| 王继霞,肖庆宪.一个有效估计: 半参数非时齐扩散模型的局部线性复合分位回归估计$^$[J].数学年刊A辑,2014,35(1):61~72 |
| 一个有效估计: 半参数非时齐扩散模型的局部线性复合分位回归估计$^$ |
| An Efficient Estimation: Local Linear Composite Quantle Regression for SemiparametricTime-Inhomogeneous Diffusion Models |
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| DOI： |
| 中文关键词: 半参数扩散模型, 时变参数, 复合分位回归估计, 渐近正态性, 渐近相对效 |
| 英文关键词:Semiparametric diffusion model, Time-dependent parameter, Composite quantile regression estimation, Asymptotic normality, Asymptotic relative efficiency |
| 基金项目:国家自然科学基金
(No.11171221) 和上海市一流学科 (No.XTKX2012) |
| Author Name | Affiliation | E-mail | | WANG Jixia | Business School, University of Shanghai for Science
and Technology, Shanghai 200093, China
College of Mathematics and
Information Science, Henan Normal University, Xinxiang
453007, Henan, China. | jixiawang@163.com | | XIAO Qingxian | Business School, University of Shanghai for Science and
Technology, Shanghai 200093, China. | qxxiao@163.com |
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| 中文摘要: |
| 主要研究半参数非时齐扩散模型的参数估计问题.
基于非时齐扩散模型的离散观测样本,
首先得到漂移参数的局部线性复合分位回归估计,
并证明估计量的渐近偏差、渐近方差和渐近正态性. 其次,
讨论了带宽的选择和局部线性复合分位回归估计关于局部线性最小二乘估计的渐近相对效,
所得到的局部估计较局部线性最小二乘估计更为有效. 最后,
通过模拟说明了局部线性复合分位回归估计比局部线性最小二乘估计的模拟效果更好. |
| 英文摘要: |
| The authors study the estimations of parameters
for semiparametric time-inhomogeneous diffusion models. Based on
discretely observed sample of time-inhomogeneous diffusion models,
the local linear composite quantile regression (or CQR for short)
estimations of the drift parameters are proposed, and the asymptotic
bias, asymptotic variance and asymptotic normality of the local
estimations are verified. The authors discuss the bandwidth
selection and the asymptotic relative efficiency of the local linear
{\rm CQR} estimations comparing with the local linear least squares
estimations, and it is shown that the proposed local estimations are
much more efficient than the local linear least squares estimations.
Furthermore, simulation results show that the proposed estimations have
better performance than the local least squares estimations in
diffusion models. |
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