Showing papers on "Outlier published in 1976"
TL;DR: A survey of robust alternatives to the mean, standard deviation, product moment correlation, t-test, and analysis of variance is offered in this paper, with a focus on the effects of outliers.
Abstract: It is noted that the usual estimators that are optimal under a Gaussian assumption are very vulnerable to the effects of outliers. A survey of robust alternatives to the mean, standard deviation, product moment correlation, t-test, and analysis of variance is offered. Robust methods of factor analysis, principal components analysis and multivariate analysis of variance are also surveyed, as are schemes for outlier detection.
115 citations
TL;DR: In this article, the authors have considered the notions of outlier-proneness and outlierresistance of families of distributions and showed the connection with the classical laws of large numbers for maxima.
Abstract: Neyman and Scott [3] have considered the ideas of outlier-proneness and outlier-resistance of families of distributions. Under their definition, individual distributions (one-member families) cannot be outlier-prone. This paper offers definitions of outlier-proneness and outlier-resistance that apply to individual distributions, and theorems are given showing the connection with the classical laws of large numbers for maxima.
50 citations
TL;DR: It is shown that the three approaches to detection of outliers from the general linear model Y = Xbeta + mu are exactly equivalent.
Abstract: Several authors have considered the problem of detection of outliers from the general linear model Y = Xbeta + mu. Ellenberg [1973] among others, has advocated use of a detection method which involves examination of the set of internally standardized least squares residuals. Mickey [1974] and Snedecor and Cochran [1968], apparently concerned about the usefulness of an outlier detection method which is based on residual estimates that themselves are biassed by the presence of the outlier, have proposed two other alternatives. It is shown that the three approaches are exactly equivalent. A detection procedure is described which uses as its test statistic the maximum of the internally standardized least squares residuals, and upper and lower bounds for the percentage points of the test statistic are given by Bonferroni inequalities. The computations required to obtain these approximate percentage points are illustrated in a numerical example. Finally, a brief simulation study of the performance of the procedure illustrates that the power of the test can be influenced by the position of the outlier vis-a-vis the structure of the design matrix X.
48 citations
TL;DR: In this paper, a Neyman-Pearson approach is taken to the problem of detecting structural shifts in naturally ordered regression problems, and two methods with optimality properties for outlier detection are developed, assuming that the observations may be divided into two parts.
Abstract: A Neyman-Pearson approach is taken to the problem of detecting structural shifts in naturally ordered regression problems. When the variance is known, backwards CUSUM methods are shown to maximize average power, and their application is discussed. Two methods with optimality properties for outlier detection are developed, assuming that the observations may be divided into two parts, where the first part satisfies the model assumptions, while outliers may be present in the other.
46 citations
TL;DR: In this article, the authors investigate the subjective nature of outlier procedures and find that there are variations both between individuals in their reaction to surprising values and also between judgments made by the same individual on different occasions.
Abstract: SUMMARY Procedures for rejecting outliers are essentially two stage, involving first an individual's judgment that a value in a given set of data is surprising, and then testing the surprising value for discordancy. The conventional frequency interpretation of the significance level for outlier tests is shown to be invalid and an experiment designed to investigate the inherent subjective nature of outlier procedures is described. This confirms that there are variations both between individuals in their reaction to surprising values and also between judgments made by the same individual on different occasions. The method of presentation of the data is shown to affect an individual's ability to perceive possible outliers. More surprising, it turns out that factors such as scale and pattern of the data are also very relevant.
42 citations
TL;DR: In this article, the estimation of parameter β in the type of distribution f(x)=b xα−1βα/b exp (−αx� b�� Γ(α/ b),x>0, when several outliers of the type θ, β,r=1,2,...,k, are present in the data is put in the closed form.
Abstract: The estimation of parameter β in the type of distributionf(x)=b x
α−1
β
α/b exp (−αx
b
Γ(α/b),x>0, is considered, when several outliers of the type θ, β,r=1,2, ...,k, are present in the data. The estimates of β as well as of θ's are put in the closed form. Special cases, Weibull, Gamma and Exponential are considered for the case of single outlier. Actual estimates are calculated from the generated samples of size 2 and 3 for the Weibull and Exponential.
10 citations
Journal Article•
TL;DR: The literature on statistical outlier procedures applicable to the CAP Survey program is briefly reviewed in this article, where limited Monte Carlo evaluations of selected procedures are performed, and it is shown that the application of these procedures has little effect on estimates of measures of central tendency and spread.
Abstract: The literature on statistical outlier procedures applicable to the CAP Survey program is briefly reviewed. Limited Monte Carlo evaluations of selected procedures were performed. For a light degree of contamination in random samples of moderate size, it is shown that the application of these procedures has little effect on estimates of measures of central tendency and spread. Moreover, in this situation these procedures detect a very small percentage of the outliners.
1 citations
TL;DR: This paper presents a FORTRAN program which computes the rejection criteria of ten procedures for detecting outlying observations, defined on comment cards, and calculates the mean and standard deviation of the censored sample.
Abstract: This paper presents a FORTRAN program which computes the rejection criteria of ten procedures for detecting outlying observations. These ten criteria are defined on comment cards. Appropriate journal sources for the statistical equations are listed in the bibliography. After applying the rejection rules for outliers, the program calculates the mean and standard deviation of the censored sample.
1 citations
TL;DR: In this article, a procedure for data editing and outlier identification based on an application of discriminant analysis is presented, and a hypothetical example is included along with some suggested applications.