References
- D.W.K. Andrews and D. Pollard, An introduction to functional central limit theorems for dependent stochastic processes, Int. Stat. Rev. 62 (1994), pp. 119–132. doi: 10.2307/1403549
- R.C. Bradley, Basic properties of strong mixing conditions, in Dependence in Probability and Statistics, E. Eberlein and M.S. Taqqu, eds., Birkhäuser, Boston, 1985, pp. 165–192.
- M.D. Burke and G. Bewa, Change-point detection for general nonparametric regression models, Open J. Stat. 3 (2013), pp. 261–267. doi: 10.4236/ojs.2013.34030
- J. Dedecker and S. Louhichi, Maximal inequalities and empirical central limit theorems, in Empirical Process Techniques for Dependent Data, H. Dehling, T. Mikosch, and M. Sørensen, eds., Birkhäuser, Boston, 2002, pp. 137–159.
- H. Dehling, O. Durieu and M. Tusche, A sequential empirical CLT for multiple mixing processes with application to B-geometrically ergodic Markov chains, Electron. J. Probab. 19 (2014), pp. 1–26. doi: 10.1214/EJP.v19-3216
- H. Dehling, O. Durieu and M. Tusche, Approximating class approach for empirical processes of dependent sequences indexed by functions, Bernoulli 20 (2014), pp. 1372–1403. doi: 10.3150/13-BEJ525
- P. Doukhan, Mixing: Properties and Examples, Springer, New York, 2004.
- P. Doukhan, P. Massart and E. Rio, Invariance principles for absolutely regular empirical processes, Ann. Inst. H. Poincaré 31 (1995), pp. 393–427.
- A. Hagemann, Stochastic equicontinuity in nonlinear times series models, Econom. J. 17 (2014), pp. 188–196. doi: 10.1111/ectj.12013
- B.E. Hansen, Stochastic equicontinuity for unbounded dependent heterogeneous arrays, Econom. Theory 12 (1996), pp. 347–359. doi: 10.1017/S0266466600006629
- S.B. Hariz, Uniform CLT for empirical process, Stochastic Process. Appl. 115 (2005), pp. 339–358. doi: 10.1016/j.spa.2004.09.006
- P. Massart, Invariance principles for empirical processes: The weakly dependent case, Chapter 1B of Ph.D. dissertation, University of Paris-South, Orsay, 1987, pp. 58–102.
- M. Mohr and N. Neumeyer, Consistent nonparametric change point detection combining CUSUM and marked empirical processes, preprint on arXiv Available at https://arxiv.org/abs/1901.08491.2019.
- M. Ossiander, A central limit theorem under metric entropy with L2-bracketing, Ann. Probab. 15 (1987), pp. 897–919. doi: 10.1214/aop/1176992072
- D.N. Politis, J.P. Romano and M. Wolf, Subsampling, Springer, New York, 1999.
- S. Su and C.Y. Chiang, Limiting behavior of the perturbed empirical distribution functions evaluated at U-statistics for strongly mixing sequences of random variables, J. Appl. Math. Stoch. Anal. 10 (1997), pp. 3–20. doi: 10.1155/S1048953397000026
- L. Su and A. Ullah, A nonparametric goodness-of-fit-based test for conditional heteroscedasticity, Econom. Theory 29 (2013), pp. 187–212. doi: 10.1017/S0266466612000278
- L. Su and Z. Xiao, Testing structural change in time-series nonparametric regression models, Stat. Interface 1 (2008), pp. 347–366. doi: 10.4310/SII.2008.v1.n2.a12
- H. Tong, Threshold Models in Non-linear Times Series Analysis, Springer, New York, 1983.
- A.W. van der Vaart and J.A. Wellner, Weak Convergence and Empirical Processes, Springer, New York, 1996.
- S. Volgushev and X. Shao, A general approach to the joint asymptotic analysis of statistics from sub-samples, Electron. J. Stat. 8 (2014), pp. 390–431. doi: 10.1214/14-EJS888