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B-spline estimation for varying coefficient regression with spatial data

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Abstract

This paper considers a nonparametric varying coefficient regression with spatial data. A global smoothing procedure is developed by using B-spline function approximations for estimating the coefficient functions. Under mild regularity assumptions, the global convergence rates of the B-spline estimators of the unknown coefficient functions are established. Asymptotic results show that our B-spline estimators achieve the optimal convergence rate. The asymptotic distributions of the B-spline estimators of the unknown coefficient functions are also derived. A procedure for selecting smoothing parameters is given. Finite sample properties of our procedures are studied through Monte Carlo simulations. Application of the proposed method is demonstrated by examining voting behaviors across US counties in the 1980 presidential election.

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Authors and Affiliations

  1. School of Economics and Management, Nanjing University of Science and Technology, Nanjing, 210094, China

    QingGuo Tang & LongSheng Cheng

  2. Institute of Sciences, PLA University of Science and Technology, Nanjing, 210007, China

    QingGuo Tang

Authors
  1. QingGuo Tang
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  2. LongSheng Cheng
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Corresponding author

Correspondence to QingGuo Tang.

Additional information

This work was partially supported by National Natural Science Foundation of China (Grant No. 10671089), China Postdoctoral Science Foundation and Jiangsu Planned Projects for Postdoctoral Research Funds

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Tang, Q., Cheng, L. B-spline estimation for varying coefficient regression with spatial data. Sci. China Ser. A-Math. 52, 2321–2340 (2009). https://doi.org/10.1007/s11425-009-0111-x

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  • DOI: https://doi.org/10.1007/s11425-009-0111-x

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