湖北师范大学学报(自然科学版)2024,Vol.44Issue(1) :16-22.DOI:10.3969/j.issn.2096-3149.2024.01.003

基于线性模型岭估计的未知参数的最小体积置信集

Minimum-volume confidence sets of unknown parameters based on ridge estimator of linear models

胡宏昌 郭童格
湖北师范大学学报(自然科学版)2024,Vol.44Issue(1) :16-22.DOI:10.3969/j.issn.2096-3149.2024.01.003

基于线性模型岭估计的未知参数的最小体积置信集

Minimum-volume confidence sets of unknown parameters based on ridge estimator of linear models

胡宏昌 1郭童格1
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作者信息

  • 1. 湖北师范大学 数学与统计学院,湖北 黄石 435002
  • 折叠

摘要

考虑误差为正态分布的线性回归模型,通过利用附加伪观测数据模型的最小二乘估计与岭估计的关系,得到了基于岭估计的未知参数的最小体积置信集(区间或区域).与经典置信集相比较,在最小体积意义下我们所得到的置信集是最佳的.最后给出了一个算例,结果表明所得的置信集比经典置信集更精确体积更小.

Abstract

This studys selects linear regression models with a normal distribution of errors and uses the relation between the least squares estimation and the ridge estimation of the additional pseudo-observational data model,to calculate the minimum volume confidence sets(intervals or regions)of unknown parameters based on ridge estimate.Compared with the classical confidence sets,the confidence sets gained on the basis of minimum volume is the best.Finally,it also gives some model examples,the results of which show that the confidence sets obtained in this study is more accurate and smaller in volume than the classical confidence sets.

关键词

岭估计/线性回归/置信集/估计效率

Key words

ridge estimation/linear regression/confidence set/estimation efficiency

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出版年

2024
湖北师范大学学报(自然科学版)
湖北师范学院

湖北师范大学学报(自然科学版)

影响因子:0.376
ISSN:2096-3149
参考文献量11
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