Journal of Nonparametric Statistics 17, pp. 891-913, 2005.
- M. Kohler, A. Krzyzak und H. Walk. Rates of convergence for partitioning and nearest neighbor regression estimates with unbounded data. Journal of Multivariate Analysis 97, pp. 311-323, 2006.
- M. Kohler. Nonparametric regression with additional measurement errors in the dependent variable. Journal of Statistical Planning and Inference 136, pp. 3339-3361, 2006.
- M. Hamers und M. Kohler. Nonasymptotic bounds on the $L_2$ error of neural network regression estimates. Annals of the Institute of Statistical Mathematics 58, pp. 131-151, 2006.
- M. Kohler und A. Krzyzak. Asymptotic confidence intervals for Poisson regression. Preprint herunterladbar als ps- und pdf-file. Journal of Multivariate Analysis 98, pp. 1072-1094. 2007.
- L. Györfi und M. Kohler. Nonparametric estimation of conditional distributions. Preprint herunterladbar als ps- und pdf-file. IEEE Transactions on Information Theory 53, pp. 1872-1879, 2007.
- M. Kohler und A. Krzyzak. On the rate of convergence of local averaging plug-in classification rules under a margin condition. Preprint herunterladbar als ps- und pdf-file. IEEE Transactions on Information Theory 53, pp. 1735-1742, 2007.
- D. Egloff, M. Kohler und N. Todorovic. A dynamic look-ahead Monte Carlo algorithm for pricing American options. Herunterladbar als ps- und pdf-file. Annals of Applied Probability 17, pp. 1138-1171, 2007.
- M. Kohler. A regression based smoothing spline Monte Carlo algorithm for pricing American options. Herunterladbar als ps- und pdf-file. AStA Advances in Statistical Analysis 92, pp. 153-178, 2008.
- M. Kohler. Multivariate orthogonal series estimates for random design regression. Journal of Statistical Planning and Inference 138, pp. 3217-3237, 2008.
- J. Eckle-Kohler, M. Kohler und J. Mehnert. Automatic recognition of German news focussing on future-directed beliefs and intentions. Computer Speech and Language 22, pp. 394-414, 2008.
- M. Kohler, A. Krzyzak und H. Walk. Upper bounds for Bermudan options on Markovian data using nonparametric regression and a reduced number of nested Monte Carlo steps. Herunterladbar als ps- und pdf-file. Statistics and Decision 26, pp. 275-288, 2008.
- M. Kohler, A. Krzyzak und H. Walk. Optimal global rates of convergence in nonparametric regression with unbounded data. Journal of Statistical Planning and Inference 123, pp. 1286-1296, 2009.
- A. M. Bagirov, C. Clausen und M. Kohler. Estimation of a regression function by maxima of minima of linear functions. Herunterladbar als ps- und pdf-file .IEEE Transactions on Information Theory 55, pp. 833-845, 2009.
- A. M. Bagirov, C. Clausen und M. Kohler. An L2-boosting algorithm for estimation of a regression function. Herunterladbar als ps- und pdf-file.
IEEE Transcations on Information Theory 56, pp. 1417-1429, 2009. - M. Kohler, A. Krzyzak und N. Todorovic. Pricing of high-dimensional American options by neural networks. Preprint herunterladbar als ps- und pdf-file. Mathematical Finance 20, pp. 383-410, 2010.
- A. M. Bagirov, C. Clausen und M. Kohler. An algorithm for the estimation of a regression function by continuous piecewise linear functions. Herunterladbar als ps- und pdf-file. Computational Optimization and Applications 45, pp. 159-179, 2010.
- A. Fromkorth und M. Kohler. Analysis of least squares regression estimates in case of additional errors in the variables. Herunterladbar als ps- und pdf-file. Journal of Statistical Planning and Inference 141, pp. 172-188, 2011.
- M. Kohler und J. Mehnert. Analysis of the rate of convergence of least squares neural network regression estimates in case of measurement errors. Herunterladbar als ps- und pdf-file. Neural Networks 24, pp. 273-279, 2011.
- M. Kohler, A. Krzyzak und H. Walk. Estimation of the essential supremum of a regression function. Herunterladbar als ps- und pdf-file. Statistics and Probability Letters 81, pp. 685-693, 2011.
- M. Kohler, D. Jones und H. Walk. Weakly universally consistent forecasting of stationary and ergodic time series. Herunterladbar als ps- und pdf-file. IEEE Transcations on Information Theory 58, pp. 1191-1202, 2012.
- M. Kohler und A. Krzyzak. Nonparametric estimation of non-stationary velocity fields from 3D particle tracking velocimetry data. Preprint herunterladbar als ps- und pdf-file. Computational Statistics and Data Analysis 56, pp. 1566-1580, 2012.
- L. Devroye, T. Felber, M. Kohler und A. Krzyzak. L_1-consistent estimation of the density of residuals in random design regression models. Herunterladbar als ps- und pdf-file. Statistics and Probability Letters 82, pp. 173-179, 2012.
- M. Kohler und A. Krzyzak. Pricing of American options in discrete time using least squares estimates with complexity penalties. Herunterladbar als ps- und pdf-file. Journal of Statistical Planning and Inference 142, pp. 2289-2307, 2012.
- M. Kohler und H. Walk. On data-based optimal stopping under stationarity and ergodicity. Herunterladbar als ps- und pdf-file. Bernoulli 19, pp. 931-953, 2013. Zusatzmaterial: Beweis von Lemma 1 und Lemma 2: pdf-file.
- L. Devroye, T. Felber und M. Kohler.Estimation of a density using real and artificial data. Herunterladbar als ps- und pdf-file. IEEE Transactions on Information Theory 59, pp. 1917-1928, 2013.
- I. Hertel und M. Kohler. Estimation of the optimal design of a nonlinear parametric regression problem via Monte Carlo experiments. Herunterladbar als pdf- und als ps-file. Computational Statistics and Data Analysis 59, pp. 1-12, 2013.
- A. Fromkorth und M. Kohler. On the consistency of regression based Monte
Carlo methods for pricing Bermudan options in case of estimated financial models. Herunterladbar als pdf-file. Mathematical Finance 25, pp. 371-399, 2015. - D. Furer, M. Kohler und A. Krzyzak. Fixed design regression estimation based on real and artificial data.Herunterladbar als pdf- und als ps-file. Journal of Nonparametric Statistics 25, pp. 223-241, 2013.
- M. Kohler und A. Krzyzak. Optimal global rates of convergence for interpolation problems with random design. Herunterladbar als pdf- und als ps-file. Statistics and Probability Letters 83, pp. 1871-1879, 2013.
- T. Felber, D. Jones, M. Kohler und H. Walk. Weakly universally consistent static forecasting of stationary and ergodic time series via local averaging and least squares estimates. Herunterladbar als ps- und pdf-file. Journal of Statistical Planning and Inference 143, pp. 1689-1707, 2013.
- A. Bott, L. Devroye und M. Kohler. Estimation of a distribution from data with small measurement errors. Herunterladbar als pdf- und als ps-file. Electronic Journal of Statistics 7, pp. 2457-2476, 2013.
- J. Kruppa, Y. Liu, G. Biau, M. Kohler, I. König, J. Malley und A. Ziegler. Probability estimation with machine learning methods for dichotomous and multi-category outcome: Theory. Biometrical Journal 56, pp. 534-563, 2014.
- D. Jones, M. Kohler, A. Krzyzak und A. Richter. Empirical comparison of nonparametric regression estimates on real data. Herunterladbar als pdf- und als ps-file. Communications in Statistics - Simulation and Computation 45, pp. 2309-2319, 2016.
- M. Kohler, A. Krzyzak und H. Walk. Nonparametric recursive quantile estimation. Herunterladbar als pdf-file. Statistics and Probability Letters 93, pp. 102-107, 2014.
- M. Kohler. Optimal global rates of convergence for noiseless regression estimation problems with adaptively chosen design. Herunterladbar als pdf- und als ps-file. Journal of Multivariate Analysis 132, pp. 197-208, 2014.
- T. Felber, M. Kohler und A. Krzyzak. Adaptive density estimation based on real and artificial data. Herunterladbar als pdf- und als ps-file. Journal of Nonparametric Statistics 27, pp. 1-18, 2015.
- M. Kohler, F. Müller und H. Walk. Estimation of a regression function corresponding to latent variables. Herunterladbar als pdf-file. Journal of Statistical Planing and Inference 162, pp. 88-109, 2015.
- G. Enss, B. Götz, M. Kohler, A. Krzyzak und R. Platz. Nonparametric estimation of a maximum of quantiles. Herunterladbar als pdf-file. Electronic Journal of Statistics 8, pp. 3176-3192, 2014.
- D. Furer und M. Kohler. Smoothing spline regression estimation based on real and artificial data. Herunterladbar als pdf-file. Metrika 78, pp. 711-746, 2015.
- T. Felber, M. Kohler und A. Krzyzak. Adaptive density estimation from data with small measurement errors. Herunterladbar als pdf-file. IEEE Transactions on Information Theory 61, pp. 3446-3456, 2015.
- A. Bott, T. Felber und M. Kohler. Estimation of a density in a simulation model. Herunterladbar als pdf- und als ps-file. Journal of Nonparametric Statistics 27, pp. 271-285, 2015.
- A. Bott und M. Kohler. Adaptive estimation of a conditional density. Herunterladbar als pdf-file.
International Statistical Review 84, pp. 291-316, 2016. - A. Bott und M. Kohler. Nonparametric estimation of a conditional density. Herunterladbar als pdf-file. Annals of the Institute of Statistical Mathematics 69, pp. 189-214, 2017.
- M. Kohler und A. Krzyzak. Estimation of a jump point in random design regression. Herunterladbar als pdf- und als ps-file. Statistics and Probability Letters 106, pp. 247-255, 2015.
- G. Enss, M. Kohler, A. Krzyzak und R. Platz. Nonparametric quantile estimation based on surrogate models. Herunterladbar als pdf-file. IEEE Transaction on Information Theory 62, pp. 5727-5739, 2016.
- A. Bott, T. Felber, M. Kohler und L. Kristl. Estimation of a time dependent density. Herunterladbar als pdf-file. Journal of Statistical Planning and Inference 180, pp. 81-107, 2017.
- M. Hansmann und M. Kohler. Estimation of quantiles from data with additional measurement errors. Herunterladbar als pdf-file. Statistica Sinica 27, pp. 1661-1673, 2017.
- A. Kelava, M. Kohler und A. Krzyzak. Nonparametric estimation of a latent variable model. Herunterladbar als pdf- und als ps-file. Überarbeitete Version erschienen im Journal of Multivariate Analysis 154, pp. 112-134, 2017.
- M. Kohler und A. Krzyzak. Nonparametric regression based on hierarchical interaction models. Herunterladbar als pdf-file. IEEE Transactions on Information Theory 63, pp. 1620-1630, 2017.
- M. Kohler, A. Krzyzak, R. Tent und H. Walk. Nonparametric quantile estimation using importance sampling. Herunterladbar als pdf-file. Annals of the Institute of Statistical Mathematics 70, pp. 439-465, 2018.
- B. Bauer, L. Devroye, M. Kohler, A. Krzyzak und H. Walk. Nonparametric estimation of a function from noiseless observations at random points. Herunterladbar als pdf-file. Journal of Multivariate Analysis 160, pp. 90-104, 2017.
- M. Kohler und M. Krzyzak. Adaptive estimation of quantiles in a simulation model. Herunterladbar als pdf-file. IEEE Transactions on Information Theory 64, pp. 501-512, 2018.
- B. Bauer F. Heimrich, M. Kohler und A. Krzyzak. On estimation of surrogate models for high-dimensional computer experiments. Herunterladbar als pdf-file. Annals of the Institute of Statistical Mathematics 71, pp. 107-136, 2019.
- M. Kohler, A. Krzyzak, S. Mallapur und R. Platz . Uncertainty Quantification in Case of Imperfect Models: A Non-Bayesian Approach. Herunterladbar als pdf-file. Scandinavian Journal of Statistics 45, pp. 729-752, 2018.
- F. Heimrich, M. Kohler und L. Kristl. Nonparametric estimation of time-dependent quantiles in a simulation model. Herunterladbar als pdf-file, suppl. material. Statistica Sinica 30, pp. 135-151, 2020
- H. Hansmann, M. Kohler und H. Walk. On the strong universal consistency of local averaging regression estimates. Herunterladbar als pdf-file. Annals of the Institute of Statistical Mathematics 71, pp. 1233-1263, 2019.
- H. Hansmann, M. Kohler und H. Walk. Correction to: On the strong universal consistency of local averaging regression estimates. Annals of the Institute of Statistical Mathematics 71, pp. 1265-1269, 2019.
- M. Kohler und A. Krzyzak. Estimating quantiles in imperfect simulation models using conditional density estimation. Herunterladbar als pdf-file. Annals of the Institute of Statistical Mathematics 72, pp. 123-155, 2020.
- B. Bauer und M. Kohler. On deep learning as a remedy for the curse of dimensionality in nonparametric regression. Herunterladbar als pdf-file. Annals of Statistics 47, pp. 2261-2285, 2019.
- M. Kohler und A. Krzyzak. Estimation of a density from an imperfect simulation model. Herunterladbar als pdf-file. IEEE Transactions on Information Theory 65, pp. 1535-1546, 2019.
- M. Hansmann und M. Kohler. Estimation of conditional quantiles from data with additional measurement errors. Herunterladbar als pdf-file. Journal of Statistical Planning and Inference 200, 176-195, 2019.
- M. Kohler und A. Krzyzak. Estimation of extreme quantiles in a simulation model. Herunterladbar als pdf-file.
Journal of Nonparametric Statistics 31, pp. 393-419, 2019.
- M. Kohler und R. Tent. Nonparametric Quantile Estimation Using Surrogate Models and Importance Sampling. Herunterladbar als pdf-file.
Metrika 83, pp. 141-169, 2020.
- M. Kohler und S. Langer.
Discussion of
``Nonparametric regression using deep neural networks with ReLU activation function''.
Herunterladbar als pdf-file.
Annals of Statistics 48, pp. 1906-1910, 2020.
- B. Götz, S. Kersting und M. Kohler. Estimation of an improved surrogate model in uncertainty quantification by neural networks. Herunterladbar als pdf-file.
Annals of the Institute of Statistical Mathematics 73, pp. 249-281, 2021.
- M. Kohler und S. Langer.
On the rate of convergence of fully connected very deep neural network regression estimates.
Herunterladbar als pdf-file. Annals of Statistics 49, pp. 2231-2249, 2021.
- M. Kohler und A. Krzyzak.
Estimation of a density using an improved surrogate model.
Preprint herunterladbar als pdf-file.
Electronic Journal of Statistics 15, pp. 1-41, 2021.
- M. Kohler und A. Krzyzak.
Over-parametrized deep neural networks
minimizing the empirical risk
do not generalize well.
Herunterladbar als pdf-file.
Bernoulli 27, pp. 2564-2597, 2021.
- M. Kohler, A. Krzyzak und S. Langer.
Estimation of a function of low local dimensionality by deep neural networks.
Herunterladbar als pdf-file.
IEEE Transactions on Information Theory 68, pp. 4032-4042, 2022.
- M. Kohler, A. Krzyzak und B. Walter.
On the rate of convergence of image classifiers based on convolutional neural networks.
Herunterladbar als pdf-file.
Annals of the Instiute of Statistical Mathematics 74, pp. 1085-1108, 2022.
- M. Kohler und A. Krzyzak.
On the rate of convergence of a deep recurrent neural network
estimate in a regression problem with dependent data.
Herunterladbar als pdf-file.
Bernoulli 29, pp. 1663-1685, 2023.
- M. Kohler, L. Langer und U. Reif.
Estimation of a regression function on a manifold by fully
connected deep neural networks.
Herunterladbar als pdf-file.
Journal of Statistical Planning and Inference 222, pp. 160-181, 2023.
- I. Gurevych, M. Kohler, und G. Sahin.
On the rate of convergence of a classifier based on a Transformer encoder.
Herunterladbar als pdf-file.
IEEE Transaction on Information Theory 68, pp. 8139-8155, 2022.
- A. Braun, M. Kohler, L. Langer und H. Walk.
Convergence rates for shallow neural networks learned by gradient descent.
Herunterladbar als pdf-file. Bernoulli 30, pp. 475-502, 2023.
- M. Kohler und B. Walter.
Analysis of convolutional neural network image classifiers in a rotational symmetric model.
Herunterladbar als pdf-file. Supplement herunterladbar als pdf-file.
IEEE Transaction on Information Theory 69, pp. 5203-5218, 2023.
- A. Braun, M. Kohler, J. Cho und A. Krzyzak.
Analysis of the rate of convergence of
neural network regression estimates which
are easy to implement.
Herunterladbar als pdf-file.
Electronic Journal of Statistics 18, pp. 553-598, 2024.
- S. Drews und M. Kohler.
On the universal consistency of an over-parametrized deep neural network estimate learned by gradient descent.
Herunterladbar als pdf-file.
Annals of the Institue of Statistical Mathematics
76, pp. 361-391, 2024.
- M. Kohler, A. Krzyzak und B. Walter.
Analysis of the rate of convergence of an over-parametrized
convolutional neural network image classifier learned by gradient descent.
Herunterladbar als pdf-file. To appear in
Journal of Statistical Planning and Inference 2024.
- M. Kohler und L. Langer.
Statistical theory for image classification using
deep convolutional neural networks with
cross-entropy loss under the hierarchical max-pooling model.
Preprint herunterladbar als pdf-file.
To appear in
Journal of Statistical Planning and Inference 2024.
- L. Györfi und M. Kohler. Nonparametric regression estimation. In Lecture Notes (L. Györfi, ed.) zu der Advanced School Principles of Nonparametric Learning, abgehalten im Juli 2001 im CISM, Udine, pp. 55-122. Springer-Verlag, 2002.
- M. Kohler und A. Krzyzak. Rates of convergence for adaptive regression estimates with multiple hidden layer feedforward neural networks. Proceedings of IEEE 2004 International Symposium on Information Theory, Adelaide, Australien, September 4 - 9, 2005, pp. 1436-1440.
- M. Kohler. A Review on Regression-based Monte Carlo Methods for Pricing American Options. Herunterladbar als ps- und pdf-file. In:L. Devroye, B. Karasözen, M. Kohler und R. Korn (Eds.) Recent Developments in Applied Probability and Statistics - Dedicated to the Memory of Jürgen Lehn. Springer, 2010
- M. Kohler, S. Kul und K. Mathe. Least squares estimates for censored regression.
- G. Beliakov und M. Kohler. Estimation of regression functions by Lipschitz continuous functions. Herunterladbar als ps-file.
- M. Kohler. Universally consistent upper bounds for Bermudan options based on Monte Carlo and nonparametric regression. Herunterladbar als ps- und pdf-file.