Statistical Science

A Conversation with Estate V. Khmaladze

Hira L. Koul and Roger Koenker

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Estate V. Khmaladze was born in Tbilisi, Georgia, on October 20, 1944. He earned his B.Sc. degree from the Javakhishvili Tbilisi State University in 1964, majoring in physics. and his Ph.D. in mathematics in 1971 and Doctor of Physical and Mathematical Sciences in 1988, both from the Moscow State University. From 1972 to 1990, he held appointments at the Razmadze Mathematical Institute in Tbilisi and interim appointments at the V. A. Steklov Mathematical Institute in Moscow. From 1990 to 1999, he was head of the Department of Probability and Mathematical Statistics of the Razmadze Institute. From 1996 to 2001, he was on the faculty of the Department of Statistics of the University of New South Wales. Since 2002, he holds the Chair in Statistics in the School of Mathematics and Statistics of Victoria University of Wellington, New Zealand. He is a Fellow of the Royal Society of New Zealand and of the Institute of Mathematical Statistics. In 2013, he was awarded the Javakhishvili Medal from Tbilisi I. Javakhishvili State University and was elected to be a Foreign Member of the Georgian Academy of Sciences in 2016. As the conversation reveals, Khmaladze’s research ranges widely over statistical topics and beyond.

The conversation began in the old building of I. Javakhishvili Tbilisi State University during a conference on probability theory and mathematical statistics, September 6–12, 2015, and continued in the Research Center of Ilia University, Stephantsminda, during the subsequent workshop, 12–16, September, Georgia. Mount Kazbegi, 5047 m, with its white summit was occasionally visible not too far away. In what follows, the questions are put in italics while the Estate’s answers appear in the standard font.

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Statist. Sci. Volume 31, Number 3 (2016), 453-464.

First available in Project Euclid: 27 September 2016

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Khmaladze transform asymptotically distribution-free GOF tests


Koul, Hira L.; Koenker, Roger. A Conversation with Estate V. Khmaladze. Statist. Sci. 31 (2016), no. 3, 453--464. doi:10.1214/16-STS566.

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  • Akritas, M. G. and Van Keilegom, I. (2001). Non-parametric estimation of the residual distribution. Scand. J. Stat. 28 549–567.
  • Artstein, Z. (1995). A calculus for set-valued maps and set-valued evolution equations. Set-Valued Anal. 3 213–261.
  • Aubin, J.-P. and Frankowska, H. (1990). Set-Valued Analysis. Birkhäuser, Boston, MA.
  • Brownrigg, R. and Khmaladze, È. V. (2011). Strange facts about the marginal distributions of processes based on the Ornstein–Uhlenbeck process. Risk: Journal of Computational Finance 15 105–119.
  • Chitashvili, R., Khmaladze, È. V. and Lezava, T. (1972). Use of the mathematical satellite model of determining frequencies of association of acrocentric chromosomes depending on human age. Int. J. Bio-Med. Comput. 3 181–199.
  • Durbin, J., Knott, M. and Taylor, C. C. (1975). Components of Cramér–von Mises statistics. II. J. Roy. Statist. Soc. Ser. B 37 216–237.
  • Einmahl, J. H. J. and Khmaladze, È. V. (2011). Central limit theorems for local empirical processes near boundaries of sets. Bernoulli 17 545–561.
  • Frishling, V. and Lauer, M. (2006). Global and Regional Stress Test Program 2006. National Australia Bank. Internal Working Paper.
  • Khmaladze, È. V. (1979). The use of Omega-square tests for testing parametric hypotheses. Theory Probab. Appl. 24 283–302.
  • Khmaladze, È. V. (1981). Martingale approach to nonparametric goodness of fit tests. Theory Probab. Appl. 26 240–258.
  • Khmaladze, È. V. (1983). Martingale limit theorems for divisible statistics. Theory Probab. Appl. 28 530–549.
  • Khmaladze, È. V. (1987). On the theory of large number of rare events. CWI report, Amsterdam.
  • Khmaladze, È. V. (2007). Differentiation of sets in measure. J. Math. Anal. Appl. 334 1055–1072.
  • Khmaladze, È. V. (2011). Convergence properties in certain occupancy problems including the Karlin-Rouault law. J. Appl. Probab. 48 1095–1113.
  • Khmaladze, È. V. (2013a). Note on distribution free testing for discrete distributions. Ann. Statist. 41 2979–2993.
  • Khmaladze, È. V. (2013b). Statistical Methods with Applications to Demography and Life Insurance, Russian ed. CRC Press, Boca Raton, FL.
  • Khmaladze, È. V. (2016). Unitary transformations, empirical processes and distribution free testing. Bernoulli 22 563–588.
  • Khmaladze, È. V. and Koul, H. L. (2004). Martingale transforms goodness-of-fit tests in regression models. Ann. Statist. 32 995–1034.
  • Khmaladze, È. V. and Koul, H. L. (2009). Goodness-of-fit problem for errors in nonparametric regression: Distribution free approach. Ann. Statist. 37 3165–3185.
  • Khmaladze, È. V. and Weil, W. (2008). Local empirical processes near boundaries of convex bodies. Ann. Inst. Statist. Math. 60 813–842.
  • Khmaladze, È. V. and Weil, W. (2014). Differentiation of sets—the general case. J. Math. Anal. Appl. 413 291–310.
  • Koenker, R. and Xiao, Z. (2002). Inference on the quantile regression process. Econometrica 70 1583–1612.
  • Koning, A. J. (1992). Approximation of stochastic integrals with applications to goodness-of-fit tests. Ann. Statist. 20 428–454.
  • Koning, A. J. (1994). Approximation of the basic martingale. Ann. Statist. 22 565–579.
  • Lezhava, T. and Khmaladze, È. V. (1988a). Aneuploidy in human lymphocytes in extreme old age. Proc. Japan Acad. 64, B, N5 128–130.
  • Lezhava, T. and Khmaladze, È. V. (1988b). Characteristics of cis- and transorientation chromatid types of association in human extreme old age. Proc. Japan Acad. 64, B, N5 131–134.
  • Magurran, A. (2004). Measuring Biological Diversity. Wiley, New York.
  • Müller, U. U., Schick, A. and Wefelmeyer, W. (2007). Estimating the error distribution function in semiparametric regression. Statist. Decisions 25 1–18.
  • Müller, U. U., Schick, A. and Wefelmeyer, W. (2009). Estimating the error distribution function in nonparametric regression with multivariate covariates. Statist. Probab. Lett. 79 957–964.
  • Schneider, R. (1993). Convex Bodies: The Brunn-Minkowski Theory. Encyclopedia of Mathematics and Its Applications 44. Cambridge Univ. Press, Cambridge.