Robust tests for equality of regression curves based on characteristic functions

References

• Dette H, Munk A. Testing heteroscedasticity in nonparametric regression. J R Stat Soc Ser B. 1998;60:693–708. doi: 10.1111/1467-9868.00149
   Google Scholar
• Neumeyer N, Dette H. Nonparametric comparison of regression curves: an empirical process approach. Ann Stat. 2003;31:880–920. doi: 10.1214/aos/1056562466
   Web of Science ®Google Scholar
• Pardo-Fernández JC, Van Keilegom I, Gonzánez-Manteiga W. Testing for the equality of k regression curves. Stat Sin. 2007;17:1115–1137.
   Web of Science ®Google Scholar
• Pardo-Fernández JC, Jiménez-Gamero MD, El Ghouch A. A non-parametric ANOVA-type test for regression curves based on characteristic functions. Scand J Stat. 2015;42:197–213. doi: 10.1111/sjos.v42.1
   Web of Science ®Google Scholar
• Dette H, Marchlewski M. A robust test for homoscedasticity in nonparametric regression. J Nonparametr Stat. 2010;22:723–736. doi: 10.1080/10485250903388894
   Web of Science ®Google Scholar
• Bianco A, Boente G, Martínez E. Robust tests in semiparametric partly linear models. Scand J Stat. 2006;33:435–450. doi: 10.1111/sjos.2006.33.issue-3
   Web of Science ®Google Scholar
• Sun Y. A consistent nonparametric equality test of conditional quantile functions. Econ Theory. 2006;22:614–632. doi: 10.1017/S0266466606060300
   Web of Science ®Google Scholar
• Dette H, Wagener J, Volgushev S. Comparing conditional quantile curves. Scand J Stat. 2011;38:63–88. doi: 10.1111/sjos.2011.38.issue-1
   Web of Science ®Google Scholar
• Dette H, Wagener J, Volgushev S. Nonparametric comparison of quantile curves: a stochastic process approach. J Nonparametr Stat. 2013;25:243–260. doi: 10.1080/10485252.2012.732223
   Web of Science ®Google Scholar
• Kuruwita C, Gallagher C, Kulasekera KB. Testing equality of nonparametric quantile regression functions. Int J Stat Probab. 2014;3:55–66. doi: 10.5539/ijsp.v3n1p55
   Google Scholar
• Boente G, Pardo-Fernández JC. Robust testing for superiority between two regression curves. Comput Stat Data Anal. 2016;97:151–168. doi: 10.1016/j.csda.2015.12.002
   Web of Science ®Google Scholar
• Koul H, Schick A. Testing for the equality of two nonparametric regression curves. J Stat Plan Inference. 1997;65:293–314. doi: 10.1016/S0378-3758(97)00063-3
   Web of Science ®Google Scholar
• Koul H, Schick A. Testing for superiority among two regression curves. J Stat Plan Inference. 2003;117:15–33. doi: 10.1016/S0378-3758(02)00364-6
   Web of Science ®Google Scholar
• Feng L, Zou C, Wang Z, et al. Robust comparison of regression curves. Test. 2015;24:185–204. doi: 10.1007/s11749-014-0394-2
   Web of Science ®Google Scholar
• Härdle W. Applied nonparametric regression. Cambridge: Cambridge University Press; 1990.
   Google Scholar
• Härdle W, Tsybakov AB. Robust nonparametric regression with simultaneous scale curve estimation. Ann Stat. 1988;16:120–135.
   Web of Science ®Google Scholar
• Boente G, Fraiman R. Robust nonparametric regression estimation. J Multivar Anal. 1989;29:180–198. doi: 10.1016/0047-259X(89)90023-7
   Web of Science ®Google Scholar
• Rice J. Bandwidth choice for nonparametric regression. Ann Stat. 1984;12:1215–1230. doi: 10.1214/aos/1176346788
   Web of Science ®Google Scholar
• Hall P, Kay J, Titterington D. Asymptotically optimal difference-based estimation of variance in nonparametric regression. Biometrika. 1990;77:521–528. doi: 10.1093/biomet/77.3.521
   Web of Science ®Google Scholar
• Ghement I, Ruiz M, Zamar R. Robust estimation of error scale in nonparametric regression models. J Stat Plan Inference. 2008;138:3200–3216. doi: 10.1016/j.jspi.2008.01.005
   Web of Science ®Google Scholar
• Maronna R, Martin D, Yohai V, et al. Robust statistics: theory and methods (with R). Chichester: John Wiley and Sons; 2019.
   Google Scholar
• Huber P. Robust estimation of a location parameter. Ann Math Stat. 1964;35:73–101. doi: 10.1214/aoms/1177703732
   Google Scholar
• Yohai VJ. High breakdown–point and high efficiency robust estimates for regression. In: Technical Repport No. 66. Department of Statistics, University of Washington, Seattle, USA; 1985.
   Google Scholar
• Hušková M, Meintanis S. Goodness-of-fit tests for parametric regression models based on empirical characteristic functions. Kybernetika. 2009;45:960–971.
   Web of Science ®Google Scholar
• Zhang C. Calibrating the degrees of freedom for automatic data smoothing and effective curve checking. J Am Stat Assoc. 2003;98:609–628. doi: 10.1198/016214503000000521
   Web of Science ®Google Scholar
• Hampel F, Hennig C, Ronchetti E. A smoothing principle for the Huber and other location M-estimators. Comput Stat Data Anal. 2011;55:324–337. doi: 10.1016/j.csda.2010.05.001
   Web of Science ®Google Scholar
• Bodenham D, Adams N. A comparison of efficient approximations for a weighted sum of chi–squared random variables. Stat Comput. 2016;26:917–928. doi: 10.1007/s11222-015-9583-4
   Web of Science ®Google Scholar
• Bianco A, Boente G. Robust estimators under a semiparametric partly linear autoregression model: asymptotic behaviour and bandwidth selection. J Time Ser Anal. 2007;28:274–306. doi: 10.1111/jtsa.2007.28.issue-2
   Web of Science ®Google Scholar
• Hall P, Hart J. Bootstrap test for difference between means in nonparametric regression. J Am Stat Assoc. 1990;85:1039–1049. doi: 10.1080/01621459.1990.10474974
   Web of Science ®Google Scholar
• Boente G, Vahnovan A. Strong convergence of robust equivariant nonparametric functional regression estimators. Stat Probab Lett. 2015;100:1–11. doi: 10.1016/j.spl.2015.01.028
   Web of Science ®Google Scholar