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Research Article

Non parametric regression models with additive distortions

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Received 08 Mar 2023, Accepted 06 Nov 2023, Published online: 21 Nov 2023

References

  • Bjerve, S., and K. A. Doksum. 1993. Correlation curves: Measures of association as functions of covariate values. The Annals of Statistics 21 (2):890–902.
  • Carroll, R. J., and D. Ruppert. 1988. Transformation and weighting in regression. London: Chapman and Hall.
  • Carroll, R. J., D. Ruppert, L. A. Stefanski, and C. M. Crainiceanu, 2006. Nonlinear measurement error models, A modern perspective, 2nd ed. New York: Chapman and Hall.
  • Cassotti, M., D. Ballabio, R. Todeschini, and V. Consonni. 2015. A similarity-based QSAR model for predicting acute toxicity towards the fathead minnow (Pimephales promelas). SAR AND QSAR in Environmental Research 26 (3):217–43. doi:10.1080/1062936X.2015.1018938. 25780951
  • Chen, K., Y. Lin, Z. Wang, and Z. Ying. 2016. Least product relative error estimation. Journal of Multivariate Analysis 144:91–8. doi:10.1016/j.jmva.2015.10.017.
  • Dette, H., M. Marchlewski, and J. Wagener. 2012. Testing for a constant coefficient of variation in nonparametric regression by empirical processes. Annals of the Institute of Statistical Mathematics 64 (5):1045–70. doi:10.1007/s10463-011-0346-5.
  • Dette, H., and G. Wieczorek. 2009. Testing for a constant coefficient of variation in nonparametric regression. Journal of Statistical Theory and Practice 3 (3):587–612. doi:10.1080/15598608.2009.10411949.
  • Doksum, K., S. Blyth, E. Bradlow, X.-L. Meng, and H. Zhao. 1994. Correlation curves as local measures of variance explained by regression. Journal of the American Statistical Association 89 (426):571–82. doi:10.1080/01621459.1994.10476782.
  • Eagleson, G. K., and H. G. Müller. 1997. Transformations for smooth regression models withmultiplicative errors. Journal of the Royal Statistical Society Series B: Statistical Methodology 59 (1):173–89. doi:10.1111/1467-9868.00062.
  • Fan, J., and I. Gijbels. 1996. Local polynomial modelling and its applications. London: Chapman & Hall.
  • Feng, Z., Y. Gai, and J. Zhang. 2019. Correlation curve estimation for multiplicative distortion measurement errors data. Journal of Nonparametric Statistics 31 (2):435–50. doi:10.1080/10485252.2019.1580708.
  • Feng, Z., J. Zhang, and Q. Chen. 2020. Statistical inference for linear regression models with additive distortion measurement errors. Statistical Papers 61 (6):2483–509. doi:10.1007/s00362-018-1057-2.
  • Fuller, W. A. 1987. Measurement error models. In Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. New York: John Wiley & Sons Inc.
  • Hellton, K. H., and M. Thoresen. 2014. The impact of measurement error on principal component analysis. Scandinavian Journal of Statistics 41 (4):1051–63. doi:10.1111/sjos.12083.
  • Latif, S. A., and P. A. Morettin. 2016. Curve of correlation for time series. Communications in Statistics - Simulation and Computation 45 (8):2792–809. doi:10.1080/03610918.2014.926172.
  • Li, G., J. Zhang, and S. Feng, 2016. Modern measurement error models. Beijing: Science Press.
  • 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. 20160899
  • Liang, H., W. Härdle, and R. J. Carroll. 1999. Estimation in a semiparametric partially linear errors-in-variables model. The Annals of Statistics 27 (5):1519–35.
  • Liang, H., and H. Ren. 2005. Generalized partially linear measurement error models. Journal of Computational and Graphical Statistics 14 (1):237–50. doi:10.1198/106186005X37481.
  • Liang, H., H. Su, S. W. Thurston, J. D. Meeker, and R. Hauser. 2009. Empirical likelihood based inference for additive partial linear measurement error models. Statistics and Its Interface 36 (3):433–43. doi:10.1111/j.1467-9469.2008.00632.x. 20161079
  • Nilsson, W., and T. Del Barrio Castro. 2012. Bootstrap confidence interval for a correlation curve. Statistics & Probability Letters 82 (1):1–6. doi:10.1016/j.spl.2011.09.001.
  • 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.
  • Silverman, B. W. 1986. Density estimation for statistics and data analysis. In Monographs on Statistics and Applied Probability. London: Chapman & Hall.
  • Song, Q., and L. Yang. 2009. Spline confidence bands for variance functions. Journal of Nonparametric Statistics 21 (5):589–609. doi:10.1080/10485250902811151.
  • Tomaya, L. C., and M. De Castro. 2018. A heteroscedastic measurement error model based on skew and heavy-tailed distributions with known error variances. Journal of Statistical Computation and Simulation 88 (11):2185–200. doi:10.1080/00949655.2018.1452925.
  • Wand, M. P., and M. C. Jones, 1995. Kernel smoothing. In Monographs on Statistics and Applied Probability, Vol. 60. London: Chapman and Hall, Ltd.
  • Wang, M., C. Liu, T. Xie, and Z. Sun. 2020. Data-driven model checking for errors-in-variables varying-coefficient models with replicate measurements. Computational Statistics & Data Analysis 141:12–27. doi:10.1016/j.csda.2019.06.003.
  • Wang, Q., Y. Ma, and G. Yang. 2020. Locally efficient estimation in generalized partially linear model with measurement error in nonlinear function. Test 29:553–72. doi:10.1007/s11749-019-00668-0.
  • 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.
  • 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.
  • Zhang, J., and X. Cui. 2021. Logarithmic calibration for nonparametric multiplicative distortion measurement errors models. Journal of Statistical Computation and Simulation 91:1–22.
  • Zhang, J., X. Cui, and H. Peng. 2020. Estimation and hypothesis test for partial linear single-index multiplicative models. Annals of the Institute of Statistical Mathematics 72 (3):699–740. doi:10.1007/s10463-019-00706-6.
  • Zhang, J., and Z. Feng. 2017. Partial linear single-index models with additive distortion measurement errors. Communications in Statistics- Theory and Methods 46 (24):12165–93. doi:10.1080/03610926.2017.1291971.
  • Zhang, J., S. Feng, and Y. Gai. 2022. Partial index additive models with additive distortion measurement errors. Communications in Statistics- Simulation and Computation 51 (5):2191–216. doi:10.1080/03610918.2020.1757712.
  • Zhang, J., Z. Feng, and H. Peng. 2018. Estimation and hypothesis test for partial linear multiplicative models. Computational Statistics & Data Analysis 128:87–103. doi:10.1016/j.csda.2018.06.017.
  • Zhang, J., and Y. Gai. 2022. Correlation coefficient-based measure for checking symmetry or asymmetry of a continuous variable with additive distortion. Communications in Statistics - Simulation and Computation 51 (5):2158–90. doi:10.1080/03610918.2019.1699573.
  • Zhang, J., B. Lin, and Y. Zhou. 2023. Linear regression models with multiplicative distortions under new identifiability conditions. Statistica Neerlandica doi:10.1111/stan.12304.
  • Zhang, J., B. Lin, Y. Zhou, and J. Zhang. 2018. Dimension reduction regressions with measurement errors subject to additive distortion. Journal of Statistical Computation and Simulation 88 (13):2631–49. doi:10.1080/00949655.2018.1479753.
  • Zhang, J., C. Niu, and G. Li. 2019. Exploring the constant coefficient of a single-index variation. Brazilian Journal of Probability and Statistics 33 (1):57–86.
  • Zhang, J., and Z. Xu. 2021. Exponential calibration for correlation coefficient with additive distortion measurement errors. Statistical Analysis and Data Mining: The ASA Data Science Journal 14 (3):271–89. doi:10.1002/sam.11509.
  • Zhang, J., and Y. Yang. 2022. Modal linear regression models with additive distortion measurement errors. Journal of Statistical Computation and Simulation 92 (4):921–48. 10.1080/00949655.2021.1979000.
  • Zhang, J., Y. Zhou, B. Lin, and Y. Yu. 2017. Estimation and hypothesis test on partial linear models with additive distortion measurement errors. Computational Statistics & Data Analysis 112:114–28. doi:10.1016/j.csda.2017.03.009.
  • Zhang, J., J. Zhu, and Z. Feng. 2019. Estimation and hypothesis test for single-index multiplicative models. TEST 28 (1):242–68. doi:10.1007/s11749-018-0586-2.
  • Zhang, Y., and L. Yang. 2018. A smooth simultaneous confidence band for correlation curve. TEST 27 (2):247–69. doi:10.1007/s11749-017-0543-5.
  • Zheng, Z., Y. Li, C. Yu, and G. Li. 2018. Balanced estimation for high-dimensional measurement error models. Computational Statistics & Data Analysis 126:78–91. doi:10.1016/j.csda.2018.04.009.
  • Zhu, X., J. Zhang, and Y. Yang. 2022. Additive distortion measurement errors regression models with exponential calibration. Journal of Statistical Computation and Simulation 92 (14):3020–44. doi:10.1080/00949655.2022.2055028.

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