Partial Influence Functions

Pires, Ana M.; Branco, João A.

doi:10.1006/jmva.2001.2055

Cited by 27 publications

(40 citation statements)

References 20 publications

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“…[11,14]. In this paper, the formalism of partial influence functions [27] as an extension of the traditional influence function concept to the multi-sample setting will be followed.…”

Section: Introductionmentioning

confidence: 99%

Influence of observations on the misclassification probability in quadratic discriminant analysis

Croux

Joossens

2005

Journal of Multivariate Analysis

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In this paper it is studied how observations in the training sample affect the misclassification probability of a quadratic discriminant rule. An approach based on partial influence functions is followed. It allows to quantify the effect of observations in the training sample on the performance of the associated classification rule. Focus is on the effect of outliers on the misclassification rate, merely than on the estimates of the parameters of the quadratic discriminant rule. The expression for the partial influence function is then used to construct a diagnostic tool for detecting influential observations. Applications on real data sets are provided.

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“…[11,14]. In this paper, the formalism of partial influence functions [27] as an extension of the traditional influence function concept to the multi-sample setting will be followed.…”

Section: Introductionmentioning

confidence: 99%

Influence of observations on the misclassification probability in quadratic discriminant analysis

Croux

Joossens

2005

Journal of Multivariate Analysis

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“…When considering several populations, the use of partial influence functions is advocated to measure resistance towards pointwise contamination in each population. Partial influence functions, although first introduced by Hampel et al (1986), have been formalized by Pires and Branco (2002) in order to ensure that the usual properties of the influence function for the one-population case are still valid under the multi-populations case. Let S be a sample space contained in R p and D be the set of all finite-signed measures on S. Let W be a statistical functional whose domain is the K-fold product D × · · · × D. Partial influence functions of W at the model F = F 1 × · · · × F K are defined, when the limit exists, by…”

Section: Influence Functions Of the Test Statisticsmentioning

confidence: 99%

Robust asymptotic tests for the equality of multivariate coefficients of variation

Aerts

Haesbroeck

2016

TEST

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In order to easily compare several populations on the basis of more than one feature, multivariate coefficients of variation (MCV) may be used as they allow to summarize relative dispersion in a single index. However, up to date, no test of equality of one or more MCVs has been developed in the literature. In this paper, several classical and robust Wald-type tests are proposed and studied. The asymptotic distributions of the test statistics are derived under elliptical symmetry, and the asymptotic efficiency of the robust versions is compared to the classical tests. Robustness of the proposed procedures is examined through partial influence functions of the test statistic, as well as by means of power and level influence functions. A simulation study compares the performance of the classical and robust tests under uncontaminated and contaminated schemes, and the difference with the usual covariance homogeneity test is highlighted. As a by-product, these tests may also be considered in the univariate context where they yield procedures that are both robust and easyto-use. They provide an interesting alternative to the numerous parametric tests existing in the literature, which are, in most cases, unreliable in presence of outliers. The methods are illustrated on a real data set.

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“…In our multigroup setting we consider partial influence functions (Pires and Branco 2002) assuming that the first group is contaminated. Hence, we take…”

Section: Influence Functionsmentioning

confidence: 99%

Robust and Efficient One-Way MANOVA Tests

Aelst

Willems

2011

Journal of the American Statistical Association

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We propose robust tests as alternatives to the classical Wilks' Lambda test in one-way MANOVA. The robust tests use highly robust and efficient multi-sample multivariate S-or MM-estimators instead of the empirical covariances. The properties of several robust test statistics are compared. Under the null hypothesis, the distribution of the test statistics is proportional to a chi-square distribution. As an alternative to the asymptotic distribution, we develop a fast robust bootstrap method to estimate the distribution under the null hypothesis. We show when it is asymptotically correct to estimate the null distribution in this way and we use simulations to verify the performance of the bootstrap based tests in finite samples. We also investigate the power of the new tests, as well as their robustness against outliers. Finally, we illustrate the use of these robust test statistics on a real data example. Some additional results are provided as supplemental material.

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Partial Influence Functions

Cited by 27 publications

References 20 publications

Influence of observations on the misclassification probability in quadratic discriminant analysis

Influence of observations on the misclassification probability in quadratic discriminant analysis

Robust asymptotic tests for the equality of multivariate coefficients of variation

Robust and Efficient One-Way MANOVA Tests

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