Application of discriminant function analysis and change-point problem in dating volcanic ashes

The application of Discriminant function analysis (DFA) is not a new idea in the studyof tephrochrology. In this paper, DFA is applied to compositional datasets of twodifferent types of tephras from Mountain Ruapehu in New Zealand and MountainRainier in USA. The canonical variables from the analysis are further investigated witha statistical methodology of change-point problems in order to gain a betterunderstanding of the change in compositional pattern over time. Finally, a special caseof segmented regression has been proposed to model both the time of change and thechange in pattern. This model can be used to estimate the age for the unknown tephrasusing Bayesian statistical calibration

Electron localization function at the correlated level

The electron localization function (ELF) has been proven so far a valuable tool to determine the location of electron pairs. Because of that, the ELF has been widely used to understand the nature of the chemical bonding and to discuss the mechanism of chemical reactions. Up to now, most applications of the ELF have been performed with monodeterminantal methods and only few attempts to calculate this function for correlated wave functions have been carried out. Here, a formulation of ELF valid for mono- and multiconfigurational wave functions is given and compared with previous recently reported approaches. The method described does not require the use of the homogeneous electron gas to define the ELF, at variance with the ELF definition given by Becke. The effect of the electron correlation in the ELF, introduced by means of configuration interaction with singles and doubles calculations, is discussed in the light of the results derived from a set of atomic and molecular systems

Prediction of enzyme function by combining sequence similarity and protein interactions

Background: A number of studies have used protein interaction data alone for protein function prediction. Here, we introduce a computational approach for annotation of enzymes, based on the observation that similar protein sequences are more likely to perform the same function if they share similar interacting partners. Results: The method has been tested against the PSI-BLAST program using a set of 3,890 protein sequences from which interaction data was available. For protein sequences that align with at least 40% sequence identity to a known enzyme, the specificity of our method in predicting the first three EC digits increased from 80% to 90% at 80% coverage when compared to PSI-BLAST. Conclusion: Our method can also be used in proteins for which homologous sequences with known interacting partners can be detected. Thus, our method could increase 10% the specificity of genome-wide enzyme predictions based on sequence matching by PSI-BLAST alone.

Capacity-achieving input covariance for single-user multi-antenna channels

We characterize the capacity-achieving input covariance for multi-antenna channels known instantaneously at the receiver and in distribution at the transmitter. Our characterization, valid for arbitrary numbers of antennas, encompasses both the eigenvectors and the eigenvalues. The eigenvectors are found for zero-mean channels with arbitrary fading profiles and a wide range of correlation and keyhole structures. For the eigenvalues, in turn, we present necessary and sufficient conditions as well as an iterative algorithm that exhibits remarkable properties: universal applicability, robustness and rapid convergence. In addition, we identify channel structures for which an isotropic input achieves capacity.

Capacity-approaching rate function for layered multiantenna architectures

The simultaneous use of multiple transmit and receive antennas can unleash very large capacity increases in rich multipath environments. Although such capacities can be approached by layered multi-antenna architectures with per-antenna rate control, the need for short-term feedback arises as a potential impediment, in particular as the number of antennas—and thus the number of rates to be controlled—increases. What we show, however, is that the need for short-term feedback in fact vanishes as the number of antennas and/or the diversity order increases. Specifically, the rate supported by each transmit antenna becomes deterministic and a sole function of the signal-to-noise, the ratio of transmit and receive antennas, and the decoding order, all of which are either fixed or slowly varying. More generally, we illustrate -through this specific derivation— the relevance of some established random CDMA results to the single-user multi-antenna problem.

The externalisation of the asylum function in the European Union

This paper aims to identify and assess the main items in the strategy followed by the EU and its member states on the externalisation of their asylum function. First, it analyses the European harmonisation of the return to safe third countries and to countries of first asylum, which is carried out by means of readmission agreements. Second, it refers to the strategies defined by the Hague and the Stockholm programs concerning the External Aspects of the European Union Asylum Policy, on the detention centres for illegal immigrants abroad, and on the proposals for delocalisation of asylum applications processing centres beyond the EU borders. Finally, this paper considers whether the strategy of externalisation of the function of asylum sometimes lacks legitimacy, and to what extent there is a fair balance between the interests of the states and the protection of the human rights of refugees and asylum seekers.

Asymptotic robustness in multi-sample analysis of multivariate linear relations

Standard methods for the analysis of linear latent variable models oftenrely on the assumption that the vector of observed variables is normallydistributed. This normality assumption (NA) plays a crucial role inassessingoptimality of estimates, in computing standard errors, and in designinganasymptotic chi-square goodness-of-fit test. The asymptotic validity of NAinferences when the data deviates from normality has been calledasymptoticrobustness. In the present paper we extend previous work on asymptoticrobustnessto a general context of multi-sample analysis of linear latent variablemodels,with a latent component of the model allowed to be fixed across(hypothetical)sample replications, and with the asymptotic covariance matrix of thesamplemoments not necessarily finite. We will show that, under certainconditions,the matrix $\Gamma$ of asymptotic variances of the analyzed samplemomentscan be substituted by a matrix $\Omega$ that is a function only of thecross-product moments of the observed variables. The main advantage of thisis thatinferences based on $\Omega$ are readily available in standard softwareforcovariance structure analysis, and do not require to compute samplefourth-order moments. An illustration with simulated data in the context ofregressionwith errors in variables will be presented.

Asymptotic robust inferences in the analysis of mean and covariance structures

Structural equation models are widely used in economic, socialand behavioral studies to analyze linear interrelationships amongvariables, some of which may be unobservable or subject to measurementerror. Alternative estimation methods that exploit different distributionalassumptions are now available. The present paper deals with issues ofasymptotic statistical inferences, such as the evaluation of standarderrors of estimates and chi--square goodness--of--fit statistics,in the general context of mean and covariance structures. The emphasisis on drawing correct statistical inferences regardless of thedistribution of the data and the method of estimation employed. A(distribution--free) consistent estimate of $\Gamma$, the matrix ofasymptotic variances of the vector of sample second--order moments,will be used to compute robust standard errors and a robust chi--squaregoodness--of--fit squares. Simple modifications of the usual estimateof $\Gamma$ will also permit correct inferences in the case of multi--stage complex samples. We will also discuss the conditions under which,regardless of the distribution of the data, one can rely on the usual(non--robust) inferential statistics. Finally, a multivariate regressionmodel with errors--in--variables will be used to illustrate, by meansof simulated data, various theoretical aspects of the paper.

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.

Solving higher-dimensional continuous time stochastic control problems by value function regression

The paper develops a method to solve higher-dimensional stochasticcontrol problems in continuous time. A finite difference typeapproximation scheme is used on a coarse grid of low discrepancypoints, while the value function at intermediate points is obtainedby regression. The stability properties of the method are discussed,and applications are given to test problems of up to 10 dimensions.Accurate solutions to these problems can be obtained on a personalcomputer.

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.

A singular function and its relation with the number systems involved in its definition

Minkowski's ?(x) function can be seen as the confrontation of two number systems: regular continued fractions and the alternated dyadic system. This way of looking at it permits us to prove that its derivative, as it also happens for many other non-decreasing singular functions from [0,1] to [0,1], when it exists can only attain two values: zero and infinity. It is also proved that if the average of the partial quotients in the continued fraction expansion of x is greater than k* =5.31972, and ?'(x) exists then ?'(x)=0. In the same way, if the same average is less than k**=2 log2(F), where F is the golden ratio, then ?'(x)=infinity. Finally some results are presented concerning metric properties of continued fraction and alternated dyadic expansions.

Satisfaction in choice as a function of the number of alternatives: When "goods satiate" but "bads escalate"

Whereas people are typically thought to be better off with more choices, studiesshow that they often prefer to choose from small as opposed to large sets of alternatives.We propose that satisfaction from choice is an inverted U-shaped function of thenumber of alternatives. This proposition is derived theoretically by considering thebenefits and costs of different numbers of alternatives and is supported by fourexperimental studies. We also manipulate the perceptual costs of information processingand demonstrate how this affects the resulting satisfaction function. We furtherindicate that satisfaction when choosing from a given set is diminished if people aremade aware of the existence of other choice sets. The role of individual differences insatisfaction from choice is documented by noting effects due to gender and culture. Weconclude by emphasizing the need to have an explicit rationale for knowing how muchchoice is enough.

Cost efficiency in primary care contracting: A stochastic frontier cost function approach

The principal aim of this paper is to estimate a stochastic frontier costfunction and an inefficiency effects model in the analysis of the primaryhealth care services purchased by the public authority and supplied by 180providers in 1996 in Catalonia. The evidence from our sample does not supportthe premise that contracting out has helped improve purchasing costefficiency in primary care. Inefficient purchasing cost was observed in thecomponent of this purchasing cost explicitly included in the contract betweenpurchaser and provider. There are no observable incentives for thecontracted-out primary health care teams to minimise prescription costs, whichare not explicitly included in the present contracting system.