The algebraic equality of two asymptotic tests for the hypothesis that a normal distribution has a specified correlation matrix

It is proved the algebraic equality between Jennrich's (1970) asymptotic$X^2$ test for equality of correlation matrices, and a Wald test statisticderived from Neudecker and Wesselman's (1990) expression of theasymptoticvariance matrix of the sample correlation matrix.

Compact matrix expressions for generalized Wald tests of equality of moment vectors

Asymptotic chi-squared test statistics for testing the equality ofmoment vectors are developed. The test statistics proposed aregeneralizedWald test statistics that specialize for different settings by inserting andappropriate asymptotic variance matrix of sample moments. Scaled teststatisticsare also considered for dealing with situations of non-iid sampling. Thespecializationwill be carried out for testing the equality of multinomial populations, andtheequality of variance and correlation matrices for both normal andnon-normaldata. When testing the equality of correlation matrices, a scaled versionofthe normal theory chi-squared statistic is proven to be an asymptoticallyexactchi-squared statistic in the case of elliptical data.

Improving Transition Outcomes: Resource Mapping Workshop: Service Matrix

Resource Mapping tool from the Improving Transition Outcomes Resource Mapping Workshops

Unfolding a symmetric matrix

Graphical displays which show inter--sample distances are importantfor the interpretation and presentation of multivariate data. Except whenthe displays are two--dimensional, however, they are often difficult tovisualize as a whole. A device, based on multidimensional unfolding, isdescribed for presenting some intrinsically high--dimensional displays infewer, usually two, dimensions. This goal is achieved by representing eachsample by a pair of points, say $R_i$ and $r_i$, so that a theoreticaldistance between the $i$-th and $j$-th samples is represented twice, onceby the distance between $R_i$ and $r_j$ and once by the distance between$R_j$ and $r_i$. Self--distances between $R_i$ and $r_i$ need not be zero.The mathematical conditions for unfolding to exhibit symmetry are established.Algorithms for finding approximate fits, not constrained to be symmetric,are discussed and some examples are given.

Biased representation of homothetic preferences on homogeneous sets

In the homogeneous case of one-dimensional objects, we show that any preference relation that is positive and homothetic can be represented by a quantitative utility function and unique bias. This bias may favor or disfavor the preference for an object. In the first case, preferences are complete but not transitive and an object may be preferred even when its utility is lower. In the second case, preferences are asymmetric and transitive but not negatively transitive and it may not be sufficient for an object to have a greater utility for be preferred. In this manner, the bias reflects the extent to which preferences depart from the maximization of a utility function.

Contribution biplots

In order to interpret the biplot it is necessary to know which points usually variables are the ones that are important contributors to the solution, and this information is available separately as part of the biplot s numerical results. We propose a new scaling of the display, called the contribution biplot, which incorporates this diagnostic directly into the graphical display, showing visually the important contributors and thus facilitating the biplot interpretation and often simplifying the graphical representation considerably. The contribution biplot can be applied to a wide variety of analyses such as correspondence analysis, principal component analysis, log-ratio analysis and the graphical results of a discriminant analysis/MANOVA, in fact to any method based on the singular-value decomposition. In the contribution biplot one set of points, usually the rows of the data matrix, optimally represent the spatial positions of the cases or sample units, according to some distance measure that usually incorporates some form of standardization unless all data are comparable in scale. The other set of points, usually the columns, is represented by vectors that are related to their contributions to the low-dimensional solution. A fringe benefit is that usually only one common scale for row and column points is needed on the principal axes, thus avoiding the problem of enlarging or contracting the scale of one set of points to make the biplot legible. Furthermore, this version of the biplot also solves the problem in correspondence analysis of low-frequency categories that are located on the periphery of the map, giving the false impression that they are important, when they are in fact contributing minimally to the solution.

Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size

This paper analyzes whether standard covariance matrix tests work whendimensionality is large, and in particular larger than sample size. Inthe latter case, the singularity of the sample covariance matrix makeslikelihood ratio tests degenerate, but other tests based on quadraticforms of sample covariance matrix eigenvalues remain well-defined. Westudy the consistency property and limiting distribution of these testsas dimensionality and sample size go to infinity together, with theirratio converging to a finite non-zero limit. We find that the existingtest for sphericity is robust against high dimensionality, but not thetest for equality of the covariance matrix to a given matrix. For thelatter test, we develop a new correction to the existing test statisticthat makes it robust against high dimensionality.

Honey, I shrunk the sample covariance matrix

The central message of this paper is that nobody should be using the samplecovariance matrix for the purpose of portfolio optimization. It containsestimation error of the kind most likely to perturb a mean-varianceoptimizer. In its place, we suggest using the matrix obtained from thesample covariance matrix through a transformation called shrinkage. Thistends to pull the most extreme coefficients towards more central values,thereby systematically reducing estimation error where it matters most.Statistically, the challenge is to know the optimal shrinkage intensity,and we give the formula for that. Without changing any other step in theportfolio optimization process, we show on actual stock market data thatshrinkage reduces tracking error relative to a benchmark index, andsubstantially increases the realized information ratio of the activeportfolio manager.

Improved estimation of the covariance matrix of stock returns with an application to portofolio selection

This paper proposes to estimate the covariance matrix of stock returnsby an optimally weighted average of two existing estimators: the samplecovariance matrix and single-index covariance matrix. This method isgenerally known as shrinkage, and it is standard in decision theory andin empirical Bayesian statistics. Our shrinkage estimator can be seenas a way to account for extra-market covariance without having to specifyan arbitrary multi-factor structure. For NYSE and AMEX stock returns from1972 to 1995, it can be used to select portfolios with significantly lowerout-of-sample variance than a set of existing estimators, includingmulti-factor models.

Political representation in Switzerland : democratic or plutocratic ?

Les inégalités économiques se traduisent-elles dans des inégalités politiques à travers le processus de représentation électorale? Telle est la question centrale de cette thèse qui s'attache, par ailleurs, à investiguer les mécanismes qui tendent à produire une représentation biaisée des préférences politiques des citoyens en fonction de leur statut économique. Focalisé sur le cas de la Suisse et faisant usage des données de l'enquête postélectorale Selects de 2007, ce travail démontre que sur les rares sujets qui divisent les citoyens selon des clivages économiques - la redistribution des richesses et la sécurité sociale en particulier - les élus à l'Assemblée fédérale ont des préférences qui reflètent mieux les opinions des citoyens les plus riches. Cette sous-représentation des opinions des citoyens modestes et de ceux faisant partie du centre de la distribution des revenus peut en partie être attribuée à des différences dans les taux de participation et de connaissance politiques entre ces groupes de citoyens. La thèse met également en évidence le rôle joué par la représentation descriptive - autrement dit, la similitude en termes de statut économique entre les représentants et les représentés - dans la représentation des opinions et intérêts des citoyens. Par ailleurs, la structure du système partisan en Suisse ne reflétant pas la multidimensionnalité des préférences politiques des citoyens, les électeurs ne parviennent pas à traduire la complexité de leurs préférences politiques dans un choix de vote, ce qui, dans la configuration actuelle des forces politiques, tend à favoriser l'élection de représentants aux opinions proches de la droite sur les questions économiques. Enfin, une analyse de la représentation politique au niveau cantonal tend à soutenir la thèse selon laquelle le manque de régulation en matière de financement des partis en Suisse pourrait partiellement expliquer les inégalités dans la représentation des opinions politiques des citoyens aux revenus distincts. - Do economic inequalities translate into political inequalities through electoral representation? This is the central research question of this thesis, which also investigates the mechanisms that lead to potential economically based inequalities in the representation of citizens' policy preferences. Focusing on the case of Switzerland and making use of data provided by the post- electoral survey Selects 2007, this research demonstrates that regarding the rare policy domains in which the preferences of citizens are clearly linked to economic cleavages - redistribution and social security in particular - members of the Federal Assembly have policy preferences that best reflect the policy preferences of richer citizens. The under-representation of the opinions of relatively poor citizens and of those being the in the middle of the income distribution can be to some extent be explained by differences in political participation and political information across income groups. The thesis also puts forward the role played by descriptive representation - the similarity between representatives and represented in terms of their socioeconomic status - for the representation of citizens' preferences and interests. In addition, the structure of the party system in Switzerland does not reflect the multidimensionality of policy preferences among citizens who, as a result, have a hard time translating their complex preferences into a vote choice. Given the configuration of political actors, this tends to favour the election of representatives from the right who do not represent the preferences of their voters on economic issues. Finally, an analysis of representation at the cantonal level tends to confirm that the lack of party finance regulations in Switzerland may partially explain inequalities in the representation of citizens with different levels of income.

The choice of the form of representation in multinational banking: Evidence from Spain

This paper investigates foreign direct investment in the bankingsector. The attention has been addressed to test the importanceof OLI advantages as the determinants of the bank's decisionto invest in foreign locations. Nevertheless, since banks canexpand their activities abroad through different organizationalforms that imply different levels of foreign involvement, theissue of the form of representation has been tackled. Theresults show the importance of OLI advantages in the form ofrepresentation in multinational banking.

Association of nuclear matrix proteins with granular and threaded nuclear bodies in cell lines undergoing apoptosis.

The granules which appear in the nucleolar area in apoptotic HL-60 cells after camptothecin administration (Zweyer et al., Exp. Cell Res. 221,27-40, 1995) were detected also in several other cell lines induced to undergo apoptosis by different stimuli, such as MOLT-4 treated with staurosporine, K-562 incubated with actinomycin D, P-815 exposed to temperature causing heat shock, Jurkat cells treated with EGTA, U-937 growing in the presence of cycloheximide and tumor necrosis factor-alpha, and HeLa cells treated with etoposide. Using immunoelectron microscopy techniques, we demonstrate that, besides the already described nuclear matrix proteins p125 and p160, these granules contain other nucleoskeletal polypeptides such as proliferating cell nuclear antigen, a component of ribonucleoprotein particles, a 105-kDa constituent of nuclear spliceosomes, and the 240-kDa nuclear mitotic apparatus-associated protein referred to as NuMA. Moreover, we also found in the granules SAF-A/hn-RNP-U and SATB1 proteins, two polypeptides that have been reported to bind scaffold-associated regions DNA sequences in vitro, thus mediating the formation of looped DNA structures in vivo. Fibrillarin and coilin are not present in these granules or the PML protein. Thus, the granules seen during the apoptotic process apparently are different from coiled bodies or other types of nuclear bodies. Furthermore, these granules do not contain chromatin components such as histones and DNA. Last, Western blotting analysis revealed that nuclear matrix proteins present in the granules are not proteolytically degraded except for the NuMA polypeptide. We propose that these granules might represent aggregates of nuclear matrix proteins forming during the apoptotic process. Moreover, since the granules are present in several cell lines undergoing apoptosis, they could be considered a previously unrecognized morphological hallmark of the apoptotic process.