非线性模型精度评定的Bootstrap方法及其加权采样改进方法

doi:10.11947/j.AGCS.2021.20200136

摘要/Abstract

摘要： 本文将Bootstrap方法引入非线性模型精度评定理论中，通过对原始样本值或因变量的残差向量进行重采样，以获取自助样本的方式代替复杂的求导运算，给出了Bootstrap方法解决非线性精度评定问题的完整算法。针对Bootstrap方法中对模型随机项的等概率采样，通过获取采样过程中随机变量的经验分布函数，提出了加权采样策略，并分别给出了将改进方法用于非线性模型精度评定中的详细计算步骤。通过案例研究分析表明：重采样观测值的Bootstrap方法和重采样残差的Bootstrap方法能够得到比近似函数法、Jackknife法更为合理的参数标准差，具有更强的适用性；而加权采样的重采样观测值Bootstrap方法和加权采样的重采样残差Bootstrap方法能够获取更加精确的精度信息且更具优势，从而验证了将Bootstrap方法用于非线性精度评定及本文改进算法的可行性和有效性。

关键词: 非线性模型, 精度评定, Bootstrap方法, 加权采样, 重采样

Abstract: The Bootstrap resampling method is introduced to the nonlinear theory for solving the precision estimation in this paper. By resampling the original sample observation data or the residuals of the dependent variable to obtain Bootstrap samples instead of the complex derivative calculations, the complete algorithms of Bootstrap method for solving the problem of nonlinear accuracy evaluation are given. Aiming at the equal probability resampling of model stochastic variable, this paper obtains the empirical distribution function of the stochastic variable in the sampling process, proposes the weighted sampling strategy, and gives the detailed calculation steps of the improved method for the accuracy evaluation. The results of experiments show that the Bootstrap method based on the resampling observations and the Bootstrap method based on the resampling residuals have stronger applicability, and can obtain more reasonable parameter standard deviations than the approximate function method and Jackknife method. Furthermore, the weighted resampling Bootstrap method based on the resampling observations and the weighted resampling Bootstrap method based on the resampling residuals can obtain more accurate precision information with extensive advantages. Those which verified the feasibility and effectiveness of using Bootstrap method and the improved algorithms proposed in this paper for precision estimation of nonlinear adjustment.

Key words: nonlinear model, precision estimation, Bootstrap method, weighted sampling, resampling

中图分类号:

P207

王乐洋, 李志强. 非线性模型精度评定的Bootstrap方法及其加权采样改进方法[J]. 测绘学报, 2021, 50(7): 863-878.

WANG Leyang, LI Zhiqiang. Bootstrap method and the modified method based on weighted sampling for nonlinear model precision estimation[J]. Acta Geodaetica et Cartographica Sinica, 2021, 50(7): 863-878.

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