丁建华, 张忠占. 单调约束条件下部分线性模型的Bernstein多项式估计[J]. 应用概率统计, 2014, 30(4): 381-397.
引用本文: 丁建华, 张忠占. 单调约束条件下部分线性模型的Bernstein多项式估计[J]. 应用概率统计, 2014, 30(4): 381-397.
Ding Jianhua, Zhang Zhongzhan. Bernstein Polynomial Estimation in the Partially Linear Model under Monotonicity Constraints[J]. Chinese Journal of Applied Probability and Statistics, 2014, 30(4): 381-397.
Citation: Ding Jianhua, Zhang Zhongzhan. Bernstein Polynomial Estimation in the Partially Linear Model under Monotonicity Constraints[J]. Chinese Journal of Applied Probability and Statistics, 2014, 30(4): 381-397.

单调约束条件下部分线性模型的Bernstein多项式估计

Bernstein Polynomial Estimation in the Partially Linear Model under Monotonicity Constraints

  • 摘要: 本文提出单调约束条件下部分线性模型基于Bernstein多项式的最大似然估计. 我们利用单调Bernstein多项式逼近单调非参数函数. 在相当宽松的条件下给出估计的渐近性质和最优收敛率. 最后通过理论模拟和实例分析来评价提出的方法.

     

    Abstract: In this paper, a Bernstein-polynomial-based likelihood method is proposed for the partially linear model under monotonicity constraints. Monotone Bernstein polynomials are employed to approximate the monotone nonparametric function in the model. The estimator of the regression parameter is shown to be asymptotically normal and efficient, and the rate of convergence of the estimator of the nonparametric component is established, which could be the optimal under the smooth assumptions. A simulation study and a real data analysis are conducted to evaluate the finite sample performance of the proposed method.

     

/

返回文章
返回