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Weighted local linear CQR for varying-coefficient models with missing covariates

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Abstract

This paper considers composite quantile regression (CQR) estimation and inference for varying-coefficient models with missing covariates. We propose the weighted local linear CQR (WLLCQR) estimators for unknown coefficient function when selection probabilities are known, estimated nonparametrically or parametrically. Theoretical and numerical results demonstrate that the WLLCQR estimators with estimating weights are more efficient than the true weights. Moreover, a goodness-of-fit test based on the WLLCQR fittings is developed to test whether the coefficient functions are actually varying. The finite-sample performance of the proposed methodology is assessed by simulation studies. A real data set is conducted to illustrate our proposed method.

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References

  • Cai Z, Fan J, Yao Q (2000) Functional-coefficient regression models for nonlinear time series. J Am Stat Assoc 95:941–956

    Article  MathSciNet  MATH  Google Scholar 

  • Chiang CT, Rice JA, Wu CO (2001) Smoothing spline estimation for varying coefficient models with repeatedly measured dependent variables. J Am Stat Assoc 96:605–619

    Article  MathSciNet  MATH  Google Scholar 

  • Eubank RL, Huang C, Maldonado YM, Wang N, Wang S, Buchanan RJ (2004) Smoothing spline estimation in varying coefficient models. J R Stat B 66:653–667

    Article  MATH  Google Scholar 

  • Fan J, Zhang JT (1999) Statistical estimation in varying coefficient models. Ann Stat 27:1491–1518

    Article  MathSciNet  MATH  Google Scholar 

  • Fan J, Zhang CM, Zhang J (2001) Generalized likelihood ratio statistics and Wilks phenomenon. Ann Statist 29:153–193

    Article  MathSciNet  MATH  Google Scholar 

  • Guo Xu, Xu W (2012) Goodness-of-fit tests for general linear models with covariates missed at random. J Stat Plan Inference 142:2047–2058

  • Jie Guo, Tian MZ (2012) New efficient and robust estimation in varying-coefficient models with heteroscedasticity. Stat Sin 22:1075–1101

    MATH  Google Scholar 

  • Hastie TJ, Tibishirani RJ (1993) Varying-coefficient models. J R Stat Soc Ser B 55:757–796

    MATH  Google Scholar 

  • Huang J, Wu CO, Zhou L (2002) Varying coefficient models and basis function approximations for the analysis of repeated measurements. Biometrika 89:111–128

    Article  MathSciNet  MATH  Google Scholar 

  • Jiang R, Qian WM, Zhou ZG (2012) Variable selection and coefficient estimation via composite quantile regression with randomly censored data. Stat Probab Lett 82:308–317

    Article  MathSciNet  MATH  Google Scholar 

  • Kai B, Li R, Zou H (2011) New efficient estimation and variable selection methods for semiparametric varying-coefficient partially linear models. Ann Stat 39:305–332

    Article  MathSciNet  MATH  Google Scholar 

  • Knight K (1998) Limiting distributions for L1 regression estimators under general conditions. Ann Stat 26:755–770

    Article  MATH  Google Scholar 

  • Liang H (2008) Generalized partially linear models with missing covariates. J Multivar Anal 99:880–895

    Article  MATH  Google Scholar 

  • Liang H, Wang S, Robins JM, Carroll RJ (2004) Estimation in partially linear models with missing covariates. J Am Stat Assoc 99:357–367

    Article  MathSciNet  MATH  Google Scholar 

  • Little RJA, Rubin DB (2002) Statistical analysis with missing data, 2nd edn. Wiley, New York

    MATH  Google Scholar 

  • Ning ZJ, Tang LJ (2014) Estimation and test procedures for composite quantile regression with covariates missing at random. Stat Probab Lett 95:15–25

    Article  MathSciNet  Google Scholar 

  • Parzen E (1962) On estimation of a probability density function and model. Ann Math Stat 33:1065–1076

  • Robins JM, Rotnitsky A, Zhao LP (1994) Estimation of regression coefficients when some regressors are not always observed. J Am Stat Assoc 89:846–866

    Article  MATH  Google Scholar 

  • Rubin DB (1976) Inference and missing data. Biomoetrika 63:581–592

    Article  MATH  Google Scholar 

  • Ruppert D, Sheather SJ, Wand MP (1995) An effective bandwidth selector for local least squares regression. J Am Stat Assoc 90:1257–1270

    Article  MathSciNet  MATH  Google Scholar 

  • Sherwood B, Wang L, Zhou A (2013) Weighted quantile regression for analyzing health care cost data with missing covariates. Stat Med 32:4967–4979

    Article  MathSciNet  Google Scholar 

  • Sun J, Gai Y, Lin L (2013) Weighted local linear composite quantile estimation for the case of general error distributions. J Stat Plan Inference 143:1049–1063

    Article  MathSciNet  MATH  Google Scholar 

  • Tsiatis AA (2006) Semiparametric theory and missing data. Springer, New York

    MATH  Google Scholar 

  • Wong H, Guo SJ, Chen M et al (2009) On locally weighted estimation and hypothesis testing on varying coefficient models. J Stat Plan Inference 139:2933–2951

  • Wu CO, Yu KF, Chiang CT (2000) A two-step smoothing method for varying coefficient models with repeated measurements. Ann Inst Stat Math 52:519–543

    Article  MathSciNet  MATH  Google Scholar 

  • Yang YP, Xue LG, Cheng WH (2009) Empirical likelihood for a partially linear model with covariate data missing at random. J Stat Plan Inference 139:4143–4153

    Article  MathSciNet  MATH  Google Scholar 

  • Yang H, Lv J, Guo CH (2014) Weighted composite quantile regression estimation and variable selection for varying coefficient models with heteroscedasticity. J Korean Stat Soc (Online)

  • Zhang W, Lee S, Song X (2000) Local polynomial fitting in semivarying coefficient models. J Multivar Anal 82:166–188

    Article  MathSciNet  Google Scholar 

  • Zou H, Yuan M (2008) Composite quantile regression and the oracle model selection theory. Ann Stat 36:1108–1126

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

The authors would like to thank the editor and the two referees for for the helpful comments and suggestions which greatly improved the paper. This research was partially supported by the Natural Science Foundation of China (No. 11326175).

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Authors and Affiliations

  1. Department of Statistics, Jiaxing University, Jiaxing, 314001, People’s Republic of China

    Linjun Tang & Zhangong Zhou

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  1. Linjun Tang
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  2. Zhangong Zhou
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Correspondence to Linjun Tang.

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Tang, L., Zhou, Z. Weighted local linear CQR for varying-coefficient models with missing covariates. TEST 24, 583–604 (2015). https://doi.org/10.1007/s11749-014-0425-z

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