缺失数据下部分非线性变系数EV模型的统计推断

数学物理学报 ›› 2020, Vol. 40 ›› Issue (2): 460-474.

缺失数据下部分非线性变系数EV模型的统计推断

马奕佳*(),薛留根,芦飞

^{北京工业大学应用数理学院北京 100124}

收稿日期:2018-05-18 出版日期:2020-04-26 发布日期:2020-05-21
通讯作者: 马奕佳 E-mail:redbamboo12138@126.com
基金资助:
国家自然科学基金(11971001);北京市自然科学基金(1182002)

Statistical Inference in Partially Nonlinear Varying-Coefficient Errors-in-Variables Models with Missing Responses

Yijia Ma*(),Liugen Xue,Fei Lu

^{College of Applied Sciences, Beijing University of Technology, Beijing 100124}

Received:2018-05-18 Online:2020-04-26 Published:2020-05-21
Contact: Yijia Ma E-mail:redbamboo12138@126.com
Supported by:
the NSFC(11971001);the Beijing Natural Science Foundation(1182002)

摘要/Abstract

摘要：

该文研究了响应变量缺失下半参数部分非线性变系数EV模型的统计推断问题，利用逆概率加权局部纠偏profile最小二乘法构造了模型中非参数分量和参数分量的估计，证明了估计量的渐近正态性.通过数值模拟和实际数据分析，验证了所提出的估计方法是有效的.

关键词: 部分非线性变系数模型, 缺失数据, 局部纠偏, 测量误差, 渐近正态性

Abstract:

This paper considers about the estimation of varying-coefficient partial nonlinear errors-in-variables models with missing responses. Firstly, we develop inverse probability weighted approaches and local bias-corrected restricted profile least squares estimators. Asymptotic normality of estimators is established. Moreover, both simulation results and a real data show that local bias-corrected restricted profile least squares estimated approach are better than the performance ignoring the measurement error.

Key words: Varying-coefficient partial nonlinear model, Missing data, Local bias-corrected restricted profile least-squares approach, Measurement error, Asymptotic normality

中图分类号:

O212.7

马奕佳,薛留根,芦飞. 缺失数据下部分非线性变系数EV模型的统计推断[J]. 数学物理学报, 2020, 40(2): 460-474.

Yijia Ma,Liugen Xue,Fei Lu. Statistical Inference in Partially Nonlinear Varying-Coefficient Errors-in-Variables Models with Missing Responses[J]. Acta mathematica scientia,Series A, 2020, 40(2): 460-474.

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参考文献 18

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		$\sigma_e^{2} = 0.1^{2}$			$\sigma_e^{2} = 0.5^{2}$
$n$	$\beta$	Bias	SD	MSE	Bias	SD	MSE
$100$	$\hat{\beta}_1$	-0.0016	0.0114	1.334e-04	-0.0170	0.1045	0.0112
	$\hat{\beta}_2$	0.0008	0.0146	2.148e-04	0.0141	0.1053	0.0113
$200$	$\hat{\beta}_1$	0.0001	0.0050	2.546e-05	-0.0005	0.0051	2.697e-05
	$\hat{\beta}_2$	-0.0004	0.0066	4.418e-05	-0.0008	0.0081	6.685e-05
$400$	$\hat{\beta}_1$	-0.0001	0.0022	4.916e-06	-0.0004	0.0026	6.698e-06
	$\hat{\beta}_2$	-0.0001	0.0027	7.188e-06	-0.0001	0.0025	6.395e-06

				$\hat{\beta}^{HT}$			$\hat{\beta}^{NE}$
$\beta$	$\sigma_e^{2}$	$n$	Bias	SD	MSE	Bias	SD	MSE
$\beta_1$	$0.1^{2}$	$100$	-0.0013	0.0091	8.558e-05	0.0105	0.0142	3.112e-04
		$200$	-0.0007	0.0045	2.117e-05	0.0068	0.0057	7.865e-05
		$400$	0.0003	0.0016	2.614e-06	-0.0008	0.0027	8.244e-06
	$0.5^{2}$	$100$	0.0019	0.0093	9.010e-05	0.0114	0.0147	3.461e-04
		$ 200$	-0.0008	0.0052	2.843e-05	0.0062	0.0065	8.049e-05
		$400$	0.0002	0.0018	3.443e-06	0.0048	0.0051	4.916e-05
$\beta_2$	$0.1^{2}$	$100$	0.0001	0.0116	1.345e-04	0.0022	0.0155	2.451e-04
		$200$	0.0003	0.0065	4.240e-05	-0.0009	0.0071	5.114e-05
		$400$	-0.0004	0.0019	3.881e-06	0.0003	0.0039	1.557e-05
	$0.5^{2}$	$100$	-0.0016	0.0138	1.930e-04	0.0026	0.0274	7.575e-04
		$200$	-0.0007	0.0065	4.382e-05	0.0014	0.0112	1.271e-04
		$400$	-0.0001	0.0026	7.035e-06	0.0004	0.0048	2.353e-05

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