Adaptive-to-Model Hybrid of Tests for Regressions

References

• Bierens, H. J. (1982), “Consistent Model Specification Tests,” Journal of Econometrics, 20, 105–134. DOI: 10.1016/0304-4076(82)90105-1.
   Web of Science ®Google Scholar
• Chen, F., Shi, L., Zhu, X.-H., and Zhu, L.-X. (2018), “Generalized Principal Hessian Directions for Mixture Multivariate Skew Elliptical Distributions,” Journal of Multivariate Analysis, 168, 142–159.
   Web of Science ®Google Scholar
• Cook, R. D. (1998), Regression Graphics: Ideas for Studying Regressions Through Graphics, Hoboken, NJ: Wiley.
   Google Scholar
• Cook, R. D., and Li, B. (2002), “Dimension Reduction for Conditional Mean in Regression,” The Annals of Statistics, 30, 455–474. DOI: 10.1214/aos/1021379861.
   Web of Science ®Google Scholar
• Cook, R. D., and Weisberg, S. (1991), Discussion of “Sliced Inverse Regression for Dimension Reduction,” Journal of the American Statistical Association, 86, 335. DOI: 10.2307/2290564.
   Web of Science ®Google Scholar
• Dette, H., Neumeyer, N., and Keilegom, I. V. (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.
   Google Scholar
• Dua, D., and Graf, C. (2019). “UCI Machine Learning Repository,” Available at http://archive.ics.uci.edu/ml. University of California, Irvine, School of Information and Computer Sciences.
   Google Scholar
• Duan, N.-H., and K.-C. Li (1991), “Slicing Regression: A Link-Free Regression Method,” The Annals of Statistics, 19, 505–530. DOI: 10.1214/aos/1176348109.
   Web of Science ®Google Scholar
• Escanciano, J. C., Pardo-Fernández, J. C., and Van Keilegom, I. (2018), “Asymptotic Distribution-Free Tests for Semiparametric Regressions With Dependent Data,” The Annals of Statistics, 46, 1167–1196. DOI: 10.1214/17-AOS1581.
   Web of Science ®Google Scholar
• Guo, X., Wang, T., and Zhu, L.-X. (2016), “Model Checking for Parametric Single-Index Models: A Dimension Reduction Model-Adaptive Approach,” Journal of the Royal Statistical Society, Series B, 78, 1013–1035.
   Google Scholar
• Härdle, W., and Mammen, E. (1993), “Comparing Nonparametric Versus Parametric Regression Fits,” The Annals of Statistics, 21, 1926–1947. DOI: 10.1214/aos/1176349403.
   Web of Science ®Google Scholar
• Hart, J. (1997), Nonparametric Smoothing and Lack-of-Fit Tests. New York: Springer Science & Business Media.
   Google Scholar
• Koul, H. L., and Ni, P.-P. (2004), “Minimum Distance Regression Model Checking,” Journal of Statistical Planning and Inference, 119, 109–141. DOI: 10.1016/S0378-3758(02)00415-9.
   Web of Science ®Google Scholar
• Lavergne, P., and Patilea, V. (2012), “One for All and All for One: Regression Checks With Many Regressors,” Journal of Business & Economic Statistics, 30, 41–52.
   Web of Science ®Google Scholar
• Li, B., and Dong, Y.-X. (2009), “Dimension Reduction for Nonelliptically Distributed Predictors,” The Annals of Statistics, 37, 1272–1298. DOI: 10.1214/08-AOS598.
   Web of Science ®Google Scholar
• Li, K.-C. (1991), “Sliced Inverse Regression for Dimension Reduction,” Journal of the American Statistical Association, 86, 316–327.
   Web of Science ®Google Scholar
• Li, K.-C. (1992), “On Principal Hessian Directions for Data Visualization and Dimension Reduction: Another Application of Stein’s Lemma,” Journal of the American Statistical Association, 87, 1025–1039.
   Web of Science ®Google Scholar
• Niu, C.-Z., Guo, X., and Zhu, L.-X. (2018), “Enhancements of Non-Parametric Generalized Likelihood Ratio Test: Bias Correction and Dimension Reduction,” Scandinavian Journal of Statistics, 45, 217–254.
   Web of Science ®Google Scholar
• Stute, W. (1997), “Nonparametric Model Checks for Regression,” The Annals of Statistics, 25, 613–641. DOI: 10.1214/aos/1031833666.
   Web of Science ®Google Scholar
• Stute, W., Manteiga, W. G., and Quindimil, M. P. (1998), “Bootstrap Approximations in Model Checks for Regression,” Journal of the American Statistical Association, 93, 141–149.
   Web of Science ®Google Scholar
• Stute, W., and Zhu, L.-X. (2002), “Model Checks for Generalized Linear Models,” Scandinavian Journal of Statistics, 29, 535–545.
   Web of Science ®Google Scholar
• Tan, F.-L., and Zhu, L.-X. (2019), “Adaptive-to-Model Checking for Regressions With Diverging Number of Predictors,” The Annals of Statistics, 47, 1960–1994. DOI: 10.1214/18-AOS1735.
   Web of Science ®Google Scholar
• Van Keilegom, I., Manteiga, W. G., and Sellero, C. S. (2008), “Goodness-of-Fit Tests in Parametric Regression Based on the Estimation of the Error Distribution,” Test, 17, 401–415.
   Web of Science ®Google Scholar
• Yeh, I.-C., and Hsu, T.-K. (2018), “Building Real Estate Valuation Models With Comparative Approach Through Case-Based Reasoning,” Applied Soft Computing, 65, 260–271.
   Web of Science ®Google Scholar
• Zheng, J. X. (1996), “A Consistent Test of Functional Form Via Nonparametric Estimation Techniques,” Journal of Econometrics, 75, 263–289.
   Web of Science ®Google Scholar
• Zhu, L.-X., Wong, H. L., and Fang, K.-T. (1995), “A Test for Multivariate Normality Based on Sample Entropy and Projection Pursuit,” Journal of statistical planning and inference, 45, 373–385. DOI: 10.1016/0378-3758(94)00058-4.
   Web of Science ®Google Scholar
• Zhu, X.-H., Guo, X., Wang, T., and Zhu, L.-X. (2020), “Dimensionality Determination: A Thresholding Double Ridge Ratio Approach,” Computational Statistics & Data Analysis, 146, 106910.
   Web of Science ®Google Scholar