Li and Chen (J. Amer. Statist. Assoc. 80 (1985) 759) proposed a method for principal components using projection-pursuit techniques. In classical principal components one searches for directions with maximal variance, and their approach consists of replacing this variance by a robust scale measure. Li and Chen showed that this estimator is consistent, qualitative robust and inherits the breakdown point of the robust scale estimator. We complete their study by deriving the influence function of the estimators for the eigenvectors, eigenvalues and the associated dispersion matrix. Corresponding Gaussian efficiencies are presented as well. Asymptotic normality of the estimators has been treated in a paper of Cui et al. (Biometrika 90 (2003) 953), complementing the results of this paper. Furthermore, a simple explicit version of the projection-pursuit based estimator is proposed and shown to be fast to compute, orthogonally equivariant, and having the maximal finite-sample breakdown point property. We will illustrate the method with a real data example.

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Recently a blind source separation model was suggested for spatial data together with an estimator based on the simultaneous diagonalisation of two scatter matrices. The asymptotic properties of this estimator are derived here and a new estimator, based on the joint diagonalisation of more than two scatter matrices, is proposed. The asymptotic properties and merits of the novel estimator are verified in simulation studies. A real data example illustrates the method.

We argue that the conditional bias associated with a sample unit can be a useful measure of influence in finite population sampling. We use the conditional bias to derive robust estimators that are obtained by downweighting the most influential sample units. Under the model-based approach to inference, our proposed robust estimator is closely related to the well-known estimator of Chambers (1986). Under the design-based approach, it possesses the desirable feature of being applicable with most sampling designs used in practice. For stratified simple random sampling, it is essentially equivalent to the estimator of Kokic & Bell (1994). The proposed robust estimator depends on a tuning constant. In this paper, we propose a method for determining the tuning constant and show that the resulting estimator is consistent. Results from a simulation study suggest that our approach improves the efficiency of standard nonrobust estimators when the population contains units that may be influential if selected in the sample.

In high reliability standards fields such as automotive, avionics or aerospace, the detection of anomalies is crucial. An efficient methodology for automatically detecting multivariate outliers is introduced. It takes advantage of the remarkable properties of the Invariant Coordinate Selection (ICS) method. Based on the simultaneous spectral decomposition of two scatter matrices, ICS leads to an affine invariant coordinate system in which the Euclidian distance corresponds to a Mahalanobis Distance (MD) in the original coordinates. The limitations of MD are highlighted using theoretical arguments in a context where the dimension of the data is large. Unlike MD, ICS makes it possible to select relevant components which removes the limitations. Owing to the resulting dimension reduction, the method is expected to improve the power of outlier detection rules such as MD-based criteria. It also greatly simplifies outliers interpretation. The paper includes practical guidelines for using ICS in the context of a small proportion of outliers which is relevant in high reliability standards fields. The choice of scatter matrices together with the selection of relevant invariant components through parallel analysis and normality tests are addressed. The use of the regular covariance matrix and the so called matrix of fourth moments as the scatter pair is recommended. This choice combines the simplicity of implementation together with the possibility to derive theoretical results. A simulation study confirms the good properties of the proposal and compares it with other scatter pairs. This study also provides a comparison with Principal Component Analysis and MD. The performance of our proposal is also 1 arXiv:1612.06118v3 [stat.ME] 2 Feb 2018 evaluated on several real data sets using a user-friendly R package accompanying the paper.

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Abstract. Unemployment rates vary widely at the sub-regional level. We seek to explain why such variation occurs, using data for 174 districts in the Midi-Pyrénées region of France for 1990-1991. A set of explanatory variables is derived from theory and the voluminous literature. The best model includes a correction for spatially autocorrelated errors. Unemployment rates are higher in urban areas and, where per capita income is higher, are consistent with the view that unemployment differences largely reflect variations in "amenities." Along with a lack of evidence of housing market rigidities, these suggest that subregional variations in unemployment are not mainly the result of labor market disequilibrium.JEL classification: J60, J64, R12, R23

This paper is devoted to rejective sampling. We provide an expansion of joint inclusion probabilities of any order in terms of the inclusion probabilities of order one, extending previous results by Hájek (1964) and Hájek (1981) and making the remainder term more precise. Following Hájek (1981), the proof is based on Edgeworth expansions. The main result is applied to derive bounds on higher order correlations, which are needed for the consistency and asymptotic normality of several complex estimators.