关键词: 匹配分位数估计, 信号匹配, 全局收敛算法, 稳健估计

Abstract: To address the initial value sensitivity and outlier interference issues in the application of traditional quantile matching estimation to multi-dimensional data, an improved framework integrating global optimization strategies and robust loss functions is proposed. By integrating principal component analysis, ordinary least squares estimation, least absolute deviation estimation, and random initialization to construct a diverse set of initial values, combined with a multi-start search mechanism and genetic algorithm for global optimization, the risk of parameter estimation getting trapped in local optima is effectively reduced. Meanwhile, the square loss function is reconstructed into an absolute loss function to enhance model robustness. Monte Carlo simulation results show that the success rate of parameter estimation of the improved global optimization method is significantly increased from 5% of the traditional method to 82%; in contaminated data with 20% outliers, the average absolute error of parameter estimation using the absolute loss function is reduced by 14% compared with the square loss function. Empirical studies on sensor signals show that the improved methods GLOBAL-MQE(L1) and GLOBAL-MQE(L2) reduce the Wasserstein distance index by 55% and 45% respectively compared with the benchmark method MQE. The proposed global optimization strategy and robust loss mechanism significantly enhance the global convergence and anti-interference ability of model parameter estimation. The improved quantile prediction sequence can effectively maintain the statistical characteristics consistent with the real signal, providing a more reliable modeling tool for engineering data distribution matching.

Key words: matching quantile estimation, signal matching, global convergence algorithm, robust estimation