Tests for Scale Changes Based on Pairwise Differences

References

• Andrews, D. W. (1991), “Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation,” Econometrica, 59, 817–858. DOI: 10.2307/2938229.
   Web of Science ®Google Scholar
• Aue, A., Hörmann, S., Horváth, L., and Reimherr, M. (2009), “Break Detection in the Covariance Structure of Multivariate Time Series Models,” Annals of Statistics, 37, 4046–4087. DOI: 10.1214/09-AOS707.
   Web of Science ®Google Scholar
• Bücher, A., and Kojadinovic, I. (2016a), “A Dependent Multiplier Bootstrap for the Sequential Empirical Copula Process Under Strong Mixing,” Bernoulli, 22, 927–968. DOI: 10.3150/14-BEJ682.
   Web of Science ®Google Scholar
• Bücher, A., and Kojadinovic, I. (2016b), “Dependent Multiplier Bootstraps for Non-Degenerate U-Statistics Under Mixing Conditions With Applications,” Journal of Statistical Planning and Inference, 170, 83–105.
   Web of Science ®Google Scholar
• Carlstein, E. (1986), “The Use of Subseries Values for Estimating the Variance of a General Statistic From a Stationary Sequence,” Annals of Statistics, 14, 1171–1179. DOI: 10.1214/aos/1176350057.
   Web of Science ®Google Scholar
• de Jong, R. M., and Davidson, J. (2000), “Consistency of Kernel Estimators of Heteroscedastic and Autocorrelated Covariance Matrices,” Econometrica, 68, 407–424. DOI: 10.1111/1468-0262.00115.
   Web of Science ®Google Scholar
• Dehling, H., Fried, R., Sharipov, O. S., Vogel, D., and Wornowizki, M. (2013), “Estimation of the Variance of Partial Sums of Dependent Processes,” Statistics & Probability Letters, 83, 141–147. DOI: 10.1016/j.spl.2012.08.012.
   Web of Science ®Google Scholar
• Dehling, H., Vogel, D., Wendler, M., and Wied, D. (2017), “Testing for Changes in Kendall’s Tau,” Econometric Theory, 33, 1352–1386. DOI: 10.1017/S026646661600044X.
   Web of Science ®Google Scholar
• Dehling, H., and Wendler, M. (2010), “Central Limit Theorem and the Bootstrap for U-Statistics of Strongly Mixing Data,” Journal of Multivariate Analysis, 101, 126–137. DOI: 10.1016/j.jmva.2009.06.002.
   Web of Science ®Google Scholar
• Doukhan, P., Lang, G., Leucht, A., and Neumann, M. H. (2015), “Dependent Wild Bootstrap for the Empirical Process,” Journal of Time Series Analysis, 36, 290–314. DOI: 10.1111/jtsa.12106.
   Web of Science ®Google Scholar
• Gerstenberger, C., and Vogel, D. (2015), “On the Efficiency of Gini’s Mean Difference,” Statistical Methods & Applications, 24, 569–596. DOI: 10.1007/s10260-015-0315-x.
   Web of Science ®Google Scholar
• Gombay, E., Horváth, L., and Husková, M. (1996), “Estimators and Tests for Change in Variances,” Statistics & Risk Modeling, 14, 145–160. DOI: 10.1524/strm.1996.14.2.145.
   Google Scholar
• Hampel, F. R. (1974), “The Influence Curve and Its Role in Robust Estimation,” Journal of the American Statistical Association, 69, 383–393. DOI: 10.1080/01621459.1974.10482962.
   Web of Science ®Google Scholar
• Huber, P. J., and Ronchetti, E. M. (2009), Robust Statistics (2nd ed.), Hoboken, NJ: Wiley.
   Google Scholar
• Hyndman, R. J., and Fan, Y. (1996), “Sample Quantiles in Statistical Packages,” The American Statistician, 50, 361–365. DOI: 10.1080/00031305.1996.10473566.
   Web of Science ®Google Scholar
• Inclan, C., and Tiao, G. C. (1994), “Use of Cumulative Sums of Squares for Retrospective Detection of Changes of Variance,” Journal of the American Statistical Association, 89, 913–923. DOI: 10.2307/2290916.
   Web of Science ®Google Scholar
• Kojadinovic, I., Quessy, J.-F., and Rohmer, T. (2015), “Testing the Constancy of Spearman’s Rho in Multivariate Time Series,” Annals of the Institute of Statistical Mathematics, 65, 292–954. DOI: 10.1007/s10463-015-0520-2.
   Web of Science ®Google Scholar
• Künsch, H. R. (1989), “The Jackknife and the Bootstrap for General Stationary Observations,” Annals of Statistics, 17, 1217–1241.
   Web of Science ®Google Scholar
• Lax, D. A. (1985), “Robust Estimators of Scale: Finite-Sample Performance in Long-Tailed Symmetric Distributions,” Journal of the American Statistical Association, 80, 736–741. DOI: 10.1080/01621459.1985.10478177.
   Web of Science ®Google Scholar
• Lee, S., and Park, S. (2001), “The CUSUM of Squares Test for Scale Changes in Infinite Order Moving Average Processes,” Scandinavian Journal of Statistics, 28, 625–644. DOI: 10.1111/1467-9469.00259.
   Web of Science ®Google Scholar
• Leucht, A., and Neumann, M. H. (2013), “Dependent Wild Bootstrap for Degenerate U- and V-Statistics,” Journal of Multivariate Analysis, 117, 257–280. DOI: 10.1016/j.jmva.2013.03.003.
   Web of Science ®Google Scholar
• Maronna, R. A., Martin, D. R., and Yohai, V. J. (2006), Robust Statistics: Theory and Methods, Wiley Series in Probability and Statistics, Chichester: Wiley.
   Google Scholar
• Nair, U. S. (1936), “The Standard Error of Gini’s Mean Difference,” Biometrika, 28, 428–436. DOI: 10.1093/biomet/28.3-4.428.
   Web of Science ®Google Scholar
• Paparoditis, E., and Politis, D. N. (2001), “Tapered Block Bootstrap,” Biometrika, 88, 1105–1119. DOI: 10.1093/biomet/88.4.1105.
   Web of Science ®Google Scholar
• Patton, A., Politis, D. N., and White, H. (2009), “Correction to ‘Automatic Block-Length Selection for the Dependent Bootstrap’ by D. Politis and H. White,” Econometric Reviews, 28, 372–375. DOI: 10.1080/07474930802459016.
   Web of Science ®Google Scholar
• Politis, D. N. (2003), “Adaptive Bandwidth Choice,” Journal of Nonparametric Statistics, 15, 517–533. DOI: 10.1080/10485250310001604659.
   Web of Science ®Google Scholar
• Politis, D. N. (2011), “Higher-Order Accurate, Positive Semidefinite Estimation of Large-Sample Covariance and Spectral Density Matrices,” Econometric Theory, 27, 703–744.
   Web of Science ®Google Scholar
• Politis, D. N., and Romano, J. P. (1994), “The Stationary Bootstrap,” Journal of the American Statistical Association, 89, 1303–1313. DOI: 10.1080/01621459.1994.10476870.
   Web of Science ®Google Scholar
• Politis, D. N., and White, H. (2004), “Automatic Block-Length Selection for the Dependent Bootstrap,” Econometric Reviews, 23, 53–70. DOI: 10.1081/ETC-120028836.
   Google Scholar
• R Core Team (2015), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing.
   Google Scholar
• Rousseeuw, P. J., and Croux, C. (1992), “Explicit Scale Estimators With High Breakdown Point,” in L1-Statistical Analysis and Related Methods (Vol. 1), ed. Y. Dodge, Amsterdam: North-Holland, pp. 77–92.
   Google Scholar
• Rousseeuw, P. J., and Croux, C. (1993), “Alternatives to the Median Absolute Deviation,” Journal of the American Statistical Association, 88, 1273–1283.
   Web of Science ®Google Scholar
• Shao, X. (2010), “The Dependent Wild Bootstrap,” Journal of the American Statistical Association, 105, 218–235. DOI: 10.1198/jasa.2009.tm08744.
   Web of Science ®Google Scholar
• Shao, X., and Zhang, X. (2010), “Testing for Change Points in Time Series,” Journal of the American Statistical Association, 105, 1228–1240. DOI: 10.1198/jasa.2010.tm10103.
   Web of Science ®Google Scholar
• Sharipov, O. S., and Wendler, M. (2013), “Normal Limits, Nonnormal Limits, and the Bootstrap for Quantiles of Dependent Data,” Statistics & Probability Letters, 83, 1028–1035. DOI: 10.1016/j.spl.2012.12.017.
   Web of Science ®Google Scholar
• Sun, S., and Lahiri, S. N. (2006), “Bootstrapping the Sample Quantile of a Weakly Dependent Sequence,” Sankhyā, 68, 130–166.
   Google Scholar
• Tukey, J. W. (1960), “A Survey of Sampling From Contaminated Distributions,” in Contributions to Probability and Statistics. Essays in Honor of Harold Hotteling, eds. Olkin, I., Ghurye, S. G., Hoeffding, W. Madow, W. G., and Mann, H. B., Stanford, CA: Stanford University Press, pp. 448–485.
   Google Scholar
• Vogel, D., and Wendler, M. (2017), “Studentized U-Quantile Processes Under Dependence With Applications to Change-Point Analysis,” Bernoulli, 23, 3114–3144. DOI: 10.3150/16-BEJ838.
   Web of Science ®Google Scholar
• Wied, D., Arnold, M., Bissantz, N., and Ziggel, D. (2012), “A New Fluctuation Test for Constant Variances With Applications to Finance,” Metrika, 75, 1111–1127. DOI: 10.1007/s00184-011-0371-7.
   Web of Science ®Google Scholar