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Jackknifing in partially linear regression models with serially correlated errors

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  • You, Jinhong
  • Zhou, Xian
  • Chen, Gemai

Abstract

In this paper jackknifing technique is examined for functions of the parametric component in a partially linear regression model with serially correlated errors. By deleting partial residuals a jackknife-type estimator is proposed. It is shown that the jackknife-type estimator and the usual semiparametric least-squares estimator (SLSE) are asymptotically equivalent. However, simulation shows that the former has smaller biases than the latter when the sample size is small or moderate. Moreover, since the errors are correlated, both the Tukey type and the delta type jackknife asymptotic variance estimators are not consistent. By introducing cross-product terms, a consistent estimator of the jackknife asymptotic variance is constructed and shown to be robust against heterogeneity of the error variances. In addition, simulation results show that confidence interval estimation based on the proposed jackknife estimator has better coverage probability than that based on the SLSE, even though the latter uses the information of the error structure, while the former does not.

Suggested Citation

  • You, Jinhong & Zhou, Xian & Chen, Gemai, 2005. "Jackknifing in partially linear regression models with serially correlated errors," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 386-404, February.
    • Handle: RePEc:eee:jmvana:v:92:y:2005:i:2:p:386-404
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    References listed on IDEAS

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    1. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
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    4. Rice, John, 1986. "Convergence rates for partially splined models," Statistics & Probability Letters, Elsevier, vol. 4(4), pages 203-208, June.
    5. Eubank, R. L. & Hart, J. D. & Speckman, Paul, 1990. "Trigonometric series regression estimators with an application to partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 32(1), pages 70-83, January.
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    Cited by:

    1. Liang, Han-Ying & Fan, Guo-Liang, 2009. "Berry-Esseen type bounds of estimators in a semiparametric model with linear process errors," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 1-15, January.
    2. 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.

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