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Nonparametric inference for covariate-adjusted model

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  • Dai, Shuang
  • Huang, Zhensheng

Abstract

In this paper, we provide a nonparametric test for the covariate-adjusted model where the variables are not directly observed, but are observed after being distorted by unknown functions of a commonly observable covariate in a multiplicative fashion. We estimate the distorting functions by nonparametrically regressing the response and predictors on the distorting covariate, and calculate the estimators of the unobserved variables. Based on the calibrated variables, we propose a generalized likelihood ratio (GLR) test statistic to check the adequacy for the covariate-adjusted model and establish the asymptotic property of the GLR test statistic. Moreover, we carry out some simulated and real examples to evaluate the performance of the GLR test statistic, and make comparisons with these results obtained by Zhang et al. (2015).

Suggested Citation

  • Dai, Shuang & Huang, Zhensheng, 2020. "Nonparametric inference for covariate-adjusted model," Statistics & Probability Letters, Elsevier, vol. 162(C).
    • Handle: RePEc:eee:stapro:v:162:y:2020:i:c:s0167715220300699
    DOI: 10.1016/j.spl.2020.108766
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    References listed on IDEAS

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    1. Zhao, Jingxin & Xie, Chuanlong, 2018. "A nonparametric test for covariate-adjusted models," Statistics & Probability Letters, Elsevier, vol. 133(C), pages 65-70.
    2. Zhang, Jun & Li, Gaorong & Feng, Zhenghui, 2015. "Checking the adequacy for a distortion errors-in-variables parametric regression model," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 52-64.
    3. Zhang, Jun & Zhu, Li-Xing & Liang, Hua, 2012. "Nonlinear models with measurement errors subject to single-indexed distortion," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 1-23.
    4. Jianqing Fan & Jiancheng Jiang, 2007. "Rejoinder on: Nonparametric inference with generalized likelihood ratio tests," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(3), pages 471-478, December.
    5. Jianqing Fan & Jiancheng Jiang, 2007. "Nonparametric inference with generalized likelihood ratio tests," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(3), pages 409-444, December.
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