Outliers effect

If no procedure for dealing with outliers was foreseen in the trial protocol, one analysis with the actual values and at least one other analysis eliminating or reducing the outlier effect should be performed and differences between their results discussed. ... 

While the estimates of the autocorrelation coefficients for the Cg time series (lower rows in 1 to ordy change slightly, the estimates the autocorrelation coefficients for the Benzene time series (upper rows in to 3) are clearly affected since three parameters are dropped from the model. The remaining coefficients are affected, too. In particular, the lagged cross-correlations to the Cg time series change from 1.67 to 2.51 and from -2.91 to -2.67 (right upper entries in 1 and This confirms the serious effect of even unobtrusive outliers in multivariate times series analysis. By incorporating the outliers effects, the model s AIC decreases from -4.22 to -4.72. Similarly, SIC decreases from -4.05 to -4.17. The analyses of residuals. show a similar pattern as for the initial model and reveal no serious hints for cross- or auto-correlation. i Now, the multivariate Jarque-Bera test does not reject the hypothesis of multivariate normally distributed variables (at a 5% level). The residuals empirical covariance matrix is finally estimated as... 

Chen, C., and Liu, L.-M. (1993a). Joint estimation of model parameters and outlier effects in time series. Journal of the American Statistical Association, 88(421), 284-297. 

FIGURE 11.22 Control charts and outliers, (a) pEC50 values (ordinates) run as a quality control for a drug screen over the days on which the screen is run (abscissae). Dotted lines are the 95% c.l. and the solid lines the 99.7% c.l. Data points that drift beyond the action lines indicate significant concern over the quality of the data obtained from the screen on those days, (b) The effect of significant outliers on the criteria for rejection. For the data set shown, the inclusion of points A and B lead to a c.l. for 95% confidence that includes point B. Removal of point A causes the 95% limits to fall below points B, causing them to be suspect as well. Thus, the presence of the data to be possibly rejected affects the criteria for rejection of other data. 

Instead of a detailed presentation of the effect of extreme values and outliers on least squares estimation, the following common sense approach is recommended in the analysis of engineering data ... 

After inspecting the tabular and graphic data, the operator is allowed to remove runs which appear to be outliers. Any run can be deleted or restored in any order, and the comparative statistics are recalculated with each operation. By comparing the standard deviation before and after deleting a run, the effect of that run can by determined. The editing process can continue indefinitely until the operator is satisfied with the validity of his results. 

Occasionally it is convenient to refer to the p function in (11.21), but generally the form (11.22) is used in robust M-estimation. The use of the t(r form is due to Hampel s concept of the influence function (Hampel et al., 1986). According to the IF concept, the value of it represents the effect of the residuals on the parameter estimation. If iff is unbounded, it means that an outlier has an infinite effect on the estimation. Thus, the most important requirement for robustness is that iff must be bounded and should have a small value when the residual is large. In fact, the value of the iff function corresponds to the gross error sensitivity (Hampel etal., 1986), which measures the worst (approximate) influence that a small amount of contamination of fixed size can have on the value of the estimator. 

Another unanswered question is the evaluation of the effect on cardiac repolarization of oncologic drugs, for which the thorough QT/QTc study in volunteers cannot be performed [166], In these cases, not only central tendency (i.e. mean QTc increase) and proportion of outliers but also other findings such as syncope, ventricular tachyarrhythmias and other cardiac effects should be more closely defined. 

Less straightforward is the problem of rogue data points, which appear to satisfy the usual criteria of quality, but fall well outside the norms established by the data set or by reliable precedent. If there is no apparent reason for the discrepancy — and a careful search for an explanation may reveal a perturbing effect of interest — such data points may be treated as outliers,2 and may legitimately be omitted from the correlation. 

Finally, it is worth noting the effect of these errors on the resulting phylogenetic analysis. If a complete outlier is included, it will tend to join the rest of the sequences on a long branch, as it will be only randomly related to each of them. These can be identified relatively easily when the final analysis is carried out. Sequences with frameshifts are harder... 

PCA is sensitive with respect to outliers. Outliers are unduly increasing classical measures of variance (that means nonrobust measures), and since the PCs are following directions of maximum variance, they will be attracted by outliers. Figure 3.8 (left) shows this effect for classical PCA. In Figure 3.8 (right), a robust version of PCA was taken (the method is described in Section 3.5). The PCs are defined as directions maximizing A robust measure of variance (see Section 2.3) which is not inflated by the outlier group. As a result, the PCs explain the variability of the nonoutliers which refer to the reliable data information. 

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