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Efficient Statistical Inference Procedures for Partially Nonlinear Models and their Applications

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  • Runze Li
  • Lei Nie

Abstract

Summary Motivated by an analysis of a real data set in ecology, we consider a class of partially nonlinear models where both a nonparametric component and a parametric component are present. We develop two new estimation procedures to estimate the parameters in the parametric component. Consistency and asymptotic normality of the resulting estimators are established. We further propose an estimation procedure and a generalized F‐test procedure for the nonparametric component in the partially nonlinear models. Asymptotic properties of the newly proposed estimation procedure and the test statistic are derived. Finite sample performance of the proposed inference procedures are assessed by Monte Carlo simulation studies. An application in ecology is used to illustrate the proposed methods.

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  • Runze Li & Lei Nie, 2008. "Efficient Statistical Inference Procedures for Partially Nonlinear Models and their Applications," Biometrics, The International Biometric Society, vol. 64(3), pages 904-911, September.
    • Handle: RePEc:bla:biomet:v:64:y:2008:i:3:p:904-911
    DOI: 10.1111/j.1541-0420.2007.00937.x
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    References listed on IDEAS

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    1. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
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    4. Jianqing Fan & Runze Li, 2004. "New Estimation and Model Selection Procedures for Semiparametric Modeling in Longitudinal Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 710-723, January.
    5. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    6. Zonghui Hu, 2004. "Profile-kernel versus backfitting in the partially linear models for longitudinal/clustered data," Biometrika, Biometrika Trust, vol. 91(2), pages 251-262, June.
    7. Yatchew, A., 1997. "An elementary estimator of the partial linear model," Economics Letters, Elsevier, vol. 57(2), pages 135-143, December.
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    Cited by:

    1. Nian-Sheng Tang & Pu-Ying Zhao, 2013. "Empirical likelihood semiparametric nonlinear regression analysis for longitudinal data with responses missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(4), pages 639-665, August.
    2. Rui Li & Yuanyuan Zhang, 2021. "Two-stage estimation and simultaneous confidence band in partially nonlinear additive model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(8), pages 1109-1140, November.
    3. Wang, Zhaoliang & Xue, Liugen & Liu, Juanfang, 2019. "Checking nonparametric component for partially nonlinear model with missing response," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 1-8.
    4. Song, Lixin & Zhao, Yue & Wang, Xiaoguang, 2010. "Sieve least squares estimation for partially nonlinear models," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1271-1283, September.
    5. Xiaoshuang Zhou & Peixin Zhao & Yujie Gai, 2022. "Imputation-based empirical likelihood inferences for partially nonlinear quantile regression models with missing responses," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(4), pages 705-722, December.
    6. Yunlu Jiang & Guo-Liang Tian & Yu Fei, 2019. "A robust and efficient estimation method for partially nonlinear models via a new MM algorithm," Statistical Papers, Springer, vol. 60(6), pages 2063-2085, December.

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