Abstract
In this paper the empirical likelihood method due to Owen (1988,Biometrika,75, 237–249) is applied to partial linear random models. A nonparametric version of Wilks' theorem is derived. The theorem is then used to construct confidence regions of the parameter vector in the partial linear models, which has correct asymptotic coverage. A simulation study is conducted to compare the empirical likelihood and normal approximation based method.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Chen, H. (1988). Convergent rates for parametric components in a partly linear model,Ann. Statist.,16, 136–146.
Chen, H. and Shiau, H. J. (1991). A two-stage spline smoothing method for partially linear model,J. Statist. Plann. Inference,27, 187–201.
Chen, S. X. (1993). On the accuracy of empirical likelihood confidence regions for linear regression model,Ann. Inst. Statist. Math.,45, 621–637.
Chen, S. X. (1994). Empirical likelihood confidence intervals for linear regression coefficients,J. Multivariate Anal.,49, 24–40.
DiCiccio, T. J., Hall, P. and Romano, J. P. (1991). Bartlett adjustment for empirical likelihood,Ann. Statist.,19, 1053–1061.
Engle, R., Granger, C., Rice, J. and Weiss, A. (1986). Nonparametric estimates of the relation between weather and electricity sales,J. Amer. Statist. Assoc.,81, 310–320.
Gao, J., Chen, X. and Zhao, L. (1994). Asymptotic normality of a class of estimators in partial linear models,Acta Math. Sinica,37, 256–268.
Hall, P. (1990). Pseudo-likelihood theory for empirical likelihood,Ann. Statist.,18, 121–140.
Hamilton, S. A. and Truong, Y. K. (1997). Local linear estimation in partly linear models,J. Multivariate Anal.,60, 1–19.
Heckman, N. (1986). Spline smoothing in partly linear models,J. Roy. Statist. Soc. Ser. B,48, 244–248.
Kolaczyk, E. D. (1994). Empirical likelihood for generalized linear models,Statist. Sinica,4, 199–218.
Owen, A. (1988). Empirical likelihood ratio confidence intervals for single functional,Biometrika,75, 237–249.
Owen, A. (1990). Empirical likelihood ratio confidence regions,Ann. Statist.,18, 90–120.
Owen, A. (1991). Empirical likelihood for linear models,Ann. Statist.,19, 1725–1747.
Qin, J. and Lawless, J. F. (1994). Empirical likelihood and general estimating equations,Ann. Statist.,22, 300–325.
Qin, J. and Wong, A. (1996). Empirical likelihood in a semiparametric models,Scand. J. Statist.,23, 209–219.
Rice, J. (1986). Concergence rates for partially splined models,Statist. Probab. Lett.,4, 203–208.
Robinson, P. M. (1988). Rootn-consistent semiparametric regression,Econometrica,56, 931–954.
Schick, A. (1996). Root-n-consistent in partly linear regression models,Statist. Probab. Lett.,28, 353–358.
Speckman, P. (1988). Kernel smoothing in partial linear models,J. Roy. Statist. Soc. Ser. B,50, 413–436.
Wang, Q. H. and Jing, B. Y. (1999). Empirical likelihood for partial linear model with fixed design,Statist. Probab. Lett.,41, 425–433.
Wang, Q. H. and Zheng, Z. G. (1997). Some asymptotic properties for semiparametric regression models with censored data,Sci. China,40, 945–957.
Author information
Authors and Affiliations
Additional information
Research supported by NNSF of China and a grant to the first author for his excellent Ph.D. dissertation work in China.
Research supported by Hong Kong RGC CERG No. HKUST6162/97P.
About this article
Cite this article
Wang, QH., Jing, BY. Empirical likelihood for partial linear models. Ann Inst Stat Math 55, 585–595 (2003). https://doi.org/10.1007/BF02517809
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02517809