Research interests :
Asymptotic statistics, nonparametric and semiparametric estimation of copulas, methods based on a distance matrix,
permutation methods...
ORCID: 0000-0002-0396-9373, Researcher ID: I-2447-2014, Scopus ID: 16402809300.
Referred (methodological) publications :Neumeyer, N. and Omelka, M. (2025). Generalized Hadamard differentiability of the copula mapping and its applications Bernoulli 31 (2), 1451–1474. DOI: 10.3150/24-BEJ1777.
Gijbels, I., Kika, V. and Omelka, M. (2022). Choice of smoothing parameter in multivariate copula-based tail coefficients Journal of Statistical Planning and Inference. 221,136–153, DOI:10.1016/j.jspi.2022.04.002 . [Available upon the request from the author]
Gijbels, I., Omelka, M., and Veraverbeke, N. (2021). Omnibus test for covariate effects in conditional copula models. Journal of Multivariate Analysis, 186. 104804. DOI: 10.1016/j.jmva.2021.104804. [Available upon the request from the author]
Omelka, M., Hudecová, Š. and Neumeyer, N. (2021). Maximum pseudo-likelihood estimation based on estimated residuals in copula semiparametric models. Scandinavian Journal of Statistics. 48, 1433–1473 DOI: 10.1111/sjos.12498.
Gijbels, I., Kika, V. and Omelka, M. (2021). On the specification of multivariate association measures and their behaviour with increasing dimension Journal of Multivariate Analysis. 182:104704, DOI: 10.1016/j.jmva.2020.104704.
2016–2020:
Gijbels, I., Kika, V. and Omelka, M. (2020). Multivariate Tail Coefficients: Properties and Estimation. Entropy, 22, 728. DOI: 10.3390/e22070728.
R code and the data file
Côté, M.-P., Genest, Ch., Omelka, M. (2019). Rank-based inference tools for copula regression, with property and casualty insurance applications, Insurance: Mathematics and Economics, 89, 1–15. DOI: 10.1016/j.insmatheco.2019.08.001.
Neumeyer, N., Omelka, M., and Hudecová, Š. (2019). A copula approach for dependence modeling in multivariate nonparametric time series, Journal of Multivariate Analysis, 171, 139–162. DOI: 10.1016/j.jmva.2018.11.016. The draft of the paper is available at arXiv:1705.07605.
Gijbels, I., Omelka, M., Pešta, M. and Veraverbeke, N. (2017). Score tests for covariate effects in conditional copulas. Journal of Multivariate Analysis, 159, 111–133 DOI: 10.1016/j.jmva.2017.05.001. [Available upon the request from the author]
score-tests-for-covariate-effects.R (R-function implementing the suggested test),
analysis-Cs-Sc-web.R (R-code for the real data example in the paper).
Gijbels, I., Omelka, M., and Veraverbeke, N. (2017). Nonparametric testing for no covariate effects in conditional copulas, Statistics, 51, 475–509. DOI: 10.1080/02331888.2016.1258070 [Available upon the request from the author]
Nagy, S., Gijbels, I., Omelka, M., Hlubinka, D. (2016). Integrated depth for functional data: statistical properties and consistency, ESAIM: Probability and Statistics, 20, 95–130. DOI: 10.1051/ps/2016005.
2011–2015:
Gijbels, I., Omelka, M., and Veraverbeke, N. (2015). Estimation of a Copula when a Covariate Affects only Marginal Distributions, Scandinavian Journal of Statistics, Vol. 42, 1109–1126. DOI: 10.1111/sjos.12154. [Available upon the request from the author]
Gijbels, I., Omelka, M., and Veraverbeke, N. (2015). Partial and average copulas and association measures, Electronic Journal of Statistics, 9, 2420–2474, DOI: 10.1214/15-EJS1077. [The paper is freely available on the webpage of the journal.]
Hlubinka, D., Gijbels, I., Omelka, M., and Nagy, S. (2015). Integrated data depth for smooth functions and its application in supervised classification. Computational Statistics, 30, 1011–1031. DOI: 10.1007/s00180-015-0566-x.
Veraverbeke, N., Gijbels, I. and Omelka, M. (2014) Pre-adjusted nonparametric estimation of a conditional distribution function. Journal of the Royal Statistical Society: Series B, Vol. 76, 399–438. DOI: 10.1111/rssb.12041. Available upon the request from the author. An R-script to reproduce Figure 11 in Section 6.
Omelka, M. and Hudecová, Š. (2013) A comparison of the Mantel test with a generalised distance covariance test. Environmetrics, Vol. 24, 449–460. DOI: 10.1002/env.2238. Available upon the request from the author.
Gijbels, I. and Omelka, M. (2013). Testing for Homogeneity of Multivariate Dispersions Using Dissimilarity Measures. Biometrics, Vol. 69, 137–145. DOI: 10.1111/j.1541-0420.2012.01797.x. Accepted version of the paper for scholarly purposes only. Data and code used in the paper.
Omelka, M., Veraverbeke, N., and Gijbels, I. (2013). Bootstrapping the conditional copula. Journal of Statistical Planning and Inference, Vol. 143, 1–23. DOI: 10.1016/j.jspi.2012.06.001. Available online. ---- Downloadable PDF preprint for scholarly purposes only.
Gijbels, I., Omelka, M., and Veraverbeke, N. (2012). Multivariate and functional covariates and conditional copulas. Electronic Journal of Statistics, Vol. 6, 1273–1306. DOI: 10.1214/12-EJS712. -- The paper is freely available on the webpage of the journal.
Omelka, M. and Pauly, M. (2012). Testing equality of correlation coefficients in two populations via permutation methods. Journal of Statistical Planning and Inference, 142, 1396–1406. DOI: 10.1016/j.jspi.2011.12.018. Downloadable PDF preprint for scholarly purposes only.
Veraverbeke, N., Omelka, M., and Gijbels, I. (2011). Estimation of a conditional copula and association measures, Scandinavian Journal of Statistics, Vol. 38, 766–780. DOI: 10.1111/j.1467-9469.2011.00744.x Downloadable accepted version of the paper for scholarly purposes only.
Gijbels, I., Veraverbeke, N., and Omelka, M. (2011). Conditional copulas, association measures and their applications, Computational Statistics and Data Analysis, 55, 1919–1932. DOI: 10.1016/j.csda.2010.11.010 ---- Downloadable PDF preprint for scholarly purposes only.
2006–2010:
Omelka, M. (2010). Second-order asymptotic representation of M-estimators in a linear model, Nonparametrics and Robustness in Modern Statistical Inference and Time Series Analysis: A Festschrift in honor of Professor Jana Jurečková, Vol. 7, 194–203. IMS Collections.
Gijbels, I., Sznajder, D., and Omelka, M. (2010). Positive quadrant dependence tests for copulas, The Canadian Journal of Statistics, Vol. 38, No. 4, 555–581. DOI: 10.1002/cjs.10088 ---- Downloadable PDF preprint for scholarly purposes only.
Omelka, M. and Salibian-Barrera M. (2010). Uniform asymptotics for S- and MM-regression estimators. Annals of the Institute of Statistical Mathematics, Vol. 62, 897–927.
Jurečková, J. and Omelka, M. (2010), Estimator of the Pareto index based on nonparametric test, Communications in Statistics - Theory and Methods, 39 (8-9), pp. 1536–1551.
Omelka, M., Gijbels, I., and Veraverbeke, N. (2009). Improved kernel estimation of copulas: weak convergence and goodness-of-fit testing. Annals of Statistics, Vol. 37, 3023–3058.
Omelka, M. (2008). Comparison of two types of confidence intervals based on Wilcoxon-type R-estimators. Statistics and Probability Letters, Vol. 78, 3366–3372.
Omelka, M. (2007). Second Order Linearity of Wilcoxon Rank Statistics. Annals of the Institute of Statistical Mathematics, Volume 59, 385–402
2005 and earlier:
Omelka, M. (2005). The Behavior of Locally Most Powerful Tests. Kybernetika, Volume 41, Number 6, 699–712.
Omelka, M. (2004). The Test of Full Specification of the Normal Distribution. In: Antoch, J., Dohnal, G. (Eds.) ROBUST 2004, Proceedings of the 13th Summer School of the Union of Czech Mathematicians and Physicists, 267–275.
Other publications:
Omelka, M., (2006). Second order properties of some M-estimators and R-estimators. Ph.D. Thesis. Charles University in Prague.
Omelka, M. (2006). An alternative method for constructing confidence intervals from M-estimates in linear models. In the proceedings of Prague Stochastics 2006.