Statistical inference on restricted partial linear regression models with partial distortion measurement errors
We consider the estimation and hypothesis testing problems for the partial linear regression models when some variables are distorted with errors by some unknown functions of commonly observable confounding variable. The proposed estimation procedure is designed to accommodate undistorted as well as...
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| Published in | Statistica Neerlandica Vol. 70; no. 4; pp. 304 - 331 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Oxford
Blackwell Publishing Ltd
01.11.2016
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0039-0402 1467-9574 |
| DOI | 10.1111/stan.12089 |
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| Abstract | We consider the estimation and hypothesis testing problems for the partial linear regression models when some variables are distorted with errors by some unknown functions of commonly observable confounding variable. The proposed estimation procedure is designed to accommodate undistorted as well as distorted variables. To test a hypothesis on the parametric components, a restricted least squares estimator is proposed under the null hypothesis. Asymptotic properties for the estimators are established. A test statistic based on the difference between the residual sums of squares under the null and alternative hypotheses is proposed, and we also obtain the asymptotic properties of the test statistic. A wild bootstrap procedure is proposed to calculate critical values. Simulation studies are conducted to demonstrate the performance of the proposed procedure, and a real example is analyzed for an illustration. |
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| AbstractList | We consider the estimation and hypothesis testing problems for the partial linear regression models when some variables are distorted with errors by some unknown functions of commonly observable confounding variable. The proposed estimation procedure is designed to accommodate undistorted as well as distorted variables. To test a hypothesis on the parametric components, a restricted least squares estimator is proposed under the null hypothesis. Asymptotic properties for the estimators are established. A test statistic based on the difference between the residual sums of squares under the null and alternative hypotheses is proposed, and we also obtain the asymptotic properties of the test statistic. A wild bootstrap procedure is proposed to calculate critical values. Simulation studies are conducted to demonstrate the performance of the proposed procedure, and a real example is analyzed for an illustration. |
| Author | Wei, Zhenghong Sun, Zipeng Zhou, Nanguang Li, Gaorong Zhang, Jun |
| Author_xml | – sequence: 1 givenname: Jun surname: Zhang fullname: Zhang, Jun email: zhangjunstat@gmail.com, Correspondence to:, zhangjunstat@gmail.com organization: College of Mathematics and Statistics, Institute of Statistical Sciences, Shen Zhen-Hong Kong Joint Research Center for Applied Statistical Sciences, Shenzhen University, 518060, Shenzhen, China – sequence: 2 givenname: Nanguang surname: Zhou fullname: Zhou, Nanguang email: zhounanguang123@gmail.com organization: College of Mathematics and Statistics, Shenzhen University, 518060, Shenzhen, China – sequence: 3 givenname: Zipeng surname: Sun fullname: Sun, Zipeng email: zipengs@163.com organization: College of Mathematics and Statistics, Shenzhen University, 518060, Shenzhen, China – sequence: 4 givenname: Gaorong surname: Li fullname: Li, Gaorong email: ligaorong@gmail.com organization: Beijing Center for Scientific and Engineering Computing, College of Applied Sciences, Beijing University of Technology, 100124, Beijing, China – sequence: 5 givenname: Zhenghong surname: Wei fullname: Wei, Zhenghong organization: College of Mathematics and Statistics, Institute of Statistical Sciences, Shenzhen University, 518060, Shenzhen, China |
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| References_xml | – reference: Carroll R. J., D. Ruppert, L. A. Stefanski, and C. M. Crainiceanu (2006), Nonlinear measurement error models, a modern perspective 2nd edn., Chapman and Hall, New York. – reference: Cui X., W. Guo, L. Lin, and L. Zhu (2009), Covariate-adjusted nonlinear regression, Annals of Statistics 37, 1839-1870. – reference: Zhang J., Y. Yu, B. Zhou, and H. Liang (2014c), Nonlinear measurement errors models subject to additive distortion, Journal of Statistical Planning and Inference 150, 49-65. – reference: Fan J., and I. Gijbels (1996), Local polynomial modelling and its applications, Chapman & Hall, London. – reference: Silverman B. W. (1986), Density estimation for statistics and data analysis, Monographs on Statistics and Applied Probability, Chapman & Hall, London. – reference: Zhou Y., and H. Liang (2009), Statistical inference for semiparametric varying-coefficient partially linear models with error-prone linear covariates, Annals of Statistics 37, 427-458. – reference: Li G., L. Xue, and H. Lian (2011), Semi-varying coefficient models with a diverging number of components, Journal of Multivariate Analysis 102, 1166-1174. – reference: Wang H. J., Z. Zhu, and J. Zhou (2009), Quantile regression in partially linear varying coefficient models, Annals of Statistics 37, 3841-3866. – reference: Mack Y. P., and B. W. Silverman (1982), Weak and strong uniform consistency of kernel regression estimates, Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete 61, 405-415. – reference: Şentürk D., and D. V. Nguyen (2009), Partial covariate adjusted regression, Journal of Statistical Planning and Inference 139, 454-468. – reference: Şentürk D., and H.-G. Müller (2009), Covariate-adjusted generalized linear models, Biometrika 96, 357-370. – reference: Yang Y., G. Li, and H. Lian (2016), Nonconcave penalized estimation for partially linear models with longitudinal data, Statistics 50, 43-59. – reference: Escanciano J. C. (2006), A consistent diagnostic test for regression models using projections, Econometric Theory 22, 1030-1051. – reference: Liang H., X. Liu, R. Li, and C. L. Tsai (2010), Estimation and testing for partially linear single-index models, The Annals of Statistics 38, 3811-3836. – reference: Liang H., S. W. Thurston, D. Ruppert, T. Apanasovich, and R. Hauser (2008), Additive partial linear models with measurement errors, Biometrika 95, 667-678. – reference: Şentürk D., and H.-G. Müller (2006), Inference for covariate adjusted regression via varying coefficient models, Annals of Statistics 34, 654-679. – reference: Li F., L. Lin, and X. Cui (2010), Covariate-adjusted partially linear regression models, Communications in Statistics-Theory and Methods 39, 1054-1074. – reference: Li Q., D. Ouyang, and J. S. 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| SubjectTerms | Asymptotic properties Bootstrap method bootstrap procedure Distortion distortion measurement errors Errors Estimating techniques Estimators Hypotheses Hypothesis testing Least squares method local linear smoothing Mathematical models Measurement errors Regression Regression analysis restricted estimator Statistical inference Statistical tests Statistics Studies |
| Title | Statistical inference on restricted partial linear regression models with partial distortion measurement errors |
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