A Functional Law of the Iterated Logarithm for U-Statistic Type Processes

Csörgő, M. and Horváth, L.: Invariance principles for change-point problems, J. Multivariate Anal. 27(1988), 151–168.

Dehling, H.: The functional law of the iterated logarithm for von Mises functionals and multiple Wiener integrals, J. Multivariate Anal. 28(1989), 177–189.

Dehling, H., Denker, M. and Walter, W.: Invariance principles for von Mises and U-statistics, Z. Wahrsch. verw. Gebiete 67(1984), 139–167.

Ferger, D.: An extension of the Csörgő–Horváth functional limit theorem and its applications to changepoint problems, J. Multivariate Anal. 51(1994), 338–351.

Ferger, D.: On exact rates of convergence in functional limit theorems for U-statistics type processes, J. Theoret. Probab. 7(1994), 709–723.

Ferger, D.: Optimal bounds for the Prokhorov distance of the Miller–Sen process and Brownian motion, Theory Probab. Appl. 42(1997), 155–162.

Ferger, D.: Analysis of change-point estimators under the null hypothesis, Bernoulli 7(2001), 487–506.

Ferger, D.: Exponential and polynomial tailbounds for change-point estimators, J. Statist. Plann. Inference 92(2001), 73–109.

Ferger, D. and Stute, W.: Convergence of change-point estimators, Stochastic Process. Appl. 42(1992), 345–351.

Finkelstein, H.: The law of the iterated logarithm for empirical distributions, Ann. Math. Statist. 42(1971), 607–615.

Freedman, D.: Brownian Motion and Diffusion, Springer, New York, 1983.

Hall, P.: On the invariance principle for U-statistics, Stochastic Process. Appl. 9(1979), 163–174.

Horváth, L.: Strong laws for randomly indexed U-statistics, Math. Proc. Cambridge Philos. Soc. 98(1985), 559–567.

Janson, S. and Wichura, M. J.: Invariance principles for stochastic area and related stochastic integrals, Stochastic Process. Appl. 16(1983), 71–84.

Miller, R. G., Jr. and Sen, P. K.: Weak convergence of U-statistics and von Mises differentiable statistical functions, Ann. Math. Statist. 43(1972), 31–41.

Neuhaus, G.: Functional limit theorems for U-statistics in the degenerate case, J. Multivariate Anal. 7(1977), 424–439.

Strassen, V.: An invariance principle for the law of the iterated logrithm, Z. Wahrsch. verw. Gebiete 3(1964), 211–226.