Statistical Papers

, Volume 53, Issue 2, pp 485–496 | Cite as

Empirical likelihood for partially linear additive errors-in-variables models

Regular Article
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Abstract

This study investigates the empirical likelihood method for the partially linear additive models in which certain covariates are measured with additive errors. An empirical log-likelihood ratio for the parametric component is proposed based on the profile procedure, and a nonparametric version of the Wilk’s theorem is derived. Then, the confidence regions of the parametric component with asymptotically correct coverage probabilities are constructed by the obtained results. Furthermore, a simulation study is conducted to illustrate the performance of the proposed method.

Keywords

Backfitting Confidence region Empirical likelihood Errors-in-variables Partially linear additive model 

Mathematics Subject Classification (2000)

62G05 62G10 
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References

  1. Chen SX (1994) Empirical likelihood confidence intervals for linear regression coefficients. J Multivar Anal 49: 24–40MATHCrossRefGoogle Scholar
  2. Engle RF, Granger CWJ, Rice J, Weiss A (1986) Semiparametric estimates of the relation between weather and electricity sales. J Am Stat Assoc 81: 310–320CrossRefGoogle Scholar
  3. Fan J, Jiang J (2005) Nonparametric inferences for additive models. J Am Stat Assoc 100: 890–907MathSciNetMATHCrossRefGoogle Scholar
  4. Hastie TJ, Tibshirani RJ (1990) Generalized additive models. Chapman & Hall, New YorkMATHGoogle Scholar
  5. Jiang J, Zhou H, Jiang X, Peng J (2007) Generalized likelihood ratio tests for the structures of semiparametric additive models. Can J Stat 35: 381–398MathSciNetMATHCrossRefGoogle Scholar
  6. Kolaczyk E (1994) Empirical likelihood for generalized linear models. Stat Sin 4: 199–218MathSciNetMATHGoogle Scholar
  7. Li Q (2002) Efficient estimation of additive partially linear models. Int Econ Rev 41: 1073–1092CrossRefGoogle Scholar
  8. Liang H, Thurston H, Ruppert D, Apanasovich T (2008) Additive partial linear models with measurement errors. Biometrika 95: 667–678MathSciNetMATHCrossRefGoogle Scholar
  9. Mack YP, Silverman BW (1982) Weak and strong uniform consistency of kernel regression estimates. Z Wahrsch Verw Gebiete 61: 405–415MathSciNetMATHCrossRefGoogle Scholar
  10. Manzana S, Zeromb D (2005) Kernel estimation of a partially linear additive model. Stat Probab Lett 72: 313–322CrossRefGoogle Scholar
  11. Opsomer JD (2000) Asymptotic properties of backfitting estimators. J Multivar Anal 73: 166–179MathSciNetMATHCrossRefGoogle Scholar
  12. Opsomer JD, Ruppert D (1997) Fitting a bivariate additive model by local polynomial regression. Ann Stat 25: 186–211MathSciNetMATHCrossRefGoogle Scholar
  13. Opsomer JD, Ruppert D (1999) A root-n consistent backfitting estimator for semiparametric additive modelling. J Comput Graph Stat 8: 715–732CrossRefGoogle Scholar
  14. Owen AB (1988) Empirical likelihood ratio confidence intervals for a single functional. Biometrika 75: 237–249MathSciNetMATHCrossRefGoogle Scholar
  15. Owen AB (1990) Empirical likelihood and confidence regions. Ann Stat 18: 90–120MathSciNetMATHCrossRefGoogle Scholar
  16. Owen AB (1991) Empirical likelihood for linear models. Ann Stat 19: 1725–1747MathSciNetMATHCrossRefGoogle Scholar
  17. Owen AB (2001) Empirical likelihood. Chapman & Hall, New YorkMATHCrossRefGoogle Scholar
  18. Qin J, Lawless J (1994) Empirical likelihood and general estimating equations. Ann Stat 22: 300–325MathSciNetMATHCrossRefGoogle Scholar
  19. Wang QH, Jing BY (1999) Empirical likelihood for partial linear models with fixed designs. Stat Probab Lett 41: 425–433MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Statistics, School of ScienceMinzu University of ChinaBeijingPeople’s Republic of China
  2. 2.School of EconomicsBeijing Technology and Business UniversityBeijingPeople’s Republic of China
  3. 3.School of StatisticsRenmin University of ChinaBeijingPeople’s Republic of China

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