Efficient estimation for partially linear varying coefficient models when coefficient functions have different smoothing variables

Yang, Seong Jun;Park, Byeong U.
(2014) Journal of Multivariate Analysis — Vol. 126, p. 100-113 (2014)

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Authors
  • Yang, Seong JunUCLouvain
    Author
  • Park, Byeong U.Seoul National University, Republic of Korea
    Author
Abstract
In this paper we consider partially linear varying coefficient models. We provide semiparametric efficient estimators of the parametric part as well as rate-optimal estimators of the nonparametric part. In our model, different nonparametric coefficients have different smoothing variables. This requires employing a projection technique to get proper estimators of the nonparametric coefficients, and thus conventional kernel smoothing cannot give semiparametric efficient estimators of the parametric components. We take the smooth backfitting approach in conjunction with the profiling technique to get semiparametric efficient estimators of the parametric part. We also show that our estimators of the nonparametric part achieve the univariate rate of convergence, regardless of the covariate's dimension. We report the finite sample properties of the semiparametric efficient estimators and compare them with those of other estimators. © 2014 Elsevier Inc.
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Yang, S. J., & Park, B. U. (2014). Efficient estimation for partially linear varying coefficient models when coefficient functions have different smoothing variables. Journal of Multivariate Analysis, 126, 100-113. https://doi.org/10.1016/j.jmva.2014.01.004 (Original work published 2014)