Showing papers on "Outlier published in 1977"

Statisticians are Fairly Robust Estimators of Location

Abstract: The performance of the outlier rejecting statistician is monitored and compared with those of several robust estimators of location. The comparisons are made by plugging a number of statisticians' location estimates into a Monte Carlo experiment. The result is that the statistician staves off the potential disasters of ordinary least squares, but he can be beaten.

Percentage Points for the RST Many Outlier Procedure

Abstract: This article is concerned with estimating percentage points for the RST (R-statistic) many outlier procedure. This procedure has been introduced in [5] and a brief discussion is given in Section 1. The algorithm used to estimate the percentage points is given in Section 2. Percentage points are given for α = .10, .05, .01, N = 10(5) 20(10) 50(25) 100, k = 2: N = 20(10) 50(25) 100, k = 3; N = 20(10) 50(25) 100, k = 4. Two examples illustrating the use of the procedure are given in Section 3. Finally some potential weaknesses of the method are discussed in Section 4: namely, when the actual number of outliers in a sample is larger than the maximum number of outliers assumed by the procedure. Alternatives are proposed for possibly modifying the procedure to allow for this contingency.

On least absolute values estimation

Abstract: The resistance of least absolute values (L1) estimators to outliers and their robustness to heavy-tailed distributions make these estimators useful alternatives to the usual least squares estimators. The recent development of efficient algorithms for L1 estimation in linear models has permitted their use in practical data analysis. Although in general the L1 estimators are not unique, there are a number of properties they all share. The set of all L1 estimators for a given model and data set can be characterized as the convex hull of some extreme estimators. Properties of the extreme estimators and of the L1-estimate set are considered.

Rejoinder: "Comment on 'a new Statistic for Testing Suspected Outliers'"

Abstract: The values of the power of Tiku's (1975) T statistic for testing outliers in normal samples are evaluated. The statistic T is shown to be more powerful than other comparable statistics under Tiku's outlier model, although slightly less powerful under Dixon's (1950) contamination model.

Normality and other statistical considerations as they relate to selected quantitative measures in the CAP survey.

Abstract: Investigation of the CAP statistical reports for quantitative tests with respect to the assumption of normality and the method for detecting outliers was performed. Specifically, laboratory measurements of several constituents from the Comprehensive Survey for 1975 were examined. The findings indicate that the assumption of normality, while not exactly valid, is reasonable and not deleterious to the purpose of the Survey, but that the method of determining outliers may be too stringent. A less strict, simpler outlier procedure is suggested as an alternative. It is also observed that other evaluation procedures would be available if more significant digits were reported for the laboratory measurements.

Applications of Exploratory Data Analysis in Regional Geochemistry

Abstract: Regional geochemistry is a relatively young field of science. The very first geochemical surveys covering large tracts of ground were carried out in the late 1950ies. No established methodology existed how to treat and study the resulting data. Computers to easily handle reports with large numbers of samples with thousands of analytical results, even if only 3 or 4 elements (Cu, Pb, Zn, Ba), were not available to the geochemist. As a first solution maps showing the analytical result at the site were the sample was taken and some statistical summaries, based on Gaussian statistics, were usually prepared. In the statistical analysis of geochemical data one of the main tasks was to detect data outliers and unusual data behaviour. Mean and standard deviation (sdev, e.g., mean §2 sdev) were most widely used to define data outliers. This is the best approach if the data are normally distributed. The calculation will result in 5 % of the data, belonging to this normal distribution, being identified as outliers, 2.5 % at the lower and 2.5 % at the upper end of the distribution. In geochemistry, the data outliers will, however, usually originate from dierent sources or processes, not related to the distribution of the main body of data. In such a case the “mean §2 sdev-rule” is no longer valid. To find better methods to deal with geochemical data the basic properties of geochemical data sets need first to be identified and understood. Main properties include: