Recent and Selected Publications

• "When Pearson χ2 and other divisible statistics are not goodness-of-fit tests", ArXiv:2406.09195v3 [Stat.ME], Aug. 2024, with S. Algeri
• "Distribution free testing for the family of Laplace distributions", Communications in Statistics - Simulation and Computation, 2023, 10, 1–12, with B. Roberts and J. Haywood
• "On evolution model for SARS-Cov-2 - infected population. The case of New Zealand", Journal of Applied Statistics, 2021, 50, 2435-2449, with G. Kvizhinadze
• "Testing hypothesis on transition distributions of a Markov sequence", Journal of Statistical Planning and Inference, 2021, v 215, 72-84
• "Distribution free testing in linear and parametric regression", Annals Institute Statistical Mathematics, 2021, 73(6), 1063 - 1087.
• "How to test that a given process is an Ornstein-Uhlenbeck process", Statistical Inference for Stochastic Processes, 2021, 24(3), 405 - 419
• "Function-parametric empirical processes, projections and unitary operators", In: La Rocca M., Liseo B., Salmaso L. (eds), Nonparametric Statistics. 4th ISNPS (2018). Springer Proceedings in Mathematics & Statistics, 339, 271-283.
• "Projection Approach to Distribution-Free Testing for Point Processes. Regular Models", Transactions of A.Razmadze Mathematical Institute, 2020, 174, 2, 155-173
• "Asymptotic hypothesis testing for the colour blind problem", Electronic Journal of Statistics 2019, Vol. 13, 4573-4595, with L.Dumitrescu
• "Fold-up derivatives of set-valued function and the change-set problem", Annals of the Institute of Statistical Mathematics, 2017, 1-38, with W. Weil
• "Distribution free testing for conditional distributions given covariates", Statistics and Probability Letters, 2017, 129, 348-354
• "Unitary transformations, empirical processes and distribution free testing", Bernoulli, 2016, 22, 563-599; printed online in 2014
• "Some new connections between the Brownian bridges and the Brownian motions", Communications in Stochastic Analysis, 2015, 9, no.3, 401-412
• "Asymptotically Distribution-Free Goodness-of-Fit Testing for Tail Copulas", The Annals of Statistics, 2015, 43, 878-902, with S.U. Can, J.H.J. Einmahl and R.J.A. Laeven
• "Differentiation of sets -- The general case", J. Mathematical Analysis and Applications, 2014, 413, 291-310, with W. Weil
• "Note on distribution free testing for discrete distributions", The Annals of Statistics, 2013, 41, 6, 2979-2993
• "A study of one null array of random variables", in Contemporary Developments in Statistical Theory, Festschrift for Hira L. Koul, Springer, 2013, 217-226
• "On evolution of set-valued functions: an example", Statistics and Probability Letters, 2013, 83, 898-901
• "Convergence properties in certain occupancy problems including Karlin-Rouault Law", J. Applied Probability, 2011, v.48,1095-1113
• "Central limit theorems for local empirical processes near boundaries of sets", Bernoulli, 2011, v.17, 545-561, with J.H.J.Einmahl
• "Strange facts about the marginal distributions of processes based on the Ornstein-Uhlenbeck process", Risk: Journal of Computational Finance, 2011, 15, 105-119, with R.Brownrigg
• "Diversity in a Sample and Large Number of Small Probabilities: the Case of Questionnaires", Proceedings of ASA and IMS Joint Statistical Meeting, Vancouver, 2010, p.42-49.
• "Memoryless reigns of the `Sons of Heaven' ", International Statistical Review, 2010, 78, 348-362, with R. Brownrigg and J.Haywood
• "Divisible statistics", in Springer Encyclopedia of Statistics, Springer Verlag, 2010.
• "Testing exponentiality of distribution", in Springer Encyclopedia of Statistics, Springer Verlag, 2010, with J. Haywood.
• "Sequential ranks", in Springer Encyclopedia of Statistics, Springer Verlag, 2010.
• "Khmaladze transformation", in Springer Encyclopedia of Statistics, Springer Verlag, 2010, with H.L. Koul.
• "Towards martingale theory for multi-dimensional survival/warranty analysis", Proceedings of the Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modeling (APARM) 2010, 313--324. McGraw-Hill.
• "On the TTT-transformation, innovation martingales and testing exponentiality", Proceedings of the Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modeling (APARM) 2010, 325--332. McGraw-Hill, with L. Roberts.
• "Goodness-of-fit problem for errors in non-parametric regression: distribution free approach", Ann.Statist., 2009, v.37, 3165-3185, with H.L.Koul
• "Local empirical processes near boundaries of convex bodies", Annals Institute Statistical Mathematics, 2008, v.60, 813-842, with W.Weil.
• "Natural and artefactual aneuploidy in human lymphocytes in extreme old age", Georgian Medical News, 2008, April (157): 72-6, with T. Lezhava, T. Jokhadze, T. Buadze
• "Statistical analysis of electricity prices", J. Data Science, 2007, v.5, N.1, 103-129
• "Differentiation of sets in measure", J. Mathemat. Analysis Applications., 2007, 342, 1055-1072.
• "Brittle power: On Roman Emperors and exponential lengths of rule", Statistics Probability Letters, 2007, 77, No. 12, 1248-1257, with R.Brownrigg, J.Haywood,
• "On distribution-free goodness-of-fit testing of exponentiality", Annals J. Econometrics, 2007, v 143, 5-18, with J.Haywood
• "Local covering numbers and change-set problem", Mathemat. Methods Statistics, 2006, 15, 289-308, with R.M.Mnatsakanov, N.Toronjadze
• "The change-set problem for VC-classes", Mathemat. Methods Statistics, 2006, 15, 224-231, with R.M.Mnatsakanov, N.Toronjadze

• "Two-sample problem in R^m", IMS Lecture Notes--Monograph Series, 2001, with J.H.J. Einmahl
• "Goodness of fit problem and scanning martingales", The Annals of Statistics, 1993,
• "On asymptotic theory of statistics based on sequential ranks" Theory Probab. Appl., 1986, v.XXXI,N4
• "Functional limit theorems for divisible statistics" Probab.Theory Related Fields, 1986, v.73
• "Martingale methods in statistics" Uspechi Mat.Nauk (Russian Mathemat. Surveys), 1985, v.33,N.2
• "Martingale limit theorems for divisible statistics" Theory Probab. Appl., 1983, v.XXVIII,N3
• "Testing of statistical hypothesis concerning unidentifiable objects" Theory Probab. Appl., 1982, v.XXVII, N1
• "Martingale approach to goodness of fit tests" Theory Probab.Appl.,1981, v.XXVI,N1
• "Use of type tests for testing parametric hypothesis" Theory Probab. Appl., 1979, v.XXIV,N2