An adaptive lack of fit test for big data

References

• Afonja, B. (1972). The moments of the maximum of correlated normal and t-variates. Journal of the Royal Statistical Society B, 34, 251–262.
   Google Scholar
• Battey, H., Fan, J., Liu, H., Lu, J., & Zhu, Z. (2015). Distributed estimation and inference with statistical guarantees. arXiv:150905457.
   Google Scholar
• Chen, X., & Xie, M. (2014). A split-and-conquer approach for analysis of extraordinarily large data. Statistica Sinica, 24, 1655–1684.
   Web of Science ®Google Scholar
• Cheng, G., & Shang, Z. (2015). Computational limits of divide-and-conquer method. arXiv:151209226.
   Google Scholar
• DasGupta, A. (2008). Asymptotic theory of statistics and probability (1st ed. ). New York, NY: Springer.
   Google Scholar
• Eubank, R. L., Ching-Shang, L., & Wang, S. (2005). Testing lack of fit of parametric regression models using nonparametric regression techniques. Statistica Sinica, 15, 135–152.
   Web of Science ®Google Scholar
• Fan, Y., & Li, Q. (2000). Consistent model specification tests: Kernel-based tests versus Bierens’ ICM tests. Econometric Theory, 16, 1016–1041.
   Web of Science ®Google Scholar
• Fan, J., Han, F., & Liu, H. (2014). Challenges of big data analysis. National science review, 1(2), 293–314.
   PubMed Web of Science ®Google Scholar
• Gao, J., & Gijbels, I. (2008). Bandwidth selection in nonparametric kernel testing. Journal of the American Statistical Association, 484, 1584–1594.
   Google Scholar
• González-Manteiga, W., & Crujeiras, R. (2013). An updated review of goodness-of-fit tests for regression models. Test, 22, 361–411.
   Web of Science ®Google Scholar
• Guerre, E., & Lavergne, P. (2005). Data-driven rate-optimal specification testing in regression models. Annals of Statistics, 33, 840–870.
   Web of Science ®Google Scholar
• Hall, P. (1984). Central limit theorem for integrated square error of multivariate nonparametric density estimators. Journal of Multivariate Analysis, 14, 1–16.
   Web of Science ®Google Scholar
• Hardle, W., & Mammen, E. (1993). Comparing nonparametric versus parametric regression fits. Annals of Statistics, 21, 1926–1947.
   Web of Science ®Google Scholar
• Hart, J. (1997). Nonparametric smoothing and lack-of-fit tests (1st ed. ). New York, NY: Springer.
   Google Scholar
• Horowitz, J., & Spokoiny, V. (2001). An adaptive, rate-optimal test of parametric mean-regression model against a nonparametric alternative. Econometrica, 69, 599–631.
   Web of Science ®Google Scholar
• Kleiner, A., Talwalkar, A., Sarkar, P., & Jordan, M. I. (2015). A scalable bootstrap for massive data. Journal of the Royal Statistical Society: Series B, 76(4), 795–816.
   Google Scholar
• Kulasekera, K., & Wang, J. (1997). Smoothing parameter selection for power optimality in testing of regression curves. Journal of the American Statistical Association, 438, 500–511.
   Google Scholar
• Ledwina, T. (1993). Data-driven version of Neymans smooth test of fit. Journal of the American Statistical Association, 89, 1000–1005.
   Web of Science ®Google Scholar
• Lin, N., & Xi, R. (2011). Aggregated estimating equation estimation. Statistics and Its Inference, 4, 73–83.
   Web of Science ®Google Scholar
• Powell, J., Stock, J., & Stoker, T. (1989). Semiparametric estimation of index coefficients. Econometrics, 57, 1403–1430.
   Web of Science ®Google Scholar
• Schifano, E., Wu, J., Wang, C., Yan, J., & Chen, M.-H. (2016). Online updating of statistical inference in the big data setting. Technometrics, 58, 393–403.
   PubMed Web of Science ®Google Scholar
• Zhang, C. (2003a). Adaptive tests of regression functions via multiscale generalized likelihood ratios. Canadian Journal of Statistics, 31, 151–171.
   Web of Science ®Google Scholar
• Zhang, C. (2003b). Calibrating the degrees of freedom for automatic data smoothing and affective curve checking. Journal of the American Statistical Association, 98, 609–629.
   Web of Science ®Google Scholar
• Zhang, Y., John, D., & Martin, W. (2013). Divide and conquer kernel ridge regression. Journal of Machine Learning Research WCP, 30, 592–617.
   Google Scholar
• Zhao, T., Cheng, G., & Liu, H. (2016). A partially linear framework for massive heterogeneous data. Annals of Statistics, 44, 1400–1437.
   PubMed Web of Science ®Google Scholar
• Zheng, J. (1996). A consistent test of functional form via nonparametric estimation techniques. Journal of Econometrics, 75, 263–289.
   Web of Science ®Google Scholar