Estimation of correlation coefficient with general distortion measurement errors

References

• Carroll, R. J., D. Ruppert, L. A. Stefanski, and C. M. Crainiceanu. 2006. Nonlinear Measurement Error Models, A Modern Perspective, 2 edn. New York: Chapman and Hall.
   Google Scholar
• Cui, X., W. Guo, L. Lin, and L. Zhu. 2009. Covariate-adjusted nonlinear regression. The Annals of Statistics 37 (4):1839–70. doi:10.1214/08-AOS627.
   Web of Science ®Google Scholar
• Cui, X., W. K. Härdle, and L. Zhu. 2011. The EFM approach for single-index models. The Annals of Statistics 39 (3):1658–88. doi:10.1214/10-AOS871.
   Web of Science ®Google Scholar
• Delaigle, A., P. Hall, and W.-X. Zhou. 2016. Nonparametric covariate-adjusted regression. The Annals of Statistics 44 (5):2190–220. doi:10.1214/16-AOS1442.
   Web of Science ®Google Scholar
• Ferguson, T. S. 1996. A course in large sample theory, Texts in Statistical Science Series. London: Chapman & Hall.
   Google Scholar
• Fu, Y., Y. Liu, H.-H. Wang, and X. Wang. 2020. Empirical likelihood estimation in multivariate mixture models with repeated measurements. Statistical Theory and Related Fields 4 (2):152–60. doi:10.1080/24754269.2019.1630544.
   Google Scholar
• Fuller, W. A. 1987. Measurement error models, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. New York: John Wiley & Sons Inc.
   Google Scholar
• He, B.-Q., X.-J. Hong, and G.-L. Fan. 2020. Penalized empirical likelihood for partially linear errors-in-variables panel data models with fixed effects. Statistical Papers 61 (6):2351–81. doi:10.1007/s00362-018-1049-2.
   Web of Science ®Google Scholar
• Kiwitt, S., and N. Neumeyer. 2012. Estimating the conditional error distribution in non-parametric regression. Scandinavian Journal of Statistics 39 (2):259–81. doi:10.1111/j.1467-9469.2011.00763.x.
   Web of Science ®Google Scholar
• Lian, H. 2012. Empirical likelihood confidence intervals for nonparametric functional data analysis. Journal of Statistical Planning and Inference 142 (7):1669–77. doi:10.1016/j.jspi.2012.02.008.
   Web of Science ®Google Scholar
• Liang, H., X. Liu, R. Li, and C. L. Tsai. 2010. Estimation and testing for partially linear single-index models. Annals of Statistics 38 (6):3811–36. doi:10.1214/10-AOS835.
   PubMed Web of Science ®Google Scholar
• Li, G., L. Lin, and L. Zhu. 2012. Empirical likelihood for a varying coefficient partially linear model with diverging number of parameters. Journal of Multivariate Analysis. 105 (1):85–111. doi:10.1016/j.jmva.2011.08.010.
   Web of Science ®Google Scholar
• Li, G., J. Zhang, and S. Feng. 2016. Modern measurement error models. Beijing: Science Press.
   Google Scholar
• Mack, Y. P., and B. W. Silverman. 1982. Weak and strong uniform consistency of kernel regression estimates. Zeitschrift für Wahrscheinlichkeitstheorie Und Verwandte Gebiete 61 (3):405–15. doi:10.1007/BF00539840.
   Web of Science ®Google Scholar
• Owen, A. 1991. Empirical likelihood for linear models. The Annals of Statistics 19 (4):1725–47. doi:10.1214/aos/1176348368.
   Web of Science ®Google Scholar
• Peng, H., and T. Huang. 2011. Penalized least squares for single index models. Journal of Statistical Planning and Inference 141 (4):1362–79. doi:10.1016/j.jspi.2010.10.003.
   Web of Science ®Google Scholar
• Şentürk, D., and H.-G. Müller. 2005. Covariate adjusted correlation analysis via varying coefficient models. Scandinavian Journal of Statistics. Theory and Applications 32 (3):365–83.
   Web of Science ®Google Scholar
• Serfling, R. J. 1980. Approximation Theorems of Mathematical Statistics. New York: John Wiley & Sons Inc.
   Google Scholar
• Xie, C., and L. Zhu. 2019. A goodness-of-fit test for variable-adjusted models. Computational Statistics & Data Analysis 138:27–48. doi:10.1016/j.csda.2019.01.018.
   Web of Science ®Google Scholar
• Yang, G., X. Cui, and S. Hou. 2017. Empirical likelihood confidence regions in the single-index model with growing dimensions. Communications in Statistics - Theory and Methods 46 (15):7562–79. doi:10.1080/03610926.2016.1157190.
   Web of Science ®Google Scholar
• Yang, Y., T. Tong, and G. Li. 2019. Simex estimation for single-index model with covariate measurement error. AStA Advances in Statistical Analysis 103 (1):137–61. doi:10.1007/s10182-018-0327-6.
   Web of Science ®Google Scholar
• Zhang, J. 2019. Partial linear models with general distortion measurement errors. Electronic Journal of Statistics 13 (2):5360–414. doi:10.1214/19-EJS1654.
   Web of Science ®Google Scholar
• Zhang, J., Q. Chen, and N. Zhou. 2017. Correlation analysis with additive distortion measurement errors. Journal of Statistical Computation and Simulation 87 (4):664–88. doi:10.1080/00949655.2016.1222612.
   Web of Science ®Google Scholar
• Zhang, J., Z. Feng, and B. Zhou. 2014. A revisit to correlation analysis for distortion measurement error data. Journal of Multivariate Analysis 124:116–29. doi:10.1016/j.jmva.2013.10.004.
   Web of Science ®Google Scholar
• Zhang, J., Y. Gai, and B. Lin. 2021. Detection of marginal heteroscedasticity for partial linear single-index models. Communications in Statistics – Simulation and Computation 50 (3):724–43. doi:10.1080/03610918.2019.1565585.
   Web of Science ®Google Scholar
• Zhang, J., B. Lin, and G. Li. 2019. Nonlinear regression models with general distortion measurement errors. Journal of Statistical Computation and Simulation 89 (8):1482–504. doi:10.1080/00949655.2019.1586904.
   Web of Science ®Google Scholar
• Zhang, J., Z. Xu, and Z. Wei. 2020. Absolute logarithmic calibration for correlation coefficient with multiplicative distortion. Communications in Statistics – Simulation and Computation. Advance online publication. doi:10.1080/03610918.2020.1859541.
   PubMed Web of Science ®Google Scholar
• Zhang, J., Y. Yang, S. Feng, and Z. Wei. 2020. Logarithmic calibration for partial linear models with multiplicative distortion measurement errors. Journal of Statistical Computation and Simulation 90 (10):1875–96. doi:10.1080/00949655.2020.1750614.
   Web of Science ®Google Scholar
• Zhang, J., Y. Yang, and G. Li. 2020. Logarithmic calibration for multiplicative distortion measurement errors regression models. Statistica Neerlandica 74 (4):462–88. doi:10.1111/stan.12204.
   Web of Science ®Google Scholar
• Zhang, J., Y. Yu, L. Zhu, and H. Liang. 2013. Partial linear single index models with distortion measurement errors. Annals of the Institute of Statistical Mathematics 65 (2):237–67. doi:10.1007/s10463-012-0371-z.
   Web of Science ®Google Scholar
• Zhang, J., J. Zhang, X. Zhu, and T. Lu. 2018. Testing symmetry based on empirical likelihood. Journal of Applied Statistics 45 (13):2429–54. doi:10.1080/02664763.2017.1421917.
   Web of Science ®Google Scholar
• Zhang, J., and Y. Zhou. 2020. Calibration procedures for linear regression models with multiplicative distortion measurement errors. Brazilian Journal of Probability and Statistics 34 (3):519–36. doi:10.1214/19-BJPS451.
   Web of Science ®Google Scholar
• Zhu, L., L. Lin, X. Cui, and G. Li. 2010. Bias-corrected empirical likelihood in a multi-link semiparametric model. Journal of Multivariate Analysis. 101 (4):850–68. doi:10.1016/j.jmva.2009.08.009.
   Web of Science ®Google Scholar
• Zou, Y., G. Fan, and R. Zhang. 2021. Empirical likelihood and variable selection for partially linear single-index EV models with missing censoring indicators. Journal of the Korean Statistical Society 50 (1):134–62. doi:10.1007/s42952-020-00065-6.
   Web of Science ®Google Scholar