Estate Khmaladze - List of Publications

1. 1. “Probabilistic Model of Consumption of Durable Goods” Proc. III Conference of the Institute of Applied Mathematics, Tbilisi, 1971, Tbilisi University Pbl., 29-31, with L. Todua.

   2. “Estimation of Necessary Sample Size for Discrimination between Close Hypotheses” Theory Probab. Appl., 1971, v.XVI, N3, 570-572.

   3. “Estimation of Necessary Sample Size for Discrimination between Parametric Hypotheses” Bulletin of Georgian Acad. Sc., 1972, v.65, 285-288.

   4. “Use of the Mathematical Satellite Model of determining Frequencies of Association of Acro- centric Chromosomes Depending on Human Age” Internat. J. Bio-Medical Computing, 1972, v.3, N3, 181-199, with R. Chitashvili and T. Lezava.

   5. “On Detection of Systematically Larger Chromosomes among B Human Chromosomes” Proc.of 1-st Conference of Tbilisi State University on Human Cytogenetics, 14-16, Tbilisi, 1974, Metsniereba, with E. Parsadanishvili.

   6. “Association of Acrocentric Chromosomes Depending on Age” Proc. of 1-st Conference of Tbilisi State University on Human Cytogenetics, 95-102, Tbilisi, 1974, Metsniereba.

   7. “Estimation of Necessary Sample Size for Discrimination between Close Hypotheses and Distance in Variation” Theory Probab. Appl., 1975, v.XX, N1, 116-127.

   8. “Mathematical and Physical Modelling of the Bioelectrical Rythm 55 c/sec” Internat. J. Bio-Medical Computing, 1974, v.5, N1, 17-21, with D. Gedevani and R. Chitashvili.

   9. “Occurrence of acrocentric chromosomes with expressed satellites in the presence of associ- ations and without them in respect to the age” Trudi Tbilisi University (Russ.), 1977, 192, 93-95, with R. Chitashvili and T. Lezava.

   10. “On Errors Related to the Use of Expert Estimates” Internat. J. Bio-Medical Computing, 1977, v.8, N1, 11-20, with F. Nefedov.

   11. “On Omega-square Tests for Parametric Hypotheses” Theory Probab. Appl., 1977, v.XXII, N3, 627-629.

   12. “Rank Tests for Hypotheses Concerning Unidentifiable Objects” Theory Probab. Appl., 1977, v.XXII, N3, 630-631, with E. Parsadanishvili.

   13. “Frequencies of Association of Acrocentric Chromosomes in Extreme Old Age” Proc. Tbilisi State University, 1977, v.192, 68-79, with R. Chitashvili and T. Lezava.

   14. “Spontaneous Level of Qualitative Changes of Chromosomes in Extreme Old Age” Proc. Georgian Acad. Sc., Ser. Biology 1978, v.24, N2, 162-170, with T. Lezava.

   15. “The use of Omega-square Tests for Testing Parametric Hypotheses” Theory Probab. Appl., 1979, v.XXIV, N2, 283-302.

   16. “RankTestsforHypothesesConcerningUnidentifiableObjects”BanachCenterPublications, 1980, v.6, 179-182, Polish Acad. Sc..

   17. “On Asymptotic Theory of Rank Tests” Theory Probab. Appl., 1980, v.XXV, N3, 661-662.

   1

   18. “A Remark on Weak Convergence of Linear Divisible Statistics” Theory Probab. Appl., 1980, v.XXV, N3, 622-624.

   19. “On L1 -convergence of Statistical Kernel Density Estimates” Sov. Math. Doklady, 1981, v.258, N5, 1052-1056, with R. Mnatsakanov.

   20. “Martingale Approach to Nonparametric Goodness of Fit Tests” Theory Probab. Appl., 1981, v.XXVI, N2, 240-258.

   21. “On the book of B.Mandelbrot ”Fractals” Theory Probab. Appl., 1981, v.XXVI, N2, 436.

   22. “Testing of Statistical Hypotheses on Unidentifiable Objects” Theory Probab. Appl., 1982, v.XXVII, N1, 175-183, with E. Parsadanishvili.

   23. “On Computing the Probability of an Empirical Process not Crossing a Curvelinear Bound- ary” Theory Probab. Appl., 1982, v.XXVII, N3, 640-649, with V. Kotel’nikova.

   24. “One Approximation of Distribution of Positively Defined Quadratic Form of Normal Ran- dom Variables” Bulletin of Georgian Acad. Sc., 1982, v.107, N2, 211-216, with V. Felker and G. Mania.

   25. “Some Applications of the Theory of Martingales to Statistics” Russian Math. Surveys, 1982, v.37/6, 215-237.

   26. “Martingale Limit Theorems for Divisible Statistics” Theory Probab. Appl., 1983, v.XXVIII, N3, 530-549.

   27. “Nonparametric Tests for Hypotheses on Unidentifiable Objects” in ”Stochastic Analysis and Asymptotic Problems of Probab. Theory and Math. Statistics”, 45-56, 1984, Tbilisi, Metsniereba, with E. Parsadanishvili.

   28. “Functional Limit Theorems for Linear Statistics of Sequential Ranks” Probab. Theory. Related Fields, 1986, v.73, 585-595, with A. Parjanadze.

   29. “Innovation Fields and the Problem of Testing a Simple Hypothesis in Rm” Sov. Math. Doklady, 1986, v.290, N2, 301-304.

   30. “On Asymptotic Theory of Statistics Based on Sequential Ranks” Theory Probab. Appl., 1986, v.XXXI, N4, 669-683, with A. Parjanadze.

   31. “CommentsonA.N.Kolmogorov’sPaper”SullaDeterminazionediUnaLeggediDistribuzione” of 1933”, 514-520, in A.N. Kolmogorov ”Theory of Probability and Mathematical Statistics. Selected Papers”, 1986, Moscow, Nauka Pbl..

   32. “On Goodness of Fit Tests in Rm for Parametric Hypotheses” Sov. Math. Doklady, 1987, v.294, N5, 1058-1061, with A. Nikabadze.

   33. “Comments on L.N.Bol’shev’s Papers ”Chi-square Goodness of Fit Tests for Poisson, Bi- nomial and Negative Binomial Distributions” and ”One Solution of Two-sample Problem”, 279-281 in L.N. Bol’shev ”Probability Theory and Mathematical Statistics. Selected Papers”, 1987, Moscow, Nauka Pbl..

   34. “An Innovation Approach to Goodness of Fit Tests in Rm” Ann. Statist., 1988, v.16, N4, 1503-1517.

   2

   35. “Characteristics of Cis- and Trans- Orientation Chromatid Types of Association in Human Lymphocytes in Extreme Old Age” Proc. Japan Acad., 1988, v.64, B, N5, 131-134, with T. Lezhava.

   36. “Aneuploidy in Human Lymphocytes in Extreme Old Age” Proc. Japan Acad., 1988, v.64, B, N5, 128-130, with T.A. Lezhava.

   37. “Characteristics of Cis- and Trans-orientation Chromatid Types of Association in Human Extreme Old Age” Proc. Japan Acad.,1988, v.64, B, N5, 131-134, with T.A. Lezhava.

   38. “The Statistical Analysis of a Large Number of Rare Events and Related Topics” in ”Prob- ability Theory and Mathematical Statistics”, Proc. A.M. Razmadze Mathemat. Inst., 1989, 196-245, with R. Chitashvili.

   39. “Characterization of Gis- and Transposition of Chromatids of the Association Type at Hu- man Extreme Old Age” Genetika (Russ.), 1989, 15, 4, 727-733, with T. Lezava.

   40. “Goodness of Fit Problem and Scanning Innovation Martingales” Ann. Statist., 1993, v.21, N2, 798-830.

   41. “On Polynomial Distributions with Large Number of Rare Events” Mathematical Methods Statistics, 1993, v.2, N3, 240-247, with Z. Tsigroshvili.

   42. “Asymptotic behaviour of a number of repeated records” Statist. Probab. Letters, 1997, v.35, N2, 49-58, with M. Nadareishvili and A. Nikabadze.

   43. “Goodness of fit tests for “chimeric” alternatives” Statistica Neerlandica, 1998, v.51, N1, 90-121..

   44. “Introduction to mathematical demography and insurance mathematics” GSA, Tbilisi, 2000, iii+152p, with G. Mirzashvili.

   45. “Two-sample problem in Rm and measure-valued martingales” IMS Lecture Notes-Monograph Series, (2001) v.36, ”State of the Art in Statistics and Probability Theory; Festschrift for Willem R. van Zwet”, 434-464, with J.H.J. Einmahl.

   46. “Towards innovation theory of spatial Brownian motion under boundary conditions” Geor- gian Mathemat. J., (2001) v.8, N2, 365-379.

   47. “Calculation of non-crossing probabilities for Poisson process and its corollaries”, Adv. Ap- plied Probability, (2001) v.33, N3, 702-718, with E. Shinjikashvili.

   48. “On a.s. coverage property of Voronoi tessellation”, Adv. Applied Probability, (2001) v.33, N4, 756-764, with N.Toronjadze.

   49. “Zipf’s Law”, Encyclopaedia of Mathematics, Supplement III, (2002) Kluwer Academic Pub- lishers, Dordrecht, 460-463.

   50. “Analysis of Bank Failure Using Published Financial Statements: The Case of Indonesia (Part 1)”, J. Data Science, (2003) v.1, N2, pp. 199-230, with Judijanto, L.

   51. “Analysis of Bank Failure Using Published Financial Statements: The Case of Indonesia (Part 2)”, J. Data Science, (2003) v.1, N3, pp. 313-336, with Judijanto, L.

   52. “Martingale transforms goodness of fit tests in regression models”, Ann. Statist., (2004), 32, 955-1034, with H.L.Koul.

   3

   53. “Local covering numbers and change-set problem”, Mathemat. Methods Statist., (2006) 15, 289-308, with R.M.Mnatsakanov, N.Toronjadze

   54. “The change-set problem for VC-classes”, Mathemat. Methods Statist., (2006) 15, 224-231, with R.M.Mnatsakanov, N.Toronjadze

   55. “Statistical analysis of electricity prices”, J. Data Science, (2007) v.5, N.1, 103-129

   56. “Differentiation of sets in measure”, J. Mathemat. Analysis Appl., 334 (2007), No.2, 1055- 1072.

   57. “Brittle power: On Roman Emperors and exponential lengths of rule”, Stat. Prob. Letters, (2007) 77, No. 12, 1248-1257, with R.Brownrigg, J.Haywood,

   58. “On distribution-free goodness-of-fit testing of exponentiality”, Annals J. Econometrics, (2007) v 143, 5-18, with J.Haywood

   59. “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

   60. “Local empirical processes near boundaries of convex bodies”, Ann. Inst. Statistical Math- ematics, (2008) v.60, 813-842, with W.Weil.

   61. “Goodness of fit problem for errors in non-parametric regression: distribution free approach”, Annals Statistics, 2009, 37, No. 6A, 3165-3185, with H.L.Koul

   62. “Divisible statistics”, in International Encyclopedia of Statistical Science, Springer Verlag, 2010.

   63. “Testing exponentiality of distribution”, in Springer Encyclopedia of Statistics, Springer Verlag, 2010, with J. Haywood.

   64. “Sequential ranks”, in International Encyclopedia of Statistical Science, Springer Verlag, 2010.

   65. “Khmaladze transformation”, in International Encyclopedia of Statistical Science, 715-718, Springer Verlag, 2010, with H.L. Koul.

   66. “Towards martingale theory for multi-dimensional survival/warranty analysis”, Proceedings of the Asia-Pacific International Symposium on Advanced Reliability and Maintenance Mod- eling (APARM) 2010, 313–324. McGraw-Hill.

   67. “On the TTT-transformation, innovation martingales and testing exponentiality”, Proceed- ings of the Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modeling (APARM) 2010, 325–332. McGraw-Hill, with L. Roberts.

   68. “Memoryless reigns of the ‘Sons of Heaven’ ”, International Statistical Review, 78 (2010), 3, 348-362, with R. Brownrigg and J.Haywood

   69. “Diversity in a Sample and Large Number of Small Probabilities: the Case of Question- naires”, Proceedings of ASA and IMS Joint Statistical Meeting, Vancouver, 2010, p.42-49.

   70. “Central limit theorems for local empirical processes near boundaries of sets”, Bernoulli 2011,17(2), 545-561, with J.H.J. Einmahl.

   71. “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.

   4

   72. “Convergence properties in certain occupancy problems including the Karlin-Rauoult law”, Journal of Applied Probability, 2011, 48, 1095-1113

   73. “On evolution of set-valued functions: an example”, Statistics and Probability Letters, 2013, 83, 898-901

   74. “A study of one null array of random variables”, in Contemporary Developments in Statistical Theory, Festschrift for Hira L. Koul, Springer, 2013, 217-226

   75. “Note on distribution free testing for discrete distributions”, The Annals of Statistics, 2013, 41, 6, 2979-2993

   76. “Differentiation of sets – The general case”, J. Mathematical Analysis and Applications, 2014, 413, 291-310, with W. Weil

   77. “Unitary transformations, empirical processes and distribution free testing”, Bernoulli, 2016, 22, 563-599; printed online in 2014

   78. “Asymptotically distribution-free goodness of fit testing for tail copulas”, The Annals of Statistics, 2015, Vol. 43, No. 2, 878-902. with S.U. Can, J.H.J. Einmahl and R.J.A. Laeven

   79. “Some new connections between the Brownian bridges and the Brownian motions”, Com- munications in Stochastic Analysis, 2015, 9, no.3, 401-412

   80. “Distribution free testing for conditional distributions given covariates”, Statistics and Prob- ability Letters, 2017, 129, 348-354,

   81. “Fold-up derivatives of set-valued functions and the change-set problem”, Invited paper, AISM, in print, with W. Weil

   82. “Eight Lectures in Demography and Insurance Mathematics”, 2007, Georgian University Press, Tbilisi.

   83. “Statistical Methods in Demography and Life Insurance”, URSS, Moscow, 2009

   84. “Statistical methods with application to demography and life insurance”, 2013, CRC Press (Chapman and Hall books)

   5