Correlation curve estimation for multiplicative distortion measurement errors data

References

• Bjerve, S., and Doksum, K.A. (1993), ‘Correlation Curves: Measures of Association As Functions of Covariate Values’, The Annals of Statistics, 21(2), 890–902. doi: 10.1214/aos/1176349156
   Web of Science ®Google Scholar
• Carroll, R.J., Ruppert, D., Stefanski, L.A., and Crainiceanu, C.M. (2006), Nonlinear Measurement Error Models, A Modern Perspective (2 ed.), New York: Chapman and Hall.
   Google Scholar
• Cheng, C.-L., Shalabh, and Garg, G. (2016), ‘Goodness of Fit in Restricted Measurement Error Models’, Journal of Multivariate Analysis, 145, 101–116. doi: 10.1016/j.jmva.2015.12.005
   Web of Science ®Google Scholar
• Cui, X., Guo, W., Lin, L., and Zhu, L. (2009), ‘Covariate-adjusted Nonlinear Regression’, The Annals of Statistics, 37, 1839–1870. doi: 10.1214/08-AOS627
   Web of Science ®Google Scholar
• Delaigle, A., Hall, P., and Zhou, W.-X. (2016), ‘Nonparametric Covariate-adjusted Regression’, The Annals of Statistics, 44(5), 2190–2220. doi: 10.1214/16-AOS1442
   Web of Science ®Google Scholar
• Doksum, K., Blyth, S., Bradlow, E., Meng, X., and Zhao, H. (1994), ‘Correlation Curves As Local Measures of Variance Explained by Regression’, Journal of the American Statistical Association, 89, 571–582. doi: 10.1080/01621459.1994.10476782
   Web of Science ®Google Scholar
• Fan, J., and Gijbels, I. (1996), Local Polynomial Modelling and Its Applications, London: Chapman & Hall.
   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
• Hellton, K.H., and Thoresen, M. (2014), ‘The Impact of Measurement Error on Principal Component Analysis’, Scandinavian Journal of Statistics. Theory and Applications, 41(4), 1051–1063. doi: 10.1111/sjos.12083
   Web of Science ®Google Scholar
• Kaysen, G.A., Dubin, J.A., Müller, H.-G., Mitch, W.E., Rosales, L.M., and Nathan, W., and Levin the Hemo Study Group (2002), ‘Relationships Among Inflammation Nutrition and Physiologic Mechanisms Establishing Albumin Levels in Hemodialysis Patients’, Kidney International, 61, 2240–2249. doi: 10.1046/j.1523-1755.2002.00076.x
   PubMed Web of Science ®Google Scholar
• Latif, S.A., and Morettin, P.A. (2016), ‘Curve of Correlation for Time Series’, Communications in Statistics – Simulation and Computation, 45(8), 2792–2809. doi: 10.1080/03610918.2014.926172
   Web of Science ®Google Scholar
• Li, F., Lin, L., and Cui, X. (2010), ‘Covariate-adjusted Partially Linear Regression Models’, Communications in Statistics – Theory and Methods, 39(6), 1054–1074. doi: 10.1080/03610920902846539
   Web of Science ®Google Scholar
• Li, F., and Lu, Y. (2018), ‘Lasso-type Estimation for Covariate-adjusted Linear Model’, Journal of Applied Statistics, 45(1), 26–42. doi: 10.1080/02664763.2016.1267121
   Web of Science ®Google Scholar
• Li, G., Zhang, J., and Feng, S. (2016), Modern Measurement Error Models, Beijing: Science Press.
   Google Scholar
• Liang, H. (2009), ‘Generalized Partially Linear Mixed-effects Models Incorporating Mismeasured Covariates’, Annals of the Institute of Statistical Mathematics, 61(1), 27–46. doi: 10.1007/s10463-007-0146-0
   PubMed Web of Science ®Google Scholar
• Liang, H., Härdle, W., and Carroll, R.J. (1999), ‘Estimation in a Semiparametric Partially Linear Errors-in-variables Model’, The Annals of Statistics, 27(5), 1519–1535. doi: 10.1214/aos/1017939140
   Web of Science ®Google Scholar
• Liang, H., and Ren, H. (2005), ‘Generalized Partially Linear Measurement Error Models’, Journal of Computational and Graphical Statistics, 14(1), 237–250. doi: 10.1198/106186005X37481
   Web of Science ®Google Scholar
• Nguyen, D.V., and Şentürk, D. (2008), ‘Multicovariate-adjusted Regression Models’, Journal of Statistical Computation and Simulation, 78, 813–827. doi: 10.1080/00949650701421907
   Web of Science ®Google Scholar
• Nilsson, W., and Castro, T.D.B. (2012), ‘Bootstrap Confidence Interval for a Correlation Curve’, Statistics & Probability Letters, 82(1), 1–6. doi: 10.1016/j.spl.2011.09.001
   Web of Science ®Google Scholar
• Rosman, J.B., ter Wee, P.M., Meijer, S., Piers-Becht, T.P.M., Sluiter, W.J., and Donker, A.J.M. (1984), ‘Prospective Randomized Trial of Early Protein Restriction in Chronic Renal Failure’, Lancet, 2, 1291–1296. doi: 10.1016/S0140-6736(84)90818-3
   PubMed Web of Science ®Google Scholar
• Şentürk, D., and Müller, H.-G. (2005), ‘Covariate Adjusted Correlation Analysis Via Varying Coefficient Models’, Scandinavian Journal of Statistics. Theory and Applications, 32(3), 365–383. doi: 10.1111/j.1467-9469.2005.00450.x
   Web of Science ®Google Scholar
• Şentürk, D., and Müller, H.-G. (2006), ‘Inference for Covariate Adjusted Regression Via Varying Coefficient Models’, The Annals of Statistics, 34, 654–679. doi: 10.1214/009053606000000083
   Web of Science ®Google Scholar
• Şentürk, D., and Nguyen, D.V. (2009), ‘Asymptotic Properties of Covariate-adjusted Regression with Correlated Errors’, Statistics & Probability Letters, 79, 1175–1180. doi: 10.1016/j.spl.2008.12.024
   Web of Science ®Google Scholar
• Silverman, B.W. (1986), Density Estimation for Statistics and Data Analysis, Monographs on Statistics and Applied Probability, London: Chapman & Hall.
   Google Scholar
• Song, Q., and Yang, L. (2009), ‘Spline Confidence Bands for Variance Functions’, Journal of Nonparametric Statistics, 21(5), 589–609. doi: 10.1080/10485250902811151
   Web of Science ®Google Scholar
• Wand, M.P., and Jones, M.C. (1995), Kernel Smoothing, Vol. 60 of Monographs on Statistics and Applied Probability, London: Chapman and Hall, Ltd.
   Google Scholar
• Wang, H.Y., Chen, X., and Flournoy, N. (2016), ‘The Focused Information Criterion for Varying-coefficient Partially Linear Measurement Error Models’, Statistical Papers, 57(1), 99–113. doi: 10.1007/s00362-014-0645-z
   Web of Science ®Google Scholar
• Wang, M., Zhao, P., and Kang, X. (2018), ‘Structure Identification for Varying Coefficient Models with Measurement Errors Based on Kernel Smoothing’, Statistical Papers. doi:10.1007/s00362-018-1009-x.
   Google Scholar
• Yang, Y., Tong, T., and Li, G. (2018), ‘SIMEX Estimation for Single-index Model with Covariate Measurement Error’, AStA Advances in Statistical Analysis. doi:10.1007/s10182-018-0327-6.
   Google Scholar
• Zhang, Y., and Yang, L. (2018), ‘A Smooth Simultaneous Confidence Band for Correlation Curve’, Test, 27(2), 247–269. doi: 10.1007/s11749-017-0543-5
   Web of Science ®Google Scholar
• Zhao, J., and Xie, C. (2018), ‘A Nonparametric Test for Covariate-adjusted Models’, Statistics & Probability Letters, 133(Supplement C), 65–70. doi: 10.1016/j.spl.2017.10.004
   Web of Science ®Google Scholar
• Zhou, Y., and Liang, H. (2009), ‘Statistical Inference for Semiparametric Varying-coefficient Partially Linear Models with Error-prone Linear Covariates’, The Annals of Statistics, 37, 427–458. doi: 10.1214/07-AOS561
   PubMed Web of Science ®Google Scholar