Speed of wave-front solutions to hyperbolic reaction-diffusion equations

The asymptotic speed problem of front solutions to hyperbolic reaction-diffusion (HRD) equations is studied in detail. We perform linear and variational analyses to obtain bounds for the speed. In contrast to what has been done in previous work, here we derive upper bounds in addition to lower ones in such a way that we can obtain improved bounds. For some functions it is possible to determine the speed without any uncertainty. This is also achieved for some systems of HRD (i.e., time-delayed Lotka-Volterra) equations that take into account the interaction among different species. An analytical analysis is performed for several systems of biological interest, and we find good agreement with the results of numerical simulations as well as with available observations for a system discussed recently

From bargaining solutions to claims rules: a proportional approach

Is it important to negotiate on proportions rather than on numbers? To answer this question, we analyze the behavior of well-known bargaining solutions and the claims rules they induce when they are applied to a "proportionally transformed" bargaining set SP -so-called bargaining-in-proportions set. The idea of applying bargaining solutions to claims problems was already developed in Dagan and Volij (1993). They apply the bargaining solutions over a bargaining set that is the one de ned by the claims and the endowment. A comparison among our results and theirs is provided. Keywords: Bargaining problem, Claims problem, Proportional, Constrained Equal Awards, Constrained Equal Losses, Nash bargaining solution. JEL classi fication: C71, D63, D71.

LdShake: learning design solutions sharing and co-edition

Two important challenges that teachers are currently facing are the sharing and the collaborative authoring of their learning design solutions, such as didactical units and learning materials. On the one hand, there are tools that can be used for the creation of design solutions and only some of them facilitate the co-edition. However, they do not incorporate mechanisms that support the sharing of the designs between teachers. On the other hand, there are tools that serve as repositories of educational resources but they do not enable the authoring of the designs. In this paper we present LdShake, a web tool whose novelty is focused on the combined support for the social sharing and co-edition of learning design solutions within communities of teachers. Teachers can create and share learning designs with other teachers using different access rights so that they can read, comment or co-edit the designs. Therefore, each design solution is associated to a group of teachers able to work on its definition, and another group that can only see the design. The tool is generic in that it allows the creation of designs based on any pedagogical approach. However, it can be particularized in instances providing pre-formatted designs structured according to a specific didactic method (such as Problem-Based Learning, PBL). A particularized LdShake instance has been used in the context of Human Biology studies where teams of teachers are required to work together in the design of PBL solutions. A controlled user study, that compares the use of a generic LdShake and a Moodle system, configured to enable the creation and sharing of designs, has been also carried out. The combined results of the real and controlled studies show that the social structure, and the commenting, co-edition and publishing features of LdShake provide a useful, effective and usable approach for facilitating teachers' teamwork.

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.

Consistent solutions in exchange economies: A characterization of the price mechanism

We characterize the Walrasian allocations correspondence by means offour axioms: consistency, replica invariance, individual rationality andPareto optimality. It is shown that for any given class of exchange economiesany solution that satisfies the axioms is a selection from the Walrasianallocations with slack. Preferences are assumed to be smooth, but may besatiated and non--convex. A class of economies is defined as all economieswhose agents' preferences belong to an arbitrary family (finite or infinite)of types. The result can be modified to characterize equal budget Walrasianallocations with slack by replacing individual rationality with individualrationality from equal division. The results are valid also for classes ofeconomies in which core--Walras equivalence does not hold.

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.

Geometric and long run aspects of Granger causality

This paper extends multivariate Granger causality to take into account the subspacesalong which Granger causality occurs as well as long run Granger causality. The propertiesof these new notions of Granger causality, along with the requisite restrictions, are derivedand extensively studied for a wide variety of time series processes including linear invertibleprocess and VARMA. Using the proposed extensions, the paper demonstrates that: (i) meanreversion in L2 is an instance of long run Granger non-causality, (ii) cointegration is a specialcase of long run Granger non-causality along a subspace, (iii) controllability is a special caseof Granger causality, and finally (iv) linear rational expectations entail (possibly testable)Granger causality restriction along subspaces.

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.

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.

Multiple correspondence analysis of a subset of response categories

In the analysis of multivariate categorical data, typically the analysis of questionnaire data, it is often advantageous, for substantive and technical reasons, to analyse a subset of response categories. In multiple correspondence analysis, where each category is coded as a column of an indicator matrix or row and column of Burt matrix, it is not correct to simply analyse the corresponding submatrix of data, since the whole geometric structure is different for the submatrix . A simple modification of the correspondence analysis algorithm allows the overall geometric structure of the complete data set to be retained while calculating the solution for the selected subset of points. This strategy is useful for analysing patterns of response amongst any subset of categories and relating these patterns to demographic factors, especially for studying patterns of particular responses such as missing and neutral responses. The methodology is illustrated using data from the International Social Survey Program on Family and Changing Gender Roles in 1994.