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  • 1
    Monograph available for loan
    Monograph available for loan
    Finding groups in data : an introduction to cluster analysis (2005)
    Hoboken, NJ : Wiley
    Details Availability
    Call number: PIK M 311-08-0150
    Type of Medium: Monograph available for loan
    Pages: xiv, 342 S. : graph. Darst.
    ISBN: 0471735787
    Series Statement: Wiley series in probability and mathematical statistics
    Location: A 18 - must be ordered
    Branch Library: PIK Library
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  • 2
    Electronic Resource
    Electronic Resource
    A new infinitesimal approach to robust estimation (1981)
    Springer
    Probability theory and related fields 56 (1981), S. 127-132 
    Details
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The infinitesimal robustness of the asymptotic variance of location M-estimators is investigated by means of the change-of-variance curve (CVC), which bears some resemblance to the influence curve (IC). It is proved that this CVC leads to a more stringent robustness property than the IC and that the Huber estimators are still optimal in this new sense.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00531978
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  • 3
    Electronic Resource
    Electronic Resource
    Change-of-variance sensitivities in regression analysis (1985)
    Springer
    Probability theory and related fields 68 (1985), S. 503-519 
    Details
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The change-of-variance function is defined for estimators of regression coefficients. Both an unstandardized and a standardized form of the change-of-variance sensitivity are introduced, and their relation with the corresponding gross-error-sensitivities is investigated. The problems of optimal robustness lead to the Hampel-Krasker and the Krasker-Welsch estimators. At the same time, also the scale parameter has to be estimated robustly. By means of the change-of-variance sensitivity, optimal robust redescending scale estimators are constructed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00535342
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  • 4
    Electronic Resource
    Electronic Resource
    Most robust M-estimators in the infinitesimal sense (1982)
    Springer
    Probability theory and related fields 61 (1982), S. 541-551 
    Details
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The change-of-variance curve (CVC) is generalized to M-estimators with piecewise continuous ψ-functions, in which case it becomes a Schwartz distribution. An M-estimator is called most B-robust when it minimizes Hampel's gross-error sensitivity γ *, and most V-robust when it minimizes the change-of-variance sensitivity k *. In the general case, the median is most B-robust and most V-robust. If consideration is restricted to redescending M-estimators, then the skipped median is most B-robust and the median-type tanh-estimator is most V-robust. By means of these results, complete solutions of the problems of optimal infinitesimal robustness are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00531623
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  • 5
    Electronic Resource
    Electronic Resource
    Computing location depth and regression depth in higher dimensions (1998)
    Springer
    Statistics and computing 8 (1998), S. 193-203 
    Details
    ISSN: 1573-1375
    Keywords: Algorithms ; coordinate-free ; multivariate ranking ; robustness
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The location depth (Tukey 1975) of a point θ relative to a p-dimensional data set Z of size n is defined as the smallest number of data points in a closed halfspace with boundary through θ. For bivariate data, it can be computed in O(nlogn) time (Rousseeuw and Ruts 1996). In this paper we construct an exact algorithm to compute the location depth in three dimensions in O(n2logn) time. We also give an approximate algorithm to compute the location depth in p dimensions in O(mp3+mpn) time, where m is the number of p-subsets used. Recently, Rousseeuw and Hubert (1996) defined the depth of a regression fit. The depth of a hyperplane with coefficients (θ1,...,θp) is the smallest number of residuals that need to change sign to make (θ1,...,θp) a nonfit. For bivariate data (p=2) this depth can be computed in O(nlogn) time as well. We construct an algorithm to compute the regression depth of a plane relative to a three-dimensional data set in O(n2logn) time, and another that deals with p=4 in O(n3logn) time. For data sets with large n and/or p we propose an approximate algorithm that computes the depth of a regression fit in O(mp3+mpn+mnlogn) time. For all of these algorithms, actual implementations are made available.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008945009397
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  • 6
    Electronic Resource
    Electronic Resource
    Tutorial to robust statistics (1991)
    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 5 (1991), S. 1-20 
    Details
    ISSN: 0886-9383
    Keywords: Averaging ; Median ; Outliers ; Regression ; Residuals ; Robustness ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In this tutorial we first illustrate the effect of outliers on classical statistics such as the sample average. This motivates the use of robust techniques. For univariate data the sample median is a robust estimator of location, and the dispersion can also be estimated robustly. The resulting ‘z-scores’ are well suited to detect outliers. The sample median can be generalized to very large data sets, which is useful for robust ‘averaging’ of curves or images. For multivariate data a robust regression procedure is described. Its standardized residuals allow us to identify the outliers. Finally, a survey of related approaches is given. (This review overlaps with earlier work by the same author, which appeared elsewhere.)
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cem.1180050103
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  • 7
    Electronic Resource
    Electronic Resource
    The depth function of a population distribution (1999)
    Springer
    Metrika 49 (1999), S. 213-244 
    Details
    ISSN: 1435-926X
    Keywords: Key words: Depth contour, halfspace depth, location depth, Tukey median, voting
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. Tukey (1975) introduced the notion of halfspace depth in a data analytic context, as a multivariate analog of rank relative to a finite data set. Here we focus on the depth function of an arbitrary probability distribution on ℝp, and even of a non-probability measure. The halfspace depth of any point θ in ℝp is the smallest measure of a closed halfspace that contains θ. We review the properties of halfspace depth, enriched with some new results. For various measures, uniform as well as non-uniform, we derive an expression for the depth function. We also compute the Tukey median, which is the θ in which the depth function attains its maximal value. Various interesting phenomena occur. For the uniform distribution on a triangle, a square or any regular polygon, the depth function has ridges that correspond to an 'inversion' of depth contours. And for a product of Cauchy distributions, the depth contours are squares. We also consider an application of the depth function to voting theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001840050017
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  • 8
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    Why the Wrong Papers Get Published (1991)
    Taylor & Francis
    Details
    Publication Date: 1991-01-01
    Print ISSN: 0933-2480
    Electronic ISSN: 1867-2280
    Topics: Mathematics
    Published by Taylor & Francis
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  • 9
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    Change-of-variance sensitivities in regression analysis (1985)
    Springer
    Details
    Publication Date: 1985-01-01
    Print ISSN: 0178-8051
    Electronic ISSN: 1432-2064
    Topics: Mathematics
    Published by Springer
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  • 10
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    Most robust M-estimators in the infinitesimal sense (1982)
    Springer
    Details
    Publication Date: 1982-01-01
    Print ISSN: 0178-8051
    Electronic ISSN: 1432-2064
    Topics: Mathematics
    Published by Springer
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