统计与决策2026，Vol.42Issue(15)：38-43,6.DOI:10.13546/j.cnki.tjyjc.2026.15.006
广义随机后悔最小化模型的子集抽样估计
Subset Sampling Estimation for Generalized Random Regret Minimization Model
摘要
Abstract
The generalized Random Regret Minimization(RRM)model faces the problem that the computational cost of full-sample maximum likelihood estimation increases exponentially under large-scale choice sets.To reduce computational bur-den and guarantee favorable statistical performance of estimators,this paper proposes a parameter estimation method based on subset sampling of alternatives.The proposed method extracts a subset containing the chosen alternative from the complete choice set,corrects choice probabilities by introducing sampling correction terms,adopts an approximate regret function only relying on subsets,and compensates information loss with scaling factors.The paper further theoretically proves that the estimators obtained by this method satisfy consistency and asymptotic normality and share the same asymptotic efficiency as maximum likelihood esti-mation based on complete alternative data.Therefore,the proposed method can be regarded as an effective extension of maximum likelihood estimation in the generalized RRM model.In addition,the paper adopts Monte Carlo simulation to compare and analyze the performance of full-sample maximum likelihood estimation,truncated model,repeated sampling correction method and popu-lation share correction method in terms of average bias,root mean square error and running time.The results show that the pro-posed method performs well on all three indicators.Empirical analysis based on real data further indicates that parameter esti-mates gradually converge to the results of full-sample maximum likelihood estimation as the size of sampled subsets expands,which verifies the practicability and effectiveness of the proposed method.关键词
随机后悔最小化模型/子集抽样/选择集/极大似然估计Key words
Random Regret Minimization Model/subset sampling/choice set/maximum likelihood estimation分类
数理科学引用本文复制引用
刘常彪,何利萍,周路军..广义随机后悔最小化模型的子集抽样估计[J].统计与决策,2026,42(15):38-43,6.基金项目
统计学广西一流学科建设项目(X1211900408009) （X1211900408009）
广西高等教育本科教学改革工程重点项目(2023JGZ157) （2023JGZ157）
