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Empirical likelihood for heteroscedastic partially linear errors-in-variables model with α-mixing errors

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  • Guo-Liang Fan
  • Han-Ying Liang
  • Jiang-Feng Wang

Abstract

In this paper, we apply the empirical likelihood method to heteroscedastic partially linear errors-in-variables model. For the cases of known and unknown error variances, the two different empirical log-likelihood ratios for the parameter of interest are constructed. If the error variances are known, the empirical log-likelihood ratio is proved to be asymptotic chi-square distribution under the assumption that the errors are given by a sequence of stationary α-mixing random variables. Furthermore, if the error variances are unknown, we show that the proposed statistic is asymptotically standard chi-square distribution when the errors are independent. Simulations are carried out to assess the performance of the proposed method. Copyright Springer-Verlag 2013

Suggested Citation

  • Guo-Liang Fan & Han-Ying Liang & Jiang-Feng Wang, 2013. "Empirical likelihood for heteroscedastic partially linear errors-in-variables model with α-mixing errors," Statistical Papers, Springer, vol. 54(1), pages 85-112, February.
    • Handle: RePEc:spr:stpapr:v:54:y:2013:i:1:p:85-112
    DOI: 10.1007/s00362-011-0412-3
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    References listed on IDEAS

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    Cited by:

    1. Przystalski, Marcin, 2014. "Estimation of the covariance matrix in multivariate partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 380-385.
    2. Christophe Chesneau & Salima El Kolei & Fabien Navarro, 2022. "Parametric estimation of hidden Markov models by least squares type estimation and deconvolution," Statistical Papers, Springer, vol. 63(5), pages 1615-1648, October.
    3. Ai-Ai Liu & Han-Ying Liang, 2017. "Jackknife empirical likelihood of error variance in partially linear varying-coefficient errors-in-variables models," Statistical Papers, Springer, vol. 58(1), pages 95-122, March.
    4. Hong-Xia Xu & Guo-Liang Fan & Han-Ying Liang, 2017. "Hypothesis test on response mean with inequality constraints under data missing when covariables are present," Statistical Papers, Springer, vol. 58(1), pages 53-75, March.
    5. Yu Shen & Han-Ying Liang, 2018. "Quantile regression and its empirical likelihood with missing response at random," Statistical Papers, Springer, vol. 59(2), pages 685-707, June.

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