半参数平滑转换回归模型及其级数估计

数学物理学报 ›› 2012, Vol. 32 ›› Issue (4): 797-807.

半参数平滑转换回归模型及其级数估计

王成勇

襄樊学院数学与计算机科学学院湖北襄阳 441053

收稿日期:2010-11-29 修回日期:2011-12-10 出版日期:2012-08-25 发布日期:2012-08-25
基金资助:
教育部人文社会科学青年项目(10YJC790247)资助

A Semiparametric Smooth Transition Regression Model and Its Series Estimator

WANG Cheng-Yong

College of Mathematics and Computer Science, Xiangfan University, Xiangyang 441053

Received:2010-11-29 Revised:2011-12-10 Online:2012-08-25 Published:2012-08-25
Supported by:
教育部人文社会科学青年项目(10YJC790247)资助

摘要/Abstract

摘要：

将STR类模型的转换函数设定为决定于某未知光滑有界函数的复合Logistic函数, 提出半参数平滑转换回归模型. 在独立同分布数据假设下, 对其中的未知光滑有界函数采用级数估计, 基于非线性最小二乘估计理论证明了参数估计量的相合性和渐近正态性, 并简要讨论了置信区间的构造以及模型检验等问题. 通过随机模拟与传统的STR模型进行比较, 结果表明, 该文的新模型及估计方法具有广泛的适用性和灵活性.

关键词: 平滑转换回归模型, 级数估计, 相合性, 渐近正态性, 随机模拟

Abstract:

An unknown smooth function is substituted into the traditional smooth transition regression model and a semiparametric smooth transition regression model has been proposed in this paper. Based on the i.i.d. data assumption, we estimate the unknown smooth transition function by series estimator, the consistency and asymptotic normality properties of parameters are proved applying Nonlinear Least Square regression theory. The bootstrapping consistent confidence interval and hypothesis testing problem are also discussed briefly. The simulation results shows that, compared to traditional STR type model, our new model and estimating method are more flexible and have comprehensive applicability.

Key words: Smooth Transition Regression Model, Series Estimator, Consistency, Asymptotic Normality, Simulation

中图分类号:

62G08

王成勇. 半参数平滑转换回归模型及其级数估计[J]. 数学物理学报, 2012, 32(4): 797-807.

WANG Cheng-Yong. A Semiparametric Smooth Transition Regression Model and Its Series Estimator[J]. Acta mathematica scientia,Series A, 2012, 32(4): 797-807.

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