基于BLUS残差的非线性模型误差分布的拟合优度检验
Test of Goodness of Fit for Error Distribution of Nonlinear Model Based on BLUS Residuals
摘要: 针对非线性模型误差分布的拟合优度检验问题，不同于文献中利用最小二乘残差(OLS)作为构造检验的样本的作法，这里采用了Theil的BLUS残差作为新的构造检验的样本，解决了经典的残差的奇异非同分布问题。同时利用样本分位点与来自于原假设分布的拟样本分位点间的随机距离来构造新的检验统计量，得到了一类新的拟合优度检验，并将之应用到非线性模型误差分布的检验中。模拟结果显示，在某些备择假设下，新的检验的功效高于原有的基于经验分布函数的检验的功效。
Abstract: Aiming at the problem of goodness of fit test for error distribution of nonlinear model, it is different from the method of using the least square residuals (OLS) as the sample of constructing test in the literature, in this paper, the BLUS (best linear unbiased scale) residuals of Theil are used as the samples of the new structural test, and the problem of the singular non-identical distribution of the classical residuals is solved. At the same time, a new kind of goodness of fit test is obtained by using the random distance between the sample quantiles and the quasi-sample quantiles from the origi-nal hypothesis distribution, it is applied to the test of error distribution of nonlinear model. The simulation results show that under some alternatives, the efficiency of the new test is higher than that of the original test based on the empirical distribution function.
文章引用：赵建昕. 基于BLUS残差的非线性模型误差分布的拟合优度检验[J]. 应用数学进展, 2022, 11(8): 5831-5841. https://doi.org/10.12677/AAM.2022.118615

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