Abstract
In this paper, empirical likelihood inferences for varying-coefficient single-index model with right-censored data are investigated. By a synthetic data approach, we propose an empirical log-likelihood ratio function for the index parameters, which are of primary interest, and show that its limiting distribution is a mixture of central chi-squared distributions. In order that the Wilks’ phenomenon holds, we propose an adjusted empirical log-likelihood ratio for the index parameters. The adjusted empirical log-likelihood is shown to have a standard chi-squared limiting distribution. Simulation studies are undertaken to assess the finite sample performance of the proposed confidence intervals. A real example is presented for illustration.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Carroll RJ, Fan JQ, Gijbel I, Wand MP (1997) Generalized partially linear single-index models. J Am Stat Assoc 92: 477–489
Chen M, Yuen KC, Zhu LX (2003) Asymptotics of the goodness-of-fit test for a partial linear model with randomly censored data. Sci China Ser A 46: 145–158
Engle RF, Granger CWJ, Rice J,Weiss A (1986) Nonparametric estimates of the relation between weather and electricity sales. J Am Stat Assoc 81:310–320
Fan J, Gijbels I (1996) Local polynomial modelling and its applications. Chapman and Hall, London
Gao JT (1995) Asymptotic theory for partly linear models. Commun Stat Theory Methods 24: 1985–2009
Hall P, La Scala B (1990) Methodology and algorithms of empirical likelihood. Int Stat Rev 58: 109–127
Härdle W, Hall P, Ichimura H (1993) Optimal smoothing in single-index models. Ann Stat 21: 157–178
Hastie TJ, Tibshirani R (1993) Varying-coefficient models. J Royal Stat Assoc B 55: 757–796
Huang ZS, Zhang RQ (2009) Nonparametric inference for single-index fuction in varying-coefficient single-index model. Ind J Pure Appl Math 40: 87–111
Huang ZS, Zhang RQ (2010) Tests for varying-coefficient parts on varying-coefficient single-index model. J Korean Math Soc 47: 385–407
Kolaczyk ED (1994) Empirical likelihood for generalized linear models. Stat Sin 4: 199–218
Koul H, Susarla V, van Ryzin J (1981) Regression analysis with randomly right-censored data. Ann Stat 9: 1276–1288
Lai TL, Ying Z, Zheng Z (1995) Asymptotic normality of a class of adaptive statistics with applications of synthetic data methods for censored regression. J Multivar Anal 52: 259–279
Lu XW, Cheng TL (2007) Randomly censored partially linear single-index models. J Multivar Anal 98: 1895–1922
Owen AB (1988) Empirical likelihood ratio confidence intervals for a single function. Biometrika 75: 237–249
Owen AB (1990) Empirical likelihood ratio confidence regions. Ann Stat 18: 90–120
Owen AB (1991) Empirical likelihood for linear models. Ann Stat 19: 1725–1747
Speckman JH (1988) Kernel smoothing in partial linear models. J Royal Stat Assoc B 50: 413–436
Wang QH (1996) Consistent estimators in random censorship semiparametric regression models. Sci China Ser A 39: 163–176
Wang QH, Li G (2002) Empirical likelihood semiparametric regression analysis under random censorship. J Multivar Anal 83: 469–486
Wang QH, Zheng ZG (1997) Asymptotic properties for the semiparametric regression model with randomly censored data. Sci China Ser A 40: 945–957
Wong H, Ip W, Zhang R (2008) Varying-coefficient single-index model. Comput Stat Data Anal 52: 1458–1476
Zhou M (1992) Asymptotic normality of the synthetic estimator for censored survival data. Ann Stat 20: 1002–1021
Zhu LX, Xue LG (2006) Empirical likelihood confidence regions in a partially linear single-index model. J Royal Stat Assoc B 68: 549–570
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Huang, Z. Empirical likelihood for varying-coefficient single-index model with right-censored data. Metrika 75, 55–71 (2012). https://doi.org/10.1007/s00184-010-0314-8
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00184-010-0314-8