A Smooth Nonparametric, Multivariate, Mixed-Data Location-Scale Test

References

• Aitchison, J., and Aitken, C. G. G. (1976), “Multivariate Binary Discrimination by the Kernel Method,” Biometrika, 63, 413–420. DOI: 10.1093/biomet/63.3.413.
   Web of Science ®Google Scholar
• Akritas, M., and Van Keilegom, I. (2001), “Nonparametric Estimation of the Residual Distribution,” Scandinavian Journal of Statistics, 28, 549–568. DOI: 10.1111/1467-9469.00254.
   Web of Science ®Google Scholar
• Anderson, T. W., and Darling, D. A. (1952), “Asymptotic Theory of Certain ‘Goodness of Fit’ Criteria Based on Stochastic Processes,” The Annals of Mathematical Statistics, 23, 193–212. DOI: 10.1214/aoms/1177729437.
   Google Scholar
• Billingsley, P. (1999), Convergence of Probability Measures, New York: Wiley.
   Google Scholar
• Birke, M., Neumeyer, N., and Volgushev, S. (2017), “The Independence Process in Conditional Quantile Location-Scale Models and an Application to Testing for Monotonicity,” Statistica Sinica, 27, 1815–1839.
   Web of Science ®Google Scholar
• Bowman, A. W., Hall, P., and Prvan, T. (1998), “Bandwidth Selection for the Smoothing of Distribution Functions,” Biometrika, 85, 799–808. DOI: 10.1093/biomet/85.4.799.
   Web of Science ®Google Scholar
• Choulakian, V., Lockhart, R. A., and Stephens, M. A. (1994), “Cramer-von Mises Statistics for Discrete Distributions,” The Canadian Journal of Statistics, 22, 125–137. DOI: 10.2307/3315828.
   Web of Science ®Google Scholar
• Conover, W. J. (1972), “A Kolmogorov Goodness-of-Fit Test for Discontinuous Distributions,” Journal of the American Statistical Association, 67, 591–596. DOI: 10.1080/01621459.1972.10481254.
   Web of Science ®Google Scholar
• Conover, W. J. (1999), Practical Nonparametric Statistics (3rd ed.), New York: Wiley.
   Google Scholar
• Cramér, H. (1928), “On the Composition of Elementary Errors,” Scandinavian Actuarial Journal, 1, 13–74. DOI: 10.1080/03461238.1928.10416862.
   Google Scholar
• Davidson, R., and MacKinnon, J. G. (2000), “Bootstrap Tests: How Many Bootstraps?,” Econometric Reviews, 19, 55–68. DOI: 10.1080/07474930008800459.
   Google Scholar
• Dette, H., Neumeyer, N., and Van Keilegom, I. (2007), “A New Test for the Parametric Form of the Variance Function in Non-parametric Regression,” Journal of the Royal Statistical Society, Series B, 69, 903–917. DOI: 10.1111/j.1467-9868.2007.00616.x.
   Google Scholar
• Einmahl, J. H., and Van Keilegom, I. (2008), “Specification Tests in Nonparametric Regression,” Journal of Econometrics, 143, 88–102. DOI: 10.1016/j.jeconom.2007.08.008.
   Web of Science ®Google Scholar
• Escanciano, J., and Jacho-Chávez, D. T. (2012), “n -Uniformly Consistent Density Estimation in Nonparametric Regression Models,” Journal of Econometrics, 12, 305–361. DOI: 10.1016/j.jeconom.2011.09.017.
   Google Scholar
• Escanciano, J. C., Pardo-Fernández, J. C., and Van Keilegom, I. (2018), “Asymptotic Distribution Free Tests for Semiparametric Regressions With Dependent Data,” Annals of Statistics, 46, 1167–1196. DOI: 10.1214/17-AOS1581.
   Web of Science ®Google Scholar
• Fan, J., and Gijbels, I. (1996), Local Polynomial Modelling and Its Applications, London: Chapman & Hall.
   Google Scholar
• Gijbels, I., Van Keilegom, I., and Zhao, Y. (2018), “Gaussian Copulas Adjusted for Nonparametric Regression,” Working Paper, KU Leuven.
   Google Scholar
• Gleser, L. J. (1985), “Exact Power of Goodness-of-Fit Tests of Kolmogorov Type for Discontinuous Distributions,” Journal of the American Statistical Association, 80, 954–958. DOI: 10.1080/01621459.1985.10478210.
   Web of Science ®Google Scholar
• Jones, M. (1990), “The Performance of Kernel Density Functions in Kernel Distribution Function Estimation,” Statistics & Probability Letters, 9, 129–132. DOI: 10.1016/0167-7152(92)90006-Q.
   Web of Science ®Google Scholar
• Kolmogorov, A. (1933), “Sulla determinazione empirica di una legge di distributione,” Giornale dell’Istituto Italiano degli Attuari, 4, 1–11.
   Google Scholar
• Li, C., Li, H., and Racine, J. S. (2017), “Cross-Validated Mixed-Datatype Bandwidth Selection for Nonparametric Cumulative Distribution/Survivor Functions,” Econometric Reviews, 36, 970–987. DOI: 10.1080/07474938.2017.1307900.
   Web of Science ®Google Scholar
• Li, Q., and Racine, J. S. (2004), “Cross-Validated Local Linear Nonparametric Regression,” Statistica Sinica, 14, 485–512.
   Web of Science ®Google Scholar
• Lockhart, R., Spinelli, J., and Stephens, M. (2007), “Cramér-von Mises Statistics for Discrete Distributions With Unknown Parameters,” Canadian Journal of Statistics, 35, 125–133. DOI: 10.1002/cjs.5550350111.
   Web of Science ®Google Scholar
• Neumeyer, N. (2008), “A Bootstrap Version of the Residual-Based Smooth Empirical Distribution Function,” Journal of Nonparametric Statistics, 20, 153–174. DOI: 10.1080/10485250801908363.
   Web of Science ®Google Scholar
• Neumeyer, N. (2009), “Smooth Residual Bootstrap for Empirical Processes of Non-parametric Regression Residuals,” Scandinavian Journal of Statistics, 36, 204–228.
   Web of Science ®Google Scholar
• Neumeyer, N., Noh, H., and Van Keilegom, I. (2016), “Heteroscedastic Semiparametric Transformation Models: Estimation and Testing for Validity,” Statistica Sinica, 26, 925–954.
   Web of Science ®Google Scholar
• Neumeyer, N., and Van Keilegom, I. (2010), “Estimating the Error Distribution in Nonparametric Multiple Regression With Applications to Model Testing,” Journal of Multivariate Analysis, 101, 1067–1078. DOI: 10.1016/j.jmva.2010.01.007.
   Web of Science ®Google Scholar
• Neumeyer, N., and Van Keilegom, I. (2018), “Bootstrap of Residual Processes in Regression: To Smooth or Not to Smooth?,” Biometrika (to appear).
   Google Scholar
• Pardo-Fernández, J. C., Van Keilegom, I., and González-Manteiga, W. (2007), “Testing for the Equality of k Regression Curves,” Statistica Sinica, 17, 1115–1137.
   Web of Science ®Google Scholar
• Qiu, D. (2014), “snpar: Supplementary Non-parametric Statistics Methods,” R Package Version 1.0, available at https://CRAN.R-project.org/package=snpar.
   Google Scholar
• Racine, J. S., and Li, K. (2017), “Nonparametric Conditional Quantile Estimation: A Locally Weighted Quantile Kernel Approach,” Journal of Econometrics, 201, 72–94. DOI: 10.1016/j.jeconom.2017.06.020.
   Web of Science ®Google Scholar
• Ruppert, D., and Wand, M. P. (1994), “Multivariate Locally Weighted Least Squares Regression,” Annals of Statistics, 22, 1346–1370. DOI: 10.1214/aos/1176325632.
   Web of Science ®Google Scholar
• Smirnov, N. (1948), “Table for Estimating the Goodness of Fit of Empirical Distributions,” Annals of Mathematical Statistics, 19, 279–281. DOI: 10.1214/aoms/1177730256.
   Google Scholar
• Stute, W. (1982), “The Oscillation Behavior of Empirical Processes,” The Annals of Probability, 10, 86–107. DOI: 10.1214/aop/1176993915.
   Web of Science ®Google Scholar
• Van der Vaart, A. W., and Wellner, J. A. (1996), Weak Convergence and Empirical Processes, New York: Springer.
   Google Scholar
• Van Keilegom, I., González-Manteiga, W., and Sánchez-Sellero, C. (2008), “Goodness-of-Fit Tests in Parametric Regression Based on the Estimation of the Error Distribution,” TEST, 17, 401–415. DOI: 10.1007/s11749-007-0044-z.
   Web of Science ®Google Scholar
• von Mises, R. E. (1928), Wahrscheinlichkeit, Statistik und Wahrheit, Vienna: Julius Springer.
   Google Scholar
• Wang, J., Cheng, F., and Yang, L. (2013), “Smooth Simultaneous Confidence Bands for Cumulative Distribution Functions,” Journal of Nonparametric Statistics, 25, 395–407. DOI: 10.1080/10485252.2012.759219.
   Web of Science ®Google Scholar