Rafal Kulik's Home Page

Research

Last modified: 10 April, 2021

Current Research Interests:

I do a research in probability and statistics, in particular:
- Limit theorems for weakly and strongly dependent random variables
- Time series, especially long memory and heavy tailed time series
- Extreme value theory
- Inference for traffic models
- functional data analysis
- differential privacy
- Applications to econometrics, financial mathematics and biostatistics

Papers in refereed journals - published and/or accepted

	with Y. Cissokho, Estimation of cluster functionals for regularly varying time series: sliding blocks estimators. Electronic Journal of Statistics (2021). .pdf file on Arxiv.org. Final version available at EJS webpage (coming soon).
	with Betken A., Giraudo D., Change-point tests for the tail parameter of Long Memory Stochastic Volatility time series. Statistica Sinica (2021). .pdf file on Arxiv.org.
	with Jentsch C., Bootstrapping tail array sums. Bernoulli 27(2)1409--1439 (2021). Final version available at Bernoulli webpage
	with Kriesche B., Chaput MA, Gajewski K., Schmidt V., Estimation of Spatio‐Temporal Correlations of Prehistoric Population and Vegetation in North America. Geographical Analysis 52(3)371--393 (2021). Final version available at Geographical Analysis webpage
	with Bilayi-Biakana C. and Soulier P., Statistical inference for heavy tailed series with extremal independence. Extremes 231-33 (2020). .pdf file on Arxiv.org. Final version available at Extremes webpage
	with Bilayi-Biakana C. and Ivanoff G., The tail empirical process for long memory stochastic volatility models with leverage. Electronic Journal of Statistics 133453--3484 (2019). Final version available at EJS webpage
	with Betken A., Testing for change in stochastic volatility with long-range dependence. Journal of Time Series Analysis 40707--738 (2019). .pdf file on Arxiv.org. Final version available at JTSA webpage
	with Soulier P., Wintenberger O., The tail empirical process of regularly varying functions of geometrically ergodic Markov chains. Stochastic Processes and their Applications 1294209--4238 (2019). .pdf file on Arxiv.org. Final version available at SPA webpage
	with Tong Z., Estimation for the expected shortfall given an extreme component under conditional extreme value model. Extremes 2229--70 (2019). Final version available at Extremes webpage
	with Abdelrazeq I, Ivanoff G., Goodness-of-fit tests for Lévy-driven Ornstein-Uhlenbeck processes. Canadian Journal of Statistics 46(2)353--376 (2018). Final version available at CJS webpage
	with B. Collins, T. Kousha, T. Szarek, K. Zyczkowski., The Accessibility of Convex bodies and Derandomization of the Hit and Run Algorithm. Journal of Convex Analysis 24903--916 (2017). .pdf file on Arxiv.org. Final version available at JCa webpage
	with Csaki E., Csorgo M., Strong approximations for long memory sequences based partial sums, counting and their Vervaat processes. Periodica Mathematica Hungarica.
	with Chaput M., Kriesche B., Betts M., Martindale A., Schmidt V., Gajewski K., Spatiotemporal distribution of Holocene populations in North America. Proceedings of the National Academy of Sciences 112(39) 12127-12132 (2015).
	with P. Soulier, Heavy tailed time series with extremal independence. Extremes 18(1) 273--299 (2015). .pdf file on Arxiv.org. Final version available at Extremes webpage.
	with Gaiselmann, G. and Schmidt, V., Statistical inference for curved fibrous objects in 3D - based on multiple short observations of multivariate autoregressive processes. Australian \& New Zealand Journal of Statistics 57(1) 31-54 (2015). Final version available at the journal website.
	with Sapatinas, T. and Wishart, J., Multichannel deconvolution with long-range dependence. Applied and Computational Harmonic Analysis 38(3) 357-384 (2015). .pdf file on Arxiv.org. Final version available at the journal website.
	with Abdelrazeq, I. and Ivanoff, G., Model verification for Levy-driven Ornstein-Uhlenbeck processes. Electronic Journal of Statistics 8(1) 1029-1062 (2014). Final version available at the journal website.
	with Benhaddou, R., Pensky, M., Sapatinas, T., Multichannel deconvolution with long-range dependence: A minimax study. Journal of Statistical Planning and Inference 148 1-19 (2014). .pdf file on Arxiv.org. Final version available at the journal website.
	with Lorek, P., Empirical process of residuals for regression models with long memory errors. Statistics and Probability Letters 86 7-16 (2014). .pdf file on Arxiv.org. Final version available at the journal website.
	with Basrak, B. and Palmowski, Z.., Heavy tailed branching process with immigrations. Stochastic Models 29(4) 413-434 (2013). .pdf file on Arxiv.org. Final version available at the journal website.
	with P. Soulier, Estimation of limiting conditional distributions for the heavy tailed long memory stochastic volatility process. Extremes 16(2), 203-239 (2013). .pdf file on Arxiv.org. Final version available at the journal website.
	with P. Soulier, Limit theorems for long memory stochastic volatility models with infinite variance: Partial Sums and Sample Covariances. Advances in Applied Probability 44(4), 1113-1141. (2012). .pdf file on Arxiv.org. Final version available at the journal website.
	with C. Wichelhaus, Conditional variance estimation in regression with long memory. Journal of Time Series Analysis 33(3) 468-483 (2012). .pdf file Final version available at the journal website.
	with C. Wichelhaus, Nonparametric conditional variance and error density estimation in regression models with long memory. Electronic Journal of Statistics 5 (2011), 856-898. Final version available at the journal website.
	with Z. Palmowski, Tail behaviour of the area under a random process, with applications to queueing systems, insurance and percolations. .pdf file on Arxiv.org Queueing Systems 68 (2011), 275-284. Final version available at Questa website.
	with P. Soulier, The tail empirical process for long memory stochastic volatility sequences. .pdf file on Arxiv.org. Stochastic Processes and their Applications 121 (2011), 109-134. Final version available at SPA webpage.
	with P. Lorek, Some results on random design regression with long memory errors and predictors. .pdf file on Arxiv.org. Journal of Statistical Planning and Inference 141 (2011), 508-523. Final version available at JSPI website.
	with J. Wishart, Kink estimation in stochastic regression with dependent errors and predictors. .pdf file on ARxiv.org. Electronic Journal of Statistics 4 (2010), 875-913.
	with M. Raimondo, Wavelet regression in random design with heteroscedastic dependent errors. pdf file Annals of Statistics 37 (2009), 3396-3430. Final version available at AoS webpage
	with M. Raimondo, $L^p$ wavelet regression with correlated errors and inverse problems. pdf file. Statistica Sinica 19 (2009), 1479--1489. Final version available at Statistica Sinica website.
	with G. Ivanoff, A. Dabrowski, Some notes on Poisson limits for empirical point processes. pdf file. Canadian Journal of Statistics 37 (2009), 347--360. Final version available at CJS website.
	with R. Balan, Weak invariance principle for mixing sequences in the domain of attraction of normal law. pdf file. Studia Sci. Math. Hungarica 46 (2009), 329-343. Final version available at SSMH website.
	Empirical process of long-range dependent sequences when parameters are estimated. pdf file. Journal of Statistical Planning and Inference 139 (2009), 287--294. Final version available at Elsevier website.
	Sums of extreme values of subordinated long-range dependent sequences: moving averages with finite variance. pdf file. Electronic Journal of Probability 13 (2008), 961-979. Final version available on EJP webpage.
	Nonparametric deconvolution problem for dependent sequences. pdf file. Electronic Journal of Statistics 2 (2008), 722-740.
	with M. Csorgo, Reduction principles for quantile and Bahadur-Kiefer processes of long-range dependent linear sequences. pdf file. Probability Theory and Related Fields 142 (3-4) (2008), 339-366. Final version available at Springer webpage.
	with M. Csorgo, Weak convergence of Vervaat and Vervaat Error processes of long-range dependent linear sequences. pdf file. Journal of Theoretical Probability 21 (3) (2008), 672-686. Final version available at Springer webpage.
	with M. Ould Haye, Trimmed sums of long-range dependent moving averages. pdf file. Statistics and Probability Letters 78 (15) (2008), 2536-2542. Final version available at SPL webpage.
	Bahadur-Kiefer theory for sample quantiles of weakly dependent linear processes. pdf file. Bernoulli (2007) 13, 1071--1090. Final version available at Bernoulli webpage.
	with C. Wichelhaus, Dependence in Lag for Markov chains on partially ordered state spaces with applications to degradable networks. pdf file. Stochastic Models (2007) 23, 683--696. Final version available at Taylor and Francis.
	Limit theorems for self-normalized linear processes. pdf file. Statistics and Probability Letters 76 (2006), 1947-1953. Final version available at SPL webpage
	Limit theorems for moving averages with random coefficients and heavy tailed noise. pdf file. Journal of Applied Probability 43 (2006), 245-256. Final version available at JAP webpage.
	with M. Schwarz, C. Sauer, H. Daduna, R. Szekli, M/M/1 - Queueing Systems with inventory. pdf file. Queueing Systems, 54 (2006), 57-78. Final version available at Springer website.
	with H. Daduna, C. Sauer and R. Szekli, Dependence Ordering for Queueing Networks with Breakdown and Repair. pdf file. Probability in the Engineering and Informational Sciences 20 (2006), 575-594. Final version available at Cambridge journals webpage.
	with Z. Palmowski, Tail behaviour of the area under queue length process of a single server queue with regularly varying service times. pdf file. Queueing Systems, 50 (2005), 299--323. Final version available at Springer webpage.
	with R. Szekli, Dependence orderings for some functionals of multivariate point processes. pdf file. Journal of Multivariate Analysis 92 (2005), 145--173. Final version available at Elsevier webpage.
	Monotonicity in lag for non-monotone Markov chains. pdf file. Probability in the Engineering and Informational Sciences 18, (2004), 485--492. Final version available at Cambridge journals webpage.
	Stochastic comparison of multivariate random sums. pdf file. Applicationes Mathematicae 30 (2003), 379-387.
	with R. Szekli, Sufficient conditions for long range count dependence of stationary point processes on the real line. pdf file. Journal of Applied Probability 38 (2001), 570-581.

Papers in refereed conference proceedings - published and/or accepted

with E. Csaki and M. Csorgo, On Vervaat processes for sums and renewals in weakly dependent cases. pdf file.
Dependence in probability, analysis and number theory (2010), 145-156. Kendrick Press.

Slides from the recent talks

Disjoint and sliding blocks estimators for heavy tailed time series - One World Extremes seminar, 14 December 2020.
Limit theorems for cluster functionals - Seminar in Bloomington, 4 December 2018.
The tail empirical process of regularly varying functions of geometrically ergodic Markov chains - EMS conference in Helsinki, 27 July 2017.
Statistical Inference for Extremes of Long Memory Processes - AMS Sectional Meeting in Bloomington, IN, 1 April 2017.
Estimation of the expected shortfall given an extreme component under conditional extreme value model - JNPS conference in Avignon, 12 June 2016.
Heavy Tailed Time Series with Extremal Independence given during Conference in honour of Prof. Herold Dehling, 16 January 2015.
Slides from my talk Stochastic volatility models: tails and memory given at Conference in honour of Prof. Murad Taqqu here.