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The laws of the iterated logarithm of some estimates in partly linear models

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  • Gao, Jiti

Abstract

Consider the regression model Yi = xi'[beta] + g(ti) + ei, 1 [less-than-or-equals, slant] i [less-than-or-equals, slant] n, where xi = (xi1, xi2, ..., xip)' and ti (ti [epsilon] [0, 1]) are known and nonrandom design points, [beta] = ([beta]1, ..., [beta]p)' (p [greater-or-equal, slanted] 1) is an unknown parameter, g(·) is an unknown function, and ei are i.i.d. random errors. Based on g estimated by nonparametric kernel estimation, the laws of the iterated logarithm of the least-square estimator of [beta] and an estimator of [sigma]2 = Ee12

Suggested Citation

  • Gao, Jiti, 1995. "The laws of the iterated logarithm of some estimates in partly linear models," Statistics & Probability Letters, Elsevier, vol. 25(2), pages 153-162, November.
    • Handle: RePEc:eee:stapro:v:25:y:1995:i:2:p:153-162
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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.
    2. Rice, John, 1986. "Convergence rates for partially splined models," Statistics & Probability Letters, Elsevier, vol. 4(4), pages 203-208, June.
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    Cited by:

    1. You, Jinhong & Zhou, Xian, 2005. "The law of iterated logarithm of estimators for partially linear panel data models," Statistics & Probability Letters, Elsevier, vol. 75(4), pages 267-279, December.
    2. Germán Aneiros & Nengxiang Ling & Philippe Vieu, 2015. "Error variance estimation in semi-functional partially linear regression models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(3), pages 316-330, September.
    3. You, Jinhong & Zhou, Xian, 2006. "Statistical inference in a panel data semiparametric regression model with serially correlated errors," Journal of Multivariate Analysis, Elsevier, vol. 97(4), pages 844-873, April.
    4. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    5. Hu, Jianhua & You, Jinhong & Zhou, Xian, 2017. "Improved estimation of fixed effects panel data partially linear models with heteroscedastic errors," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 96-111.
    6. Aneiros-Pérez, Germán & Vieu, Philippe, 2006. "Semi-functional partial linear regression," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1102-1110, June.
    7. You, Jinhong & Zhou, Xian & Zhou, Yong, 2010. "Statistical inference for panel data semiparametric partially linear regression models with heteroscedastic errors," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1079-1101, May.
    8. You, Jinhong & Chen, Gemai, 2006. "Estimation of a semiparametric varying-coefficient partially linear errors-in-variables model," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 324-341, February.
    9. Jinhong You & Xian Zhou & Lixing Zhu & Bin Zhou, 2011. "Weighted denoised minimum distance estimation in a regression model with autocorrelated measurement errors," Statistical Papers, Springer, vol. 52(2), pages 263-286, May.
    10. Jinhong You & Xian Zhou, 2010. "Statistical inference on seemingly unrelated varying coefficient partially linear models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(2), pages 227-253, May.
    11. Gemai Chen & Jinhong You, 2005. "An asymptotic theory for semiparametric generalized least squares estimation in partially linear regression models," Statistical Papers, Springer, vol. 46(2), pages 173-193, April.
    12. You, Jinhong & Zhou, Xian & Zhu, Li-Xing, 2009. "Inference on a regression model with noised variables and serially correlated errors," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1182-1197, July.
    13. Su, Liangjun & Jin, Sainan, 2010. "Profile quasi-maximum likelihood estimation of partially linear spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 157(1), pages 18-33, July.

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