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Empirical likelihood inferences for the semiparametric additive isotonic regression

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  • Cheng, Guang
  • Zhao, Yichuan
  • Li, Bo

Abstract

We consider the (profile) empirical likelihood inferences for the regression parameter (and its any sub-component) in the semiparametric additive isotonic regression model where each additive nonparametric component is assumed to be a monotone function. In theory, we show that the empirical log-likelihood ratio for the regression parameters weakly converges to a standard chi-squared distribution. In addition, our simulation studies demonstrate the empirical advantages of the proposed empirical likelihood method over the normal approximation method in Cheng (2009) [4] in terms of more accurate coverage probability when the sample size is small. It is worthy pointing out that we can construct the empirical likelihood based confidence region without the hassle of tuning any smoothing parameter due to the shape constraints assumed in this paper.

Suggested Citation

  • Cheng, Guang & Zhao, Yichuan & Li, Bo, 2012. "Empirical likelihood inferences for the semiparametric additive isotonic regression," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 172-182.
    • Handle: RePEc:eee:jmvana:v:112:y:2012:i:c:p:172-182
    DOI: 10.1016/j.jmva.2012.06.003
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    References listed on IDEAS

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    1. Einmahl, J.H.J. & McKeague, I.W., 1999. "Confidence tubes for multiple quantile plots via empirical likelihood," Other publications TiSEM b64493f8-1c01-40fd-b16d-7, Tilburg University, School of Economics and Management.
    2. Chen, S. X., 1994. "Empirical Likelihood Confidence Intervals for Linear Regression Coefficients," Journal of Multivariate Analysis, Elsevier, vol. 49(1), pages 24-40, April.
    3. Gang Li & Ingrid Van Keilegom, 2002. "Likelihood Ratio Confidence Bands in Non–parametric Regression with Censored Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 547-562, September.
    4. Yanqing Sun & Rajeshwari Sundaram & Yichuan Zhao, 2009. "Empirical Likelihood Inference for the Cox Model with Time‐dependent Coefficients via Local Partial Likelihood," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 444-462, September.
    5. Wen Yu & Yunting Sun & Ming Zheng, 2011. "Empirical likelihood method for linear transformation models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(2), pages 331-346, April.
    6. Xiao Wang & Jinglai Shen, 2010. "A class of grouped Brunk estimators and penalized spline estimators for monotone regression," Biometrika, Biometrika Trust, vol. 97(3), pages 585-601.
    7. McKeague, Ian W. & Zhao, Yichuan, 2002. "Simultaneous confidence bands for ratios of survival functions via empirical likelihood," Statistics & Probability Letters, Elsevier, vol. 60(4), pages 405-415, December.
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    Cited by:

    1. Yining Chen & Richard J. Samworth, 2016. "Generalized additive and index models with shape constraints," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 729-754, September.
    2. Zhang, Zhigang & Zhao, Yichuan, 2013. "Empirical likelihood for linear transformation models with interval-censored failure time data," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 398-409.

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