王成勇, 艾春荣, 王少平. 有结构变化的半参数回归模型[J]. 应用概率统计, 2010, 26(5): 501-514.
引用本文: 王成勇, 艾春荣, 王少平. 有结构变化的半参数回归模型[J]. 应用概率统计, 2010, 26(5): 501-514.
Wang Chengyong, Ai Chunrong, Wang Shaoping. A Semiparametric Regression Model with Structural Change[J]. Chinese Journal of Applied Probability and Statistics, 2010, 26(5): 501-514.
Citation: Wang Chengyong, Ai Chunrong, Wang Shaoping. A Semiparametric Regression Model with Structural Change[J]. Chinese Journal of Applied Probability and Statistics, 2010, 26(5): 501-514.

有结构变化的半参数回归模型

A Semiparametric Regression Model with Structural Change

  • 摘要: 结合半参数回归模型和含未知变点的结构变化模型提出一个新的模型\,---\,有结构变化的半参数回归模型, 给出了新模型的有关参数\beta,\beta^\ast,\gamma,k的加权最小二乘估计和f(t)的核估计, 证明了参数\, \beta,\beta^\ast,\gamma的估计的\sqrtn\,-相合性, 强相合性, 讨论了模型的检验等问题, 并进一步通过随机模拟验证了新模型的优越性.

     

    Abstract: Combined with semiparametric regression model and structural change model with unknown change point, a new regression model --- semiparametric regression model with structural change --- has been proposed. The weighted least squares estimator of parameter \beta,\beta^\ast,\gamma,k and the kernel estimator of f(t) are given, and \sqrtn-consistency properties of \beta,\beta^\ast,\gamma's estimator is proved. Also, the estimator's strong consistency properties and some test problem about the model are discussed. And, at last, we give a simulation study to verify the superiority of our new model.

     

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