Tóthfalusi L, Endrényi L
Department of Pharmacology, Department of Preventive Medicine and Biostatistics, University of Toronto, Toronto, Ontario, Canada.
Int J Biomed Comput. 1996 Aug;42(3):181-90. doi: 10.1016/0020-7101(96)01173-7.
Nonlinear regression algorithms were compared by Monte-Carlo simulations when the measurement error was dependent on the measured values (heteroscedasticity) and possibly contaminated with outliers. The tested leastsquares (LSQ) algorithms either required user-supplied weights to accommodate heteroscedasticity or the weights were estimated within the procedures. Robust versions of the LSQ algorithms, namely robust iteratively reweighted (IRR) and least absolute value (LAV) regressions, were also considered. The comparisons were based on the efficiency of the estimated parameters and their resistance to outliers. Based on these criteria, among the tested LSQ algorithms, extended least squares (ELSQ) was found to be the most reliable. The IRR versions of these algorithms were slightly more efficient than the LAV versions when there were no outliers but they provided weaker protection to outliers than the LAV variants.
当测量误差取决于测量值（异方差性）并且可能被异常值污染时，通过蒙特卡罗模拟对非线性回归算法进行了比较。测试的最小二乘法（LSQ）算法要么需要用户提供权重以适应异方差性，要么在程序中估计权重。还考虑了LSQ算法的稳健版本，即稳健迭代重加权（IRR）和最小绝对值（LAV）回归。比较基于估计参数的效率及其对异常值的抗性。基于这些标准，在测试的LSQ算法中，扩展最小二乘法（ELSQ）被发现是最可靠的。当没有异常值时，这些算法的IRR版本比LAV版本略有效率，但它们对异常值的保护比LAV变体弱。
