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Calibration of the empirical likelihood for semiparametric varying-coefficient partially linear models with diverging number of parameters

Yıl 2019, Cilt: 48 Sayı: 1, 230 - 241, 01.02.2019

Öz

This article is concerned with the calibration of the empirical likelihood for semiparametric varying-coefficient partially linear models with diverging number of parameters.
However, there is always substantial lack-of-fit, when the empirical likelihood ratio is calibrated by a bias-corrected empirical likelihood, producing tests with type I errors much larger than nominal levels. So we consider an effective calibration method and study the asymptotic behavior of this bias-corrected empirical likelihood ratio function. Some simulation studies are conducted to illustrate our approach.

Kaynakça

  • Chen, S. X. and Cui, H. J. On Bartlett correction of empirical likelihood in the presence of nuisance parameters, Biometrika 93, 215-220, 2006.
  • Chen, S. X., Peng, L. and Qin, Y. L. Effects of data dimension on empirical likelihood, Biometrika 9, 711-722, 2009.
  • DiCiccio, T. J., Hall, P. and Romano, J. P. Empirical likelihood is bartlett-correctable, Ann. Statist. 19, 1053-1061, 1991.
  • Fan, J. and Huang, T. Profile likelihood inference on semiparametric varying-coefficient partially linear models, Bernoulli 11, 1031-1057, 2005.
  • Guo, H., Zou, C. and Chen, B. Empirical likelihood for high-dimensional linear regression models, Metrika 77, 921-945, 2014.
  • Huang, Z. S. and Zhang, R. Q. Empirical likelihood for nonparametric parts in semiparametric varying-coefficient partially linear models, Statist. Probab. Lett. 79, 1798-1808, 2009.
  • Lam, C. and Fan, J. Profile-kernel likelihood inference with diverging number of parameters, Ann. Statist. 36, 2232-2260, 2008.
  • Li, G., Lin, L. and Zhu, L. Empirical likelihood for a varying coefficient partially linear model with diverging number of parameters, J. Multivar. Anal. 105, 85-111, 2012.
  • Liu, Y., Zou, C. and Wang, Z. Calibration of the empirical likelihood for high-dimensional data, Ann. Inst. Stat. Math. 65, 529-550, 2013.
  • Owen, A. B. Empirical likelihood ratio confidence intervals for single functionals, Biometrika 75, 237-249, 1988.
  • Owen, A. B. Empirical likelihood ratio for linear models, Ann. Statist. 19, 1725-1747, 1991.
  • Owen, A. B. Empirical Likelihood, Chapman & Hall, New York, 2001.
  • Qin, J. and Lawless, J. Empirical likelihood and general estimating equations, Ann. Statist. 22, 300-325, 1994.
  • Xia, Y. and Li, W.K. On the estimation and testing of functional-coefficient linear models, Statistica Sinica 9, 735-757, 1999.
  • Xue, L. G. and Zhu, L. X. Empirical Likelihood in Nonparametric and Semiparametric Models, Science Press, Beijing, 2010.
  • You, J. and Zhou, Y. Empirical likelihood for semiparametric varying-coefficient partially linear regression models, Statist. Probab. Lett. 76, 412-422, 2006.
Yıl 2019, Cilt: 48 Sayı: 1, 230 - 241, 01.02.2019

Öz

Kaynakça

  • Chen, S. X. and Cui, H. J. On Bartlett correction of empirical likelihood in the presence of nuisance parameters, Biometrika 93, 215-220, 2006.
  • Chen, S. X., Peng, L. and Qin, Y. L. Effects of data dimension on empirical likelihood, Biometrika 9, 711-722, 2009.
  • DiCiccio, T. J., Hall, P. and Romano, J. P. Empirical likelihood is bartlett-correctable, Ann. Statist. 19, 1053-1061, 1991.
  • Fan, J. and Huang, T. Profile likelihood inference on semiparametric varying-coefficient partially linear models, Bernoulli 11, 1031-1057, 2005.
  • Guo, H., Zou, C. and Chen, B. Empirical likelihood for high-dimensional linear regression models, Metrika 77, 921-945, 2014.
  • Huang, Z. S. and Zhang, R. Q. Empirical likelihood for nonparametric parts in semiparametric varying-coefficient partially linear models, Statist. Probab. Lett. 79, 1798-1808, 2009.
  • Lam, C. and Fan, J. Profile-kernel likelihood inference with diverging number of parameters, Ann. Statist. 36, 2232-2260, 2008.
  • Li, G., Lin, L. and Zhu, L. Empirical likelihood for a varying coefficient partially linear model with diverging number of parameters, J. Multivar. Anal. 105, 85-111, 2012.
  • Liu, Y., Zou, C. and Wang, Z. Calibration of the empirical likelihood for high-dimensional data, Ann. Inst. Stat. Math. 65, 529-550, 2013.
  • Owen, A. B. Empirical likelihood ratio confidence intervals for single functionals, Biometrika 75, 237-249, 1988.
  • Owen, A. B. Empirical likelihood ratio for linear models, Ann. Statist. 19, 1725-1747, 1991.
  • Owen, A. B. Empirical Likelihood, Chapman & Hall, New York, 2001.
  • Qin, J. and Lawless, J. Empirical likelihood and general estimating equations, Ann. Statist. 22, 300-325, 1994.
  • Xia, Y. and Li, W.K. On the estimation and testing of functional-coefficient linear models, Statistica Sinica 9, 735-757, 1999.
  • Xue, L. G. and Zhu, L. X. Empirical Likelihood in Nonparametric and Semiparametric Models, Science Press, Beijing, 2010.
  • You, J. and Zhou, Y. Empirical likelihood for semiparametric varying-coefficient partially linear regression models, Statist. Probab. Lett. 76, 412-422, 2006.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular İstatistik
Bölüm İstatistik
Yazarlar

Junwei He Bu kişi benim

Xia Chen

Yayımlanma Tarihi 1 Şubat 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 48 Sayı: 1

Kaynak Göster

APA He, J., & Chen, X. (2019). Calibration of the empirical likelihood for semiparametric varying-coefficient partially linear models with diverging number of parameters. Hacettepe Journal of Mathematics and Statistics, 48(1), 230-241.
AMA He J, Chen X. Calibration of the empirical likelihood for semiparametric varying-coefficient partially linear models with diverging number of parameters. Hacettepe Journal of Mathematics and Statistics. Şubat 2019;48(1):230-241.
Chicago He, Junwei, ve Xia Chen. “Calibration of the Empirical Likelihood for Semiparametric Varying-Coefficient Partially Linear Models With Diverging Number of Parameters”. Hacettepe Journal of Mathematics and Statistics 48, sy. 1 (Şubat 2019): 230-41.
EndNote He J, Chen X (01 Şubat 2019) Calibration of the empirical likelihood for semiparametric varying-coefficient partially linear models with diverging number of parameters. Hacettepe Journal of Mathematics and Statistics 48 1 230–241.
IEEE J. He ve X. Chen, “Calibration of the empirical likelihood for semiparametric varying-coefficient partially linear models with diverging number of parameters”, Hacettepe Journal of Mathematics and Statistics, c. 48, sy. 1, ss. 230–241, 2019.
ISNAD He, Junwei - Chen, Xia. “Calibration of the Empirical Likelihood for Semiparametric Varying-Coefficient Partially Linear Models With Diverging Number of Parameters”. Hacettepe Journal of Mathematics and Statistics 48/1 (Şubat 2019), 230-241.
JAMA He J, Chen X. Calibration of the empirical likelihood for semiparametric varying-coefficient partially linear models with diverging number of parameters. Hacettepe Journal of Mathematics and Statistics. 2019;48:230–241.
MLA He, Junwei ve Xia Chen. “Calibration of the Empirical Likelihood for Semiparametric Varying-Coefficient Partially Linear Models With Diverging Number of Parameters”. Hacettepe Journal of Mathematics and Statistics, c. 48, sy. 1, 2019, ss. 230-41.
Vancouver He J, Chen X. Calibration of the empirical likelihood for semiparametric varying-coefficient partially linear models with diverging number of parameters. Hacettepe Journal of Mathematics and Statistics. 2019;48(1):230-41.