nonparametric statistics; hypothesis testing;large deviations; small deviations; asymptotic efficiency of tests; U- and V-statistics; rank statistics; arc-sine law;characterization of distributions.
Subject:
The problem of large deviation probabilities for a large class of functionals of empirical measures was solved. This enabled to calculate for the first time the Bahadur, Chernoff and Hodges–Lehmann efficiencies of numerous nonparametric statistics for goodness-of-fit, homogeneity, symmetry and independence testing. The notion of local optimality domain was introduced and investigated for many nonparametric statistics. Some original characterization theorems connected with the property of local optimality were found. In a series of joint works with E.V.Ponikarov we studied the large deviation asymptotics of Chernoff type for U- and V-statistics with general kernels. Some generalizations of arc-sine law were obtained jointly with E. Orsingher. Jointly with N. Henze we introduced and studied new goodness-of-fit tests based on the integrated empirical process.
Biography
Graduated from Faculty of Mathematics and Mechanics of St.Petersburg ( former Leningrad) State University (SPbGU, former LGU) in 1968 (Department of Probability Theory and Statistics). Ph.D. thesis was defended in 1973. D.Sci. thesis was defended in 1988. A list of my works contains more than 100 titles.
In 1998 I was awarded the prize of the St. Petersburg Mathematical Society for a monograph "Asymptotic efficiency of nonparametric tests", Cambridge, 1995. Award of Federal State Scolarship (1994, 1997, 2000). Elected as Soros Professor in Mathematics in 1994 and 1997 by International Scientific Fund. Member of the Institute of Mathematical Statistics (1993). Member of Bernoulli Society (1995) and of the European Committee of Bernoulli Society (1998–2002). Member of Editorial Boards of international journals "Mathematical Methods of Statistics" and "Metron".
Main publications:
Nikitin Yakov, Asymptotic efficiency of nonparametric tests. Cambridge University Press, 1995.
Nikitin Ya. Yu., Conti P. L. Asymptotic efficiency of independence tests based on Gini's rank association coefficient, Spearman's footrule and their generalizations // Commun. in Statist. Theory and Methods, 1999, v. 28, no. 2, p. 453–465.
Nikitin Ya. Yu., Henze N. A new approach to goodness-of-fit testing based on the integrated empirical process // J. Nonpar. Statist. 12, 2000, 391–416.
Nikitin Ya. Yu., Orsingher E. Conditional sojourn distributions of "processes" related to the third-order and fourth-order heat-type equations // J. Theor. Probab., 2000, v. 13, no. 4, 997–1012.
B. Milošević, Ya. Yu. Nikitin, M. Obradović, “Bahadur efficiency of EDF based normality tests when parameters are estimated”, Zap. Nauchn. Sem. POMI, 501 (2021), 203–217
2020
2.
Ya. Yu. Nikitin, T. A. Polevaya, “On the average perimeter of the inscribed random polygon”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 7:1 (2020), 77–84; Vestn. St. Petersbg. Univ., Math., 7:2 (2020), 58–63
2019
3.
Ya. Yu. Nikitin, T. A. Polevaya, “Limit theorems for areas and perimeters of random inscribed and circumscribed polygons”, Zap. Nauchn. Sem. POMI, 486 (2019), 200–213
K. Yu. Volkova, M. S. Karakulov, Ya. Yu. Nikitin, “Goodness-of-fit tests based on the characterization of uniformity by the ratio of order statistics, and their efficiencies”, Zap. Nauchn. Sem. POMI, 466 (2017), 67–80
G. T. Bookiya, Ya. Yu. Nikitin, “Asymptotic efficiency of new distribution-free tests of symmetry for generalized skew alternatives”, Zap. Nauchn. Sem. POMI, 454 (2016), 82–101; J. Math. Sci. (N. Y.), 229:6 (2018), 651–663
V. V. Litvinova, Ya. Yu. Nikitin, “Kolmogorov tests of normality based on some variants of Polya's characterization”, Zap. Nauchn. Sem. POMI, 441 (2015), 263–273; J. Math. Sci. (N. Y.), 219:5 (2016), 782–788
K. Yu. Volkova, Ya. Yu. Nikitin, “Exponentiality tests based on Ahsanullah's characterization and their efficiencies”, Zap. Nauchn. Sem. POMI, 412 (2013), 69–87; J. Math. Sci. (N. Y.), 204:1 (2015), 42–54
Ya. Yu. Nikitin, R. S. Pusev, “The exact asymptotic of small deviations for a series of Brownian functionals”, Teor. Veroyatnost. i Primenen., 57:1 (2012), 98–123; Theory Probab. Appl., 57:1 (2013), 60–81
K. Yu. Volkova, Ya. Yu. Nikitin, “Goodness-of-fit tests for the power function distribution based on Puri–Rubin characterization and their efficiencies”, Zap. Nauchn. Sem. POMI, 408 (2012), 115–130; J. Math. Sci. (N. Y.), 199:2 (2014), 130–138
Ya. Yu. Nikitin, P. P. Sporysheva, “On the efficiency of tests of fit based on the Deheuvels' empirical process”, Zap. Nauchn. Sem. POMI, 361 (2008), 66–77; J. Math. Sci. (N. Y.), 159:3 (2009), 317–323
V. V. Litvinova, Ya. Yu. Nikitin, “On asymptotic efficiency and local
optimality of tests based on two-sample $U$- and
$V$-statistics”, Zap. Nauchn. Sem. POMI, 351 (2007), 219–231; J. Math. Sci. (N. Y.), 152:6 (2008), 921–927
S. Meintanis, Ya. Yu. Nikitin, A. V. Tchirina, “A test of exponentiality versus alternatives containing the RNBUE class derived from the Laplace empirical transform”, Zap. Nauchn. Sem. POMI, 339 (2006), 63–77; J. Math. Sci. (N. Y.), 145:2 (2007), 4871–4879
V. V. Litvinova, Ya. Yu. Nikitin, “Two families of normality tests based on Polya characterization, and their efficiency”, Zap. Nauchn. Sem. POMI, 328 (2005), 147–159; J. Math. Sci. (N. Y.), 139:3 (2006), 6582–6588
A. I. Nazarov, Ya. Yu. Nikitin, “Logarithmic $L_2$-small ball asymptotics for some fractional Gaussian processes”, Teor. Veroyatnost. i Primenen., 49:4 (2004), 695–711; Theory Probab. Appl., 49:4 (2005), 645–658
Ya. Yu. Nikitin, E. Orsingher, “Sharp small ball asymptotics for Slepian and Watson processes in Hilbert norm”, Zap. Nauchn. Sem. POMI, 320 (2004), 120–128; J. Math. Sci. (N. Y.), 137:1 (2006), 4555–4560
Ya. Yu. Nikitin, P. A. Kharinski, “Sharp small deviation asymptotics in $L_2-$norm for a class of Gaussian processes”, Zap. Nauchn. Sem. POMI, 311 (2004), 214–221; J. Math. Sci. (N. Y.), 133:3 (2006), 1328–1332
L. Beghin, Ya. Yu. Nikitin, E. Orsingher, “Exact small ball constants for some Gaussian processes under $L^2$-norm”, Zap. Nauchn. Sem. POMI, 298 (2003), 5–21; J. Math. Sci. (N. Y.), 128:1 (2005), 2493–2502
Ya. Yu. Nikitin, N. A. Stepanova, “Pitman efficiency of tests for independence based on weighted rank statistics”, Zap. Nauchn. Sem. POMI, 278 (2001), 159–176; J. Math. Sci. (N. Y.), 118:6 (2003), 5596–5606
P. L. Conti, Ya. Yu. Nikitin, “Rates of convergence for a class of rank tests for independence”, Zap. Nauchn. Sem. POMI, 260 (1999), 155–163; J. Math. Sci. (New York), 109:6 (2002), 2141–2147
1997
20.
Ya. Yu. Nikitin, N. A. Stepanova, “A generalization of Kendall's tau and asymptotic efficiency of the corresponding test of independence”, Zap. Nauchn. Sem. POMI, 244 (1997), 227–237; J. Math. Sci. (New York), 99:2 (2000), 1154–1160
I. V. Gamov, Ya. Yu. Nikitin, “New integral nonparametric test for the hypothesis of affine symmetry”, Zap. Nauchn. Sem. POMI, 228 (1996), 77–93; J. Math. Sci. (New York), 93:3 (1999), 301–310
1993
22.
L. Yu. Kopylev, Ya. Yu. Nikitin, “On conditions of chernoff local asymptotic optimality of some nonparametric symmetry tests”, Zap. Nauchn. Sem. POMI, 207 (1993), 101–108; J. Math. Sci., 81:1 (1996), 2424–2429
Ya. E. Benson, Ya. Yu. Nikitin, “On conditions of Bahadur local optimality of weighted Kolmogorov–Smirnov statistics”, Zap. Nauchn. Sem. LOMI, 194 (1992), 21–27; J. Math. Sci., 75:5 (1995), 1884–1888
Ya. Yu. Nikitin, “Local Chernoff and Hodges–Lehmann efficiencies of linear rank symmetry tests”, Zap. Nauchn. Sem. LOMI, 184 (1990), 215–226; J. Math. Sci., 68:4 (1994), 551–559
Ya. Yu. Nikitin, “Chernoff efficiency of the sign and Wilcoxon tests for testing of symmetry”, Zap. Nauchn. Sem. LOMI, 177 (1989), 101–107; J. Soviet Math., 61:1 (1992), 1891–1896
1988
26.
Ya. Yu. Nikitin, A. G. Pankratova, “The Bahadur efficiency and local asymptotic optimality of some non-parametric tests of independence”, Zap. Nauchn. Sem. LOMI, 166 (1988), 112–128
1987
27.
Ya. Yu. Nikitin, “On Hodges–Lehman Asymptotical Efficiency of Nonparametric Goodness-of-fit and Homogeneity Tests”, Teor. Veroyatnost. i Primenen., 32:1 (1987), 82–91; Theory Probab. Appl., 32:1 (1987), 77–85
Ya. Yu. Nikitin, “Bahadur efficiency of the Watson–Darling goodness-of-fit tests”, Zap. Nauchn. Sem. LOMI, 158 (1987), 138–145
1986
29.
Ya. Yu. Nikitin, B. Saidu, “On asymptotic efficiency of Kolmogorov–Smirnov-type tests for symmetry for random sample size”, Zap. Nauchn. Sem. LOMI, 153 (1986), 122–128
1985
30.
Ya. Yu. Nikitin, “Hodges–Lehmann asymptotic efficiency of the Kolmogorov and Smirnov goodness-of-fit tests”, Zap. Nauchn. Sem. LOMI, 142 (1985), 119–123; J. Soviet Math., 36:4 (1987), 517–520
1984
31.
Ya. Yu. Nikitin, “Local Bahadur optimality and characterization problems”, Teor. Veroyatnost. i Primenen., 29:1 (1984), 79–92; Theory Probab. Appl., 29:1 (1985), 79–92
Ya. Yu. Nikitin, “Characterization of distributions by the property of local asymptotic optimality of test statistics”, Zap. Nauchn. Sem. LOMI, 108 (1981), 119–133; J. Soviet Math., 25:3 (1984), 1186–1195
Ya. Yu. Nikitin, “Bahadur efficiency of $\omega^2$-type criteria in the several sample case”, Zap. Nauchn. Sem. LOMI, 98 (1980), 140–148; J. Soviet Math., 21:1 (1983), 93–99
37.
Ya. Yu. Nikitin, “Large deviations and asymptotic efficiency of integral type statistics. II”, Zap. Nauchn. Sem. LOMI, 97 (1980), 151–175; J. Soviet Math., 24:5 (1984), 585–603
Ya. Yu. Nikitin, “Large deviations and asymptotic efficiency of integral type statistics. I”, Zap. Nauchn. Sem. LOMI, 85 (1979), 175–187; J. Soviet Math., 20:3 (1982), 2224–2231
Ya. Yu. Nikitin, “Bahadur relative asymptotic efficiency of statistics based on the empirical distribution function”, Dokl. Akad. Nauk SSSR, 231:4 (1976), 802–805
40.
Ya. Yu. Nikitin, “Limit distributions and Bahadur efficiencies for Kolmogorov–Smirnov-type statistics with random indices”, Zap. Nauchn. Sem. LOMI, 55 (1976), 185–194; J. Soviet Math., 16:2 (1981), 1042–1049
Ya. Yu. Nikitin, “On a boundary-value problem for an empirical process”, Dokl. Akad. Nauk SSSR, 205:5 (1972), 1043–1045
42.
Ya. Yu. Nikitin, “Estimates of the rate of convergence of some limit theorems and statistical criteria”, Dokl. Akad. Nauk SSSR, 202:4 (1972), 758–760
2012
43.
Ya. Yu. Nikitin, “International conference “Asymptotic problems of probability theory and mathematical statistics” to honor I. A. Ibragimov’s 80th birthday”, Teor. Veroyatnost. i Primenen., 57:3 (2012), 622; Theory Probab. Appl., 57:3 (2013), 545
2007
44.
P. J. Bickel, I. A. Ibragimov, Ya. Yu. Nikitin, S. P. Novikov, C. R. Rao, L. A. Shepp, “Abram Meerovich Kagan (on his 70th birthday)”, Uspekhi Mat. Nauk, 62:6(378) (2007), 198–200; Russian Math. Surveys, 62:6 (2007), 1239–1242
2002
45.
A. A. Borovkov, M. A. Lifshits, Ya. Yu. Nikitin, Yu. V. Prokhorov, V. N. Sudakov, A. N. Shiryaev, “Il'dar Abdullovich Ibragimov (on his 70th birthday)”, Uspekhi Mat. Nauk, 57:5(347) (2002), 187–190; Russian Math. Surveys, 57:5 (2002), 1039–1043
1999
46.
Ya. Yu. Nikitin, “Book review: Boldin M. V., Simonova G. I., Tyurin Yu. N. “Signed stochastical analysis
of linear models””, Teor. Veroyatnost. i Primenen., 44:3 (1999), 685–687; Theory Probab. Appl., 44:3 (2000), 613–621
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