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Local linear regression with reciprocal inverse Gaussian kernel

Author

Listed:
  • Xu Li

    (Shanxi Normal University)

  • Juxia Xiao

    (Shanxi Normal University)

  • Weixing Song

    (Kansas State University)

  • Jianhong Shi

    (Shanxi Normal University)

Abstract

In this paper, we propose a local linear estimator for the regression model $$Y=m(X)+\varepsilon $$ Y = m ( X ) + ε based on the reciprocal inverse Gaussian kernel when the design variable is supported on $$(0,\infty )$$ ( 0 , ∞ ) . The conditional mean-squared error of the proposed estimator is derived, and its asymptotic properties are thoroughly investigated, including the asymptotic normality and the uniform almost sure convergence. The finite sample performance of the proposed estimator is evaluated via simulation studies and a real data application. A comparison study with other existing estimation methods is also made, and the pros and cons of the proposed estimator are discussed.

Suggested Citation

  • Xu Li & Juxia Xiao & Weixing Song & Jianhong Shi, 2019. "Local linear regression with reciprocal inverse Gaussian kernel," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(6), pages 733-758, August.
    • Handle: RePEc:spr:metrik:v:82:y:2019:i:6:d:10.1007_s00184-019-00717-6
    DOI: 10.1007/s00184-019-00717-6
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    References listed on IDEAS

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    1. Hira L. Koul & Weixing Song, 2013. "Large sample results for varying kernel regression estimates," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(4), pages 829-853, December.
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    4. Marchant, Carolina & Bertin, Karine & Leiva, Víctor & Saulo, Helton, 2013. "Generalized Birnbaum–Saunders kernel density estimators and an analysis of financial data," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 1-15.
    5. Igarashi, Gaku & Kakizawa, Yoshihide, 2014. "Re-formulation of inverse Gaussian, reciprocal inverse Gaussian, and Birnbaum–Saunders kernel estimators," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 235-246.
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    8. Funke, Benedikt & Kawka, Rafael, 2015. "Nonparametric density estimation for multivariate bounded data using two non-negative multiplicative bias correction methods," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 148-162.
    9. Hirukawa, Masayuki & Sakudo, Mari, 2014. "Nonnegative bias reduction methods for density estimation using asymmetric kernels," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 112-123.
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