Impact of incorrect assumptions on the covariance structure of random effects and/or residuals in nonlinear mixed models for repeated measures data

In this paper we analyse, using Monte Carlo simulation, the possible consequences of incorrect assumptions on the true structure of the random effects covariance matrix and the true correlation pattern of residuals, over the performance of an estimation method for nonlinear mixed models. The procedure under study is the well known linearization method due to Lindstrom and Bates (1990), implemented in the nlme library of S-Plus and R. Its performance is studied in terms of bias, mean square error (MSE), and true coverage of the associated asymptotic confidence intervals. Ignoring other criteria like the convenience of avoiding over parameterised models, it seems worst to erroneously assume some structure than do not assume any structure when this would be adequate.

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.

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.

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.

Finance versus costs for teaching hospitals in Spain

In this paper we analyse the observed systematic differences incosts for teaching hospitals (THhenceforth) in Spain. Concernhas been voiced regarding the existence of a bias in thefinancing of TH s has been raised once prospective budgets arein the arena for hospital finance, and claims for adjusting totake into account the legitimate extra costs of teaching onhospital expenditure are well grounded. We focus on theestimation of the impact of teaching status on average cost. Weused a version of a multiproduct hospital cost function takinginto account some relevant factors from which to derive theobserved differences. We assume that the relationship betweenthe explanatory and the dependent variables follows a flexibleform for each of the explanatory variables. We also model theunderlying covariance structure of the data. We assumed twoqualitatively different sources of variation: random effects andserial correlation. Random variation refers to both general levelvariation (through the random intercept) and the variationspecifically related to teaching status. We postulate that theimpact of the random effects is predominant over the impact ofthe serial correlation effects. The model is estimated byrestricted maximum likelihood. Our results show that costs are 9%higher (15% in the case of median costs) in teaching than innon-teaching hospitals. That is, teaching status legitimatelyexplains no more than half of the observed difference in actualcosts. The impact on costs of the teaching factor depends on thenumber of residents, with an increase of 51.11% per resident forhospitals with fewer than 204 residents (third quartile of thenumber of residents) and 41.84% for hospitals with more than 204residents. In addition, the estimated dispersion is higher amongteaching hospitals. As a result, due to the considerable observedheterogeneity, results should be interpreted with caution. From apolicy making point of view, we conclude that since a higherrelative burden for medical training is under public hospitalcommand, an explicit adjustment to the extra costs that theteaching factor imposes on hospital finance is needed, beforehospital competition for inpatient services takes place.

The mean-variance model from the inverse of the variance-covariance matrix

En este artículo, a partir de la inversa de la matriz de varianzas y covarianzas se obtiene el modelo Esperanza-Varianza de Markowitz siguiendo un camino más corto y matemáticamente riguroso. También se obtiene la ecuación de equilibrio del CAPM de Sharpe.

Exported oscillator competition: A concept to analyse complex rhytms

We study the interaction between two independent nonlinear oscillators competing through a neutral excitable element. The first oscillator, completely deterministic, acts as a normal pacemaker sending pulses to the neutral element which fires when it is excited by these pulses. The second oscillator, endowed with some randomness, though unable to make the excitable element to beat, leads to the occasional suppression of its firing. The missing beats or errors are registered and their statistics analyzed in terms of the noise intensity and the periods of both oscillators. This study is inspired in some complex rhythms such as a particular class of heart arrhythmia.

The mean-variance model from the inverse of the variance-covariance matrix

En este artículo, a partir de la inversa de la matriz de varianzas y covarianzas se obtiene el modelo Esperanza-Varianza de Markowitz siguiendo un camino más corto y matemáticamente riguroso. También se obtiene la ecuación de equilibrio del CAPM de Sharpe.

Construcción de un índice de calidad ocupacional (ICO) para el análisis de la inserción profesional de los graduados universitarios = Building an employment quality index (EQI) to analyse graduates’ access to the labour market

En este trabajo se propone la construcción de un índice de calidad ocupacional (ICO) a partir de los datos de la Encuesta de Inserción Laboral de los Graduados de las Universidades Catalanas realizada por la Agencia para la Calidad del Sistema Universitario de Catalunya (AQU), que ha de permitir un mejor análisis de la información que proporciona la encuesta y facilitar su comparación con estudios similares. La encuesta se realiza tres años después de la graduación. En este artículo, se utiliza la segunda encuesta realizada el año 2005 entre 11.456 graduados (52,63%) de la promoción 2001 (AQU, 2005, Serra-Ramoneda, 2007). El índice se ha elaborado a partir de los indicadores objetivos ‘tipo y duración del contrato laboral’, ‘retribución económica’, ‘adecuación entre la formación universitaria y el empleo’ a los que se otorga una puntuación ponderada según las respuestas dadas por los graduados. La suma de las puntuaciones se matiza con un coeficiente derivado del indicador subjetivo ‘satisfacción con el trabajo en general’. A partir de la información proporcionada por el índice, se realiza un análisis comparativo del nivel de calidad ocupacional que han logrado los graduados de áreas de conocimiento, ámbitos de trabajo, ramas de actividad y ubicaciones territoriales del empleo diferentes. Los resultados obtenidos permiten observar que entre los graduados catalanes los siguientes hechos son buenos predictores de la calidad de la ocupación: haber estudiado una carrera que no sea de Humanidades, ser un hombre, haber desempeñado durante la carrera un trabajo relacionado con los estudios, estar ocupado en la construcción, en instituciones financieras o en servicios a empresas, haber tenido algún tipo de movilidad por motivos de trabajo, trabajar fuera de Cataluña y hacerlo en empresas grandes, especialmente con más de 500 trabajadores. Finalmente, se presentan algunas reflexiones y propuestas que pueden resultar de interés para la orientación de los estudiantes y la planificación universitaria

OKKASIONALISMEN: Eine Analyse anhand ausgewählter Beispiele aus einer Wochenzeitung

Muchos lingüistas ya han estudiado los ocasionalismos en la lengua alemana por su interés lingüístico, pero lo han hecho en general y solo muy pocos los han tratado observando su contexto. Por lo tanto, este trabajo analiza con qué frecuencia se hallanocasionalismos en una edición específica del periódico semanal DIE ZEIT, qué tipos de ocasionalismos hay y cómo el lector puede descifrarlos con o sin la ayuda del contexto. Para ello, he sintetizado los conocimientos básicos necesarios sobre laformación de las palabras en alemán, poniendo el énfasis en la formación de palabras nuevas, como son los ocasionalismos. De esta manera, he podido clasificar los ocasionalismos en los tres clases principales de la formación de palabras en alemán y, asimismo, analizarlos en su contexto. El resultado son 234 ocasionalismosencontrados, un 88 % de palabras compuestas, un 7 % de derivaciones y un 5 % de conversiones. Mediante estos ejemplos, he estudiado cómo el lector puede llegar a entenderlos sin tener previo conocimiento de ellos y prescindiendo del contexto; y laconclusión es que lo consigue a través de analogías con palabras conocidas y descomponiendo la nueva palabra en sus elementos constituyentes directos; sin embargo, el contexto sigue siendo imprescindible.

L'exploitation des ressources végétales dans les Pyrénées orientales durant l'holocène: analyse anthracologique des structures d'élevage, de four et de charbonnières dans l'Alt Urgell (Chaîne du Cadí) et la Vallée du Madriu (Andorre)

Dans ce travail, nous présentons le résultat des recherches anthracologiques réalisées sur des sites archéologiques de haute montagne dans les Pyrénées orientales. Cette recherche s’insère dans un projet d’archéologie du paysage. Les zones d’étude se situent dans les Pré-Pyrénées sur le versant méridional de la chaîne du Cadí (vallée de la Vansa, Alt Urgell), et dans la vallée du Madriu, située dans les Pyrénées axiales, en Andorre. Le but principal de l’analyse anthracologique a été de connaître et comprendre la dynamique et la relation qui unissent les populations qui ont occupé ces vallées avec le milieu forestier de haute montagne. Les échantillons ont été récupérés sur des structures archéologiques associés à l’exploitation forestière (charbonnières, fours pour la fabrication de résine), au pastoralisme (cabanes et enclos) et à l’exploitation minière-métallurgique (four de grillage), avec une chronologie qui débute au Néolithique Ancien et finit à l’époque moderne et contemporaine (XVIII-XIXe siècles). Les résultats indiquent une variabilité taxonomique pauvre avec la présence majoritaire du Pinus et la présence ponctuelle d’autres espèces arbustives (Ericaceae et Juniperus) et arborées, comme Betula alba ou Abies alba. Différentes formations végétales de haute montagne ont été identifiées, selon leur localisation en versant ensoleillé ou ombragé, ainsi que leur altitude. Les résultats montrent des traces d’exploitation forestière dès le Néolithique Ancien, une intensification des activités à l’Antiquité, même si l’impact anthropique majeur correspond à l’activité de charbonnage d’époque moderne.