Download

Full Text

• ARCONES, M. A. and GINÉ, E. (1993). Limit theorems for U-processes. Ann. Probab. 21 1494–1542. MR1235426
• BARBOUR, A. D. (1990). Stein’s method for diffusion approximations. Probab. Theory Related Fields 84 297–322. MR1035659 https://doi.org/10.1007/BF01197887
• BARBOUR, A. D. and JANSON, S. (2009). A functional combinatorial central limit theorem. Electron. J. Probab. 14 2352–2370. MR2556014 https://doi.org/10.1214/EJP.v14-709
• BASALYKAS, A. (1994). Functional limit theorems for random multilinear forms. Stochastic Process. Appl. 53 175–191. MR1290712 https://doi.org/10.1016/0304-4149(94)90062-0
• BHATTACHARYA, R. N. and GHOSH, J. K. (1992). A class of U-statistics and asymptotic normality of the number of k-clusters. J. Multivariate Anal. 43 300–330. MR1193616 https://doi.org/10.1016/0047-259X(92)90038-H
• BICKEL, P. J. and RITOV, Y. (1988). Estimating integrated squared density derivatives: Sharp best order of convergence estimates. Sankhyā Ser. A 50 381–393. MR1065550
• BILLINGSLEY, P. (1999). Convergence of Probability Measures, 2nd ed. Wiley Series in Probability and Statistics: Probability and Statistics. Wiley, New York. MR1700749 https://doi.org/10.1002/9780470316962
• BOROVSKIKH, YU. V. (1996). U-Statistics in Banach Spaces. VSP, Utrecht. MR1419498
• CHEN, H. and ZHANG, N. (2015). Graph-based change-point detection. Ann. Statist. 43 139–176. MR3285603 https://doi.org/10.1214/14-AOS1269
• CHEN, X. (2018). Gaussian and bootstrap approximations for high-dimensional U-statistics and their applications. Ann. Statist. 46 642–678. MR3782380 https://doi.org/10.1214/17-AOS1563
• CHEN, X. and KATO, K. (2020). Jackknife multiplier bootstrap: Finite sample approximations to the Uprocess supremum with applications. Probab. Theory Related Fields 176 1097–1163. MR4087490 https://doi.org/10.1007/s00440-019-00936-y
• CHU, L. and CHEN, H. (2019). Asymptotic distribution-free change-point detection for multivariate and non-Euclidean data. Ann. Statist. 47 382–414. MR3910545 https://doi.org/10.1214/18-AOS1691
• CSÖRGO‟ , M. and HORVÁTH, L. (1988). Invariance principles for changepoint problems. J. Multivariate Anal. 27 151–168. MR0971179 https://doi.org/10.1016/0047-259X(88)90122-4
• CSÖRGO‟ , M. and HORVÁTH, L. (1997). Limit Theorems in Change-Point Analysis. Wiley Series in Probability and Statistics. Wiley, Chichester. MR2743035
• DE JONG, P. (1990). A central limit theorem for generalized multilinear forms. J. Multivariate Anal. 34 275–289. MR1073110 https://doi.org/10.1016/0047-259X(90)90040-O
• DE LA PEÑA, V. H. and GINÉ, E. (1999). Decoupling: From Dependence to Independence. Probability and Its Applications (New York). Springer, New York. MR1666908 https://doi.org/10.1007/978-1-4612-0537-1
• DÖBLER, C. and PECCATI, G. (2017). Quantitative de Jong theorems in any dimension. Electron. J. Probab. 22 Paper No. 2, 35 pp. MR3613695 https://doi.org/10.1214/16-EJP19
• DÖBLER, C. and PECCATI, G. (2019). Quantitative CLTs for symmetric U-statistics using contractions. Electron. J. Probab. 24 Paper No. 5, 43 pp. MR3916325 https://doi.org/10.1214/19-EJP264
• DUDLEY, R. M. (2002). Real Analysis and Probability. Cambridge Studies in Advanced Mathematics 74. Cambridge Univ. Press, Cambridge. MR1932358 https://doi.org/10.1017/CBO9780511755347
• DYNKIN, E. B. and MANDELBAUM, A. (1983). Symmetric statistics, Poisson point processes, and multiple Wiener integrals. Ann. Statist. 11 739–745. MR0707925 https://doi.org/10.1214/aos/1176346241
• FERGER, D. (1994). An extension of the Csörgo–Horváth ‟ functional limit theorem and its applications to changepoint problems. J. Multivariate Anal. 51 338–351. MR1321302 https://doi.org/10.1006/jmva.1994.1066
• FERGER, D. (1995). The joint distribution of the running maximum and its location of D-valued Markov processes. J. Appl. Probab. 32 842–845. MR1344083 https://doi.org/10.2307/3215136
• FERGER, D. (1999). On the uniqueness of maximizers of Markov–Gaussian processes. Statist. Probab. Lett. 45 71–77. MR1718353 https://doi.org/10.1016/S0167-7152(99)00044-9
• FERGER, D. (2001). Analysis of change-point estimators under the null hypothesis. Bernoulli 7 487–506. MR1836742 https://doi.org/10.2307/3318498
• GINÉ, E. and MASON, D. M. (2007). On local U-statistic processes and the estimation of densities of functions of several sample variables. Ann. Statist. 35 1105–1145. MR2341700 https://doi.org/10.1214/009053607000000154
• GOMBAY, E. (2004). U-statistics in sequential tests and change detection. Sequential Anal. 23 257–274. MR2064232 https://doi.org/10.1081/SQA-120034111
• GOMBAY, E. and HORVÁTH, L. (1995). An application of U-statistics to change-point analysis. Acta Sci. Math. (Szeged) 60 345–357. MR1348699 [28] HALL, P. (1979). On the invariance principle for U-statistics. Stochastic Process. Appl. 9 163–174. MR0548836 https://doi.org/10.1016/0304-4149(79)90028-0
• HORVÁTH, L. and RICE, G. (2014). Extensions of some classical methods in change point analysis. TEST 23 219–255. MR3210268 https://doi.org/10.1007/s11749-014-0368-4
• IBRAGIMOV, R. and SHARAKHMETOV, S. (2002). Bounds on moments of symmetric statistics. Studia Sci. Math. Hungar. 39 251–275. MR1956938 https://doi.org/10.1556/SScMath.39.2002.3-4.1
• JAMMALAMADAKA, S. R. and JANSON, S. (1986). Limit theorems for a triangular scheme of U-statistics with applications to inter-point distances. Ann. Probab. 14 1347–1358. MR0866355
• JANSON, S. (2018). Renewal theory for asymmetric U-statistics. Electron. J. Probab. 23 Paper No. 129, 27 pp. MR3896866 https://doi.org/10.1214/18-EJP252
• KARLIN, S. and RINOTT, Y. (1982). Applications of ANOVA type decompositions for comparisons of conditional variance statistics including jackknife estimates. Ann. Statist. 10 485–501. MR0653524
• KASPRZAK, M. J. (2020). Stein’s method for multivariate Brownian approximations of sums under dependence. Stochastic Process. Appl. 130 4927–4967. MR4108478 https://doi.org/10.1016/j.spa.2020.02. 006
• LACHIÈZE-REY, R. and PECCATI, G. (2013). Fine Gaussian fluctuations on the Poisson space II: Rescaled kernels, marked processes and geometric U-statistics. Stochastic Process. Appl. 123 4186–4218. MR3096352 https://doi.org/10.1016/j.spa.2013.06.004
• LAURENT, B. (1996). Efficient estimation of integral functionals of a density. Ann. Statist. 24 659–681. MR1394981 https://doi.org/10.1214/aos/1032894458
• LAURENT, B. (1997). Estimation of integral functionals of a density and its derivatives. Bernoulli 3 181–211. MR1466306 https://doi.org/10.2307/3318586
• LAURENT, B. and MASSART, P. (2000). Adaptive estimation of a quadratic functional by model selection. Ann. Statist. 28 1302–1338. MR1805785 https://doi.org/10.1214/aos/1015957395
• MAJOR, P. (2013). On the Estimation of Multiple Random Integrals and U-Statistics. Lecture Notes in Math. 2079. Springer, Heidelberg. MR3087566 https://doi.org/10.1007/978-3-642-37617-7
• MANDELBAUM, A. and TAQQU, M. S. (1984). Invariance principle for symmetric statistics. Ann. Statist. 12 483–496. MR0740907 https://doi.org/10.1214/aos/1176346501
• MILLER, R. G. JR. and SEN, P. K. (1972). Weak convergence of U-statistics and von Mises’ differentiable statistical functions. Ann. Math. Stat. 43 31–41. MR0300321 https://doi.org/10.1214/aoms/1177692698
• NEUHAUS, G. (1977). Functional limit theorems for U-statistics in the degenerate case. J. Multivariate Anal. 7 424–439. MR0455084 https://doi.org/10.1016/0047-259X(77)90083-5
• NOLAN, D. and POLLARD, D. (1987). U-processes: Rates of convergence. Ann. Statist. 15 780–799. MR0888439 https://doi.org/10.1214/aos/1176350374
• NOURDIN, I. and NUALART, D. (2020). The functional Breuer–Major theorem. Probab. Theory Related Fields 176 203–218. MR4055189 https://doi.org/10.1007/s00440-019-00917-1
• PECCATI, G. and REITZNER, M., eds. (2016). Stochastic Analysis for Poisson Point Processes: Malliavin Calculus, Wiener–Itô Chaos Expansions and Stochastic Geometry. Bocconi & Springer Series 7. Springer, Cham. MR3444831 https://doi.org/10.1007/978-3-319-05233-5
• PENROSE, M. (2003). Random Geometric Graphs. Oxford Studies in Probability 5. Oxford Univ. Press, Oxford. MR1986198 https://doi.org/10.1093/acprof:oso/9780198506263.001.0001
• RACKAUSKAS , A. and WENDLER, M. (2020). Convergence of U-processes in Hölder spaces with application to robust detection of a changed segment. Statist. Papers 61 1409–1435. MR4127480 https://doi.org/10.1007/s00362-020-01161-9
• ROBINS, J. M., LI, L., TCHETGEN, E. T. and VAN DER VAART, A. (2016). Asymptotic normality of quadratic estimators. Stochastic Process. Appl. 126 3733–3759. MR3565475 https://doi.org/10.1016/j.spa.2016.04.005
• SERFLING, R. J. (1980). Approximation Theorems of Mathematical Statistics. Wiley Series in Probability and Mathematical Statistics. Wiley, New York. MR0595165
• VITALE, R. A. (1992). Covariances of symmetric statistics. J. Multivariate Anal. 41 14–26. MR1156678 https://doi.org/10.1016/0047-259X(92)90054-J