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


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  • Gao, Jiti
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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

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Article provided by Elsevier in its journal Statistics & Probability Letters.

Volume (Year): 25 (1995)
Issue (Month): 2 (November)
Pages: 153-162

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Handle: RePEc:eee:stapro:v:25:y:1995:i:2:p:153-162

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Keywords: The law of iterated logarithm Least-square estimator Partly linear model;


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  1. Rice, John, 1986. "Convergence rates for partially splined models," Statistics & Probability Letters, Elsevier, vol. 4(4), pages 203-208, June.
  2. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July.
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Cited by:
  1. 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.
  2. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
  3. Aneiros-Pérez, Germán & Vieu, Philippe, 2006. "Semi-functional partial linear regression," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1102-1110, June.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  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. 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.


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