Results for two-level fractional factorial designs of resolution IV or more

The main theorem of this paper shows that foldover designs are the only (regular or nonregular) two-level factorial designs of resolution IV (strength 3) or more for n   runs and n/3?m?n/2$n/3?m?n/2$ factors. This theorem is a generalization of a coding theory result of Davydov and Tombak [1990. Quasiperfect linear binary codes with distance 4 and complete caps in projective geometry. Problems Inform. Transmission 25, 265–275] which, under translation, effectively states that foldover (or even) designs are the only regular two-level factorial designs of resolution IV or more for n   runs and 5n/16?m?n/2$5n/16?m?n/2$ factors. This paper also contains other theorems including an alternative proof of Davydov and Tombak's result.     

Mending Nets in the South: Anti-poverty Policies in Greece, Italy, Portugal and Spain

The marginal role of social assistance and the absence of minimum income programmes have long been thought to constitute defining characteristics of the southern European model of welfare. Nevertheless, over the 1990s significant innovations in this field have taken place. The paper aims to contribute to the analysis of recent developments by critically examining the experience of anti‐poverty policies in Greece, Italy, Portugal and Spain. It is argued that the “patchiness” of safety nets in southern Europe is due to a unique set of constraints, the most relevant of which are the role of families and the “softness” of state institutions. A review of national profiles reveals that new policies introduced in all four countries mark progress towards redressing some of the historical imbalances of that welfare model. In particular, fully fledged minimum income schemes now operate in Portugal and in certain Spanish regions, while an experiment involving a number of Italian municipalities is still in progress. In spite of this, the paper concludes that social safety nets in southern Europe remain frail in terms of institutional design as well as political support and legitimacy.     

Bayesian optimal blocking of factorial designs

The presence of block effects makes the optimal selection of fractional factorial designs a difficult task. The existing frequentist methods try to combine treatment and block wordlength patterns and apply minimum aberration criterion to find the optimal design. However, ambiguities exist in combining the two wordlength patterns and therefore, the optimality of such designs can be challenged. Here we propose a Bayesian approach to overcome this problem. The main technique is to postulate a model and a prior distribution to satisfy the common assumptions in blocking and then, to develop an optimal design criterion for the efficient estimation of treatment effects. We apply our method to develop regular, nonregular, and mixed-level blocked designs. Several examples are presented to illustrate the advantages of the proposed method.     

Finding an unknown number of multivariate outliers

Summary.  We use the forward search to provide robust Mahalanobis distances to detect the presence of outliers in a sample of multivariate normal data. Theoretical results on order statistics and on estimation in truncated samples provide the distribution of our test statistic. We also introduce several new robust distances with associated distributional results. Comparisons of our procedure with tests using other robust Mahalanobis distances show the good size and high power of our procedure. We also provide a unification of results on correction factors for estimation from truncated samples.     

Controlling the size of multivariate outlier tests with the MCD estimator of scatter

Multivariate outlier detection requires computation of robust distances to be compared with appropriate cut-off points. In this paper we propose a new calibration method for obtaining reliable cut-off points of distances derived from the MCD estimator of scatter. These cut-off points are based on a more accurate estimate of the extreme tail of the distribution of robust distances. We show that our procedure gives reliable tests of outlyingness in almost all situations of practical interest, provided that the sample size is not much smaller than 50. Therefore, it is a considerable improvement over all the available MCD procedures, which are unable to provide good control over the size of multiple outlier tests for the data structures considered in this paper.     

Outliers detection with the minimum covariance determinant estimator in practice

Robust statistics have slowly become familiar to all practitioners. Books entirely devoted to the subject (e.g. [R.A. Maronna, R.D. Martin, V.J. Yohai, Robust Statistics: Theory and Methods. John Wiley &; Sons, New York, NY, USA, 2006; P.J. Rousseeuw, A.M. Leroy, Robust Regression and Outlier Detection, John Wiley &; Sons, New York, NY, USA, 1987], …) are without any doubt responsible for the increased practice of robust statistics in all fields of applications. Even classical books often have at least one chapter (or parts of chapters) which develops robust methodology. The improvement of computing power has also contributed to the development of a wider and wider range of available robust procedures. However, this success story is now menacing to get backwards: non-specialists interested in the application of robust methodology are faced with a large set of (assumed equivalent) methods and with over-sophistication of some of them. Which method should one use? How should the (numerous) parameters be optimally tuned? These questions are not so easy to answer for non-specialists! One could then argue that default procedures are available in most statistical software (Splus, R, SAS, Matlab, …). However, using as illustration the detection of outliers in multivariate data, it is shown that, on one hand, it is not obvious that one would feel confident with the output of default procedures, and that, on the other hand, trying to understand thoroughly the tuning parameters involved in the procedures might require some extensive research. This is not conceivable when trying to compete with the classical methodology which (while clearly unreliable) is so straightforward. The aim of the paper is to help the practitioners willing to detect in a reliable way outliers in a multivariate data set. The chosen methodology is the Minimum Covariance Determinant estimator being widely available and intuitively appealing.     

Sequential estimation of a location parameter from delayed observations

The problem of sequentially estimating a location parameter is considered in the special case when the data arrive at random times. Certain classes of sequential estimation procedures are derived under a location invariant loss function and with the observation cost determined by a function of the moment of stopping and the number of observations up to this moment.     

Generalized order statistics from two parameter uniform distribution

In this paper some distributional properties of the generalized order statistics from uniform distribution are given. The minimum variance linear unbiased as well best ( in the sense of minimum mean squared error) invariant estimators of the parameters of the two parameter uniform distribution based on the first m generalized order statistics are presented.     

Efficient Estimation of the Seemingly Unrelated Regression Cointegration Model and Testing for Purchasing Power Parity

Abstract

This paper studies the efficient estimation of seemingly unrelated linear models with integrated regressors and stationary errors. We consider two cases. The first one has no common regressor among the equations. In this case, we show that by adding leads and lags of the first differences of the regressors and estimating this augmented dynamic regression model by generalized least squares using the long-run covariance matrix, we obtain an efficient estimator of the cointegrating vector that has a limiting mixed normal distribution. In the second case we consider, there is a common regressor to all equations, and we discuss efficient minimum distance estimation in this context. Simulation results suggests that our new estimator compares favorably with others already proposed in the literature. We apply these new estimators to the testing of the proportionality and symmetry conditions implied by purchasing power parity (PPP) among the G-7 countries. The tests based on the efficient estimates easily reject the joint hypotheses of proportionality and symmetry for all countries with either the United States or Germany as numeraire. Based on individual tests, our results suggest that Canada and Germany are the most likely countries for which the proportionality condition holds, and that Italy and Japan for the symmetry condition relative to the United States.