删失指标随机缺失下一般线性模型的加权最小二乘估计

数学物理学报 ›› 2025, Vol. 45 ›› Issue (3): 919-933.

删失指标随机缺失下一般线性模型的加权最小二乘估计

饶珍敏,王江峰^*(),胡康,何姗

浙江工商大学统计与数学学院杭州 310018

收稿日期:2024-07-16 修回日期:2024-11-07 出版日期:2025-06-26 发布日期:2025-06-20
通讯作者: *王江峰，Email: wjf2929@163.com
基金资助:
国家重点研发计划项目(2024YFA1013502);国家自然科学基金(U23A2064);国家自然科学基金(12031005);浙江省自然科学基金(LY24A010004);国内访问学者 “教师专业发展项目”(FX2023017)

Least Squares Estimators of General Linear Model with Censoring Indicators Missing at Random

Rao Zhenmin,Wang Jiangfeng^*(),Hu Kang,He Shan

School of Statistic and Mathematics,Zhejiang Gongshang University, Hangzhou 310018

Received:2024-07-16 Revised:2024-11-07 Online:2025-06-26 Published:2025-06-20
Supported by:
National Key R&D Program of China(2024YFA1013502);NSFC(U23A2064);NSFC(12031005);Zhejiang Province Natural Science Foundation(LY24A010004);Teacher Professional Development Program for Domestic Visiting Scholars(FX2023017)

摘要/Abstract

摘要：

该文在删失指标随机缺失下, 研究了一般线性模型的加权最小二乘回归估计; 基于校准、插值和逆概率三种加权方法, 分别构建了参数的估计量; 在适当的假设条件下, 建立了这些估计量的渐近正态性, 并提出了一种新的基于最小二乘加权残差 (LSWR) 的 Bootstrap 检验程序; 最后通过数值模拟和实证, 分析了这些估计方法和检验程序的有效性.

关键词: 删失指标, 随机缺失, 一般线性模型, 渐近正态性, Bootstrap 检验

Abstract:

This article investigates the weighted least squares regression estimators of general linear models with censoring indicators missing at random. Based on three weighting methods of calibration, interpolation, and inverse probability, parameter estimators are constructed respectively. Under appropriate assumptions, asymptotic normality of these estimators has been established, and a new bootstrap testing program based on least squares weighted residual (LSWR) is proposed. Finally, the effectiveness of these estimators and testing procedures are analyzed through numerical simulations and actual data.

Key words: censoring indicator, missing at random, general linear models, asymptotic normality, bootstrap testing

中图分类号:

O212.73

饶珍敏, 王江峰, 胡康, 何姗. 删失指标随机缺失下一般线性模型的加权最小二乘估计[J]. 数学物理学报, 2025, 45(3): 919-933.

Rao Zhenmin, Wang Jiangfeng, Hu Kang, He Shan. Least Squares Estimators of General Linear Model with Censoring Indicators Missing at Random[J]. Acta mathematica scientia,Series A, 2025, 45(3): 919-933.

图/表 4

表1

$n=200$ 时, 五种方法下 Average 和 Sd 的模拟结果"

表1

表2

$n=500$ 时, 五种方法下 Average 和 Sd 的模拟结果"

表2

表3

不同 $\lambda$ 下各估计方法的假设检验 $p$ 值"

表3

表4

参考文献 10

[1]	Miller R G. Least squares regression with censored data. Biometrika, 1976, 63(3): 449-464
[2]	Buckley J, James I. Linear regression with censored data. Biometrika, 1979, 66(3): 429-436
[3]	Koul H, Susarla V, Ryzin J V. Regression analysis with randomly right-censored data. Ann Statist, 1981, 9(6): 1276-1288
[4]	Stute W. Consistent estimation under random censorship when covariables are present. J Multivar Anal, 1993, 45: 89-103
[5]	Li X, Wang Q. The weighted least square based estimators with censoring indicators missing at random. J Statist Plann Inference, 2012, 142: 2913-2925
[6]	Wang J, Jiang W, Xu F, Fu W. Weighted composite quantile regression with censoring indicators missing at random. Comm Statist Theory Meth, 2021, 50(12): 2900-2917
[7]	Guo X, Xu W. Goodness-of-fit tests for general linear models with covariates missed at random. J Statist Plann Inference, 2012, 142(7): 2047-2058
[8]	Horvitz D G, Thompson D J. A generalization of sampling without replacement from a finite universe. J Amer Statist Assoc, 1952, 47(260): 663-685
[9]	Wang H, Wang L. Locally weighted censored quantile regression. J Amer Statist Assoc, 2009, 104(487): 1117-1128
[10]	Wang Q, Dinse G E. Linear regression analysis of survival data with missing censoring indicators. Lifetime Data Anal, 2011, 17(2): 256-279 doi: 10.1007/s10985-010-9175-8 pmid: 20559722

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