Regression robustness

Determination of model least squares multi-linear regression weighted multi-linear regression robust regression ridge regression partial least squares generalised inverse... 

Robust Regression Robust regression is based at an iterative Robustness means... 

Finally we note that, just as in the treatment of outliers in replicate measurements, non-parametric and robust methods can be very effective in handling outliers in regression robust regression methods have proved particularly popular in recent years. These topics are covered in the next chapter. 

Multiple regression—robustness, chance effects, and the comparison of models... 

Also, the excellent properties of the robust procedures are demonstrated at constmcting the nonlinear regression models for the two-atomic system potential energy curves. 

One shortcoming of Schild analysis is an overemphasized use of the control dose-response curve (i.e., the accuracy of every DR value depends on the accuracy of the control EC o value). An alternative method utilizes nonlinear regression of the Gaddum equation (with visualization of the data with a Clark plot [10], named for A. J. Clark). This method, unlike Schild analysis, does not emphasize control pECS0, thereby giving a more balanced estimate of antagonist affinity. This method, first described by Lew and Angus [11], is robust and theoretically more sound than Schild analysis. On the other hand, it is not as visual. Schild analysis is rapid and intuitive, and can be used to detect nonequilibrium steady states in the system that can corrupt... 

An extensive introduction into robust statistical methods is given in Ref. 134 a discussion of non-linear robust regression is found in Ref. 135. An example is worked in Section 3.4. 

Phillips, G. R., and Eyring, E. M., Comparison of Conventional and Robust Regression in Analysis of Chemical Data, Anal. Chem. 55, 1983, 1134-1138. 

Koscielniak, R, Non-linear Robust Regression Procedure for Calibration in Flame Atomic Absorption Spectrometry, Analytica Chimica Acta 278, 1993, 177-187. 

The %HIA, on a scale between 0 and 100%, for the same dataset was modeled by Deconinck et al. with multivariate adaptive regression splines (MARS) and a derived method two-step MARS (TMARS) [38]. Among other Dragon descriptors, the TMARS model included the Tig E-state topological parameter [25], and MARS included the maximal E-state negative variation. The average prediction error, which is 15.4% for MARS and 20.03% for TMARS, shows that the MARS model is more robust in modeling %H1A. 

E.J. Karjalainen, Spectrum reconstruction in GC/MS. The robustness of the solution found with alternating regression, in E.J. Karjalainen (Ed.), Scientific Computing and Automation (Europe). Elsevier, Amsterdam, 1990, pp. 477-488. 

Note the close analogy with the Lineweaver-Burk form of the simple Michaelis-Menten equation. In a diagram representing MV against MX one obtains a line which has the same intercept as in the simple case. The slope, however, is larger by a factor (1 + YIK-) as shown in Fig. 39.17b. Usually, one first determines and in the absence of a competitive inhibitor (F = 0), as described above. Subsequently, one obtains A" from a new set of experiments in which the initial rate V is determined for various levels of X in the presence of a fixed amount of inhibitor Y. The slope of the new line can be obtained by means of robust regression. 

Weighted regression of U- " U- °Th- Th isotope data on three or more coeval samples provides robust estimates of the isotopic information required for age calculation. Ludwig (2003) details the use of maximum likelihood estimation of the regression parameters in either coupled XY-XZ isochrons or a single three dimensional XYZ isochron, where A, Y and Z correspond to either (1) U/ Th, °Th/ Th and... 

Robust and resistant isochrons can have very different characteristics than traditional least-squares or error-weighted least squares regressions. Some methods ignore analytical errors entirely, others infer them from the observed scatter of the data, and still others make use of analytical errors only to the extent that they are validated by their observed scatter. 

Siegel AF (1982) Robust regression using repeated medians. Biometrika 69 242-244... 

Rousseeuw PJ, Leroy AM (1987) Robust regression and outlier detection. Wiley, New York... 

Penrose R (1955) A generalized inverse for matrices. Proc Cambridge Phil Soc 51 406 Rousseeuw PJ, Leroy AM (1987) Robust regression and outlier detection. Wiley, New York Sachs L (1992) Angewandte Statistik. Springer, Berlin Heidelberg New York Sharaf MA, Illman DL, Kowalski BR (1986) Chemometrics. Wiley, New York... 

Butler, R., McDonald, J., Nelson, R., and White, S. (1990). Robust and partially adaptive estimation of regression models. Rev. Ecoti. Stat. 72, 321. 

Forsythe, A. B. (1972). Robust estimation of straight line regression coefficients by minimizing p-th power deviations. Technometrics 14, 159-166. 

Rousseeuw, P. J., Leroy, A. M. Robust Regression and Outlier Detection. Wiley, New York, 1987. 

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