Catherine Dehon

Influence Functions of the Spearman and Kendall Correlation Measures

Nonparametric correlation estimators as the Kendall and Spearman correlation are widely used in the applied sciences. They are often said to be robust, in the sense of being resistant to outlying observations. In this paper we formally study their robustness by means of their influence functions and gross-error sensitivities. Since robustness of an estimator often comes at the price of an increased variance, we also compute statistical efficiencies at the normal model. We conclude that both the Spearman and Kendall correlation estimators combine a bounded and smooth influence function with a high efficiency. In a simulation experiment we compare these nonparametric estimators with correlations based on a robust covariance matrix estimator.

Uncovering excellence in academic rankings: A closer look at the Shanghai ranking

In this paper, we examine whether the quality of academic research can be accurately captured by a single aggregated measure such as a ranking. With Shanghai University’s Academic Ranking of World Universities as the basis for our study, we use robust principal component analysis to uncover the underlying factors measured by this ranking. Based on a sample containing the top 150 ranked universities, we find evidence that, for the majority of these institutions, the Shanghai rankings reflect not one but in fact two different and uncorrelated aspects of academic research: overall research output and top-notch researchers. Consequently, the relative weight placed upon these two factors determines to a large extent the final ranking.

Robust Methods for Canonical Correlation Analysis

Canonical correlation analysis studies associations between two sets of random variables. Its standard computation is based on sample covariance matrices, which are however very sensitive to outlying observations. In this note we introduce, discuss and compare four different ways for performing a robust canonical correlation analysis. One method uses robust estimators of the involved covariance matrices, another one uses the signs of the observations, a third approach is based on projection pursuit, and finally an alternating regression algorithm for canonical analysis is proposed.

Bounded influence regression using high breakdown scatter matrices

In this paper we estimate the parameters of a regression model using S-estimators of multivariate location and scatter. The approach is proven to be Fisher-consistent, and the influence functions are derived. The corresponding asymptotic variances are obtained and it is shown how they can be estimated in practice. A comparison with other recently proposed robust regression estimators is made.

The k-step spatial sign covariance matrix

The Sign Covariance Matrix is an orthogonal equivariant estimator of multivariate scale. It is often used as an easy-to-compute and highly robust estimator. In this paper we propose a k-step version of the Sign Covariance Matrix, which improves its efficiency while keeping the maximal breakdown point. If k tends to infinity, Tyler’s M-estimator is obtained. It turns out that even for very low values of k, one gets almost the same efficiency as Tyler’s M-estimator.

Robust estimation of the conditional median function at elliptical models

In this note we study the problem of estimating the parameters of the conditional median function at elliptical models. For this we use positive-breakdown estimators of multivariate location and scatter, and obtain influence functions and asymptotic variances of the resulting slope and intercept. We also consider a technique to gain efficiency by artificially increasing the dimension.

Outlier resistant estimators for canonical correlation analysis

Canonical correlation analysis studies associations between two sets of random variables. Its standard computation is based on sample covariance matrices, which are however very sensitive to outlying observations. In this note we introduce, discuss and compare different ways for performing a robust canonical correlation analysis. Two methods are based on robust estimators of covariance matrices, the others on projection-pursuit techniques.

Extending the Hausman Test to Check for the presence of Outliers

In this paper, we follow the same logic as in Hausman (1978) to create a testing procedure that checks for the presence of outliers by comparing a regression estimator that is robust to outliers (S-estimator), with another that is more e¢ cient but a¤ected by them. Some simulations are presented to illustrate the good behavior of the test for both its size and its power.

Are dropout and degree completion in doctoral study significantly dependent on type of financial support and field of research

In this article, the determinants of ‘time to dropout’ from doctoral studies and ‘time to PhD completion’ are studied using a discrete-time competing risks survival analysis for a sample of 3092 doctoral candidates from the Université libre de Bruxelles. Not surprisingly, results show that students supported with research fellowships have much higher PhD completion hazards than teaching assistants or unfinanced students. Concerning dropout, students with no financing showed the highest withdrawal rate, while students with selective research fellowships showed the lowest one. Dropout is also influenced by the ability of the student, which is correlated to their success in the fellowship allocation procedure. However, the type of financial support influences time to dropout from doctoral studies even when controlling for the ability of the student. Finally, our findings suggest that there are no significant differences in dropout and degree completion between fields of study, except for unfinanced students.

The robustness of the hyperbolic efficiency estimator

The robustness properties of a specific type of orientation in the context of efficiency measurement using partial frontiers are investigated. This so called unconditional hyperbolic quantile estimator of efficiency has been recently studied and can be seen as an extension of the input/output methodology of partial frontiers that was introduced previously. The influence function as well as the breakdown point of this fully non-parametric and unconditional estimator are derived for a complete multivariate setup (multiple inputs and outputs). Like for the input and output quantile estimators, the hyperbolic quantile estimator is B-robust but unlike the two former types of estimator its breakdown point does not depend on the actual input or output level of the production unit. Some examples are given to assess the relevance of this type of estimator and to show the differences with the input and output quantile estimators of efficiency from both a robustness and a statistical efficiency point of view. Finally, a real life example is used to illustrate how the hyperbolic efficiency estimator might be used in a robust context.