Influence diagnostics in nonlinear mixed-effects elliptical models

In this work we propose and analyze nonlinear elliptical models for longitudinal data, which represent an alternative to gaussian models in the cases of heavy tails, for instance. The elliptical distributions may help to control the influence of the observations in the parameter estimates by naturally attributing different weights for each case. We consider random effects to introduce the within-group correlation and work with the marginal model without requiring numerical integration. An iterative algorithm to obtain maximum likelihood estimates for the parameters is presented, as well as diagnostic results based on residual distances and local influence [Cook, D., 1986. Assessment of local influence. journal of the Royal Statistical Society - Series B 48 (2), 133-169; Cook D., 1987. Influence assessment. journal of Applied Statistics 14 (2),117-131; Escobar, L.A., Meeker, W.Q., 1992, Assessing influence in regression analysis with censored data, Biometrics 48, 507-528]. As numerical illustration, we apply the obtained results to a kinetics longitudinal data set presented in [Vonesh, E.F., Carter, R.L., 1992. Mixed-effects nonlinear regression for unbalanced repeated measures. Biometrics 48, 1-17], which was analyzed under the assumption of normality. (C) 2009 Elsevier B.V. All rights reserved.

A note on influence diagnostics in nonlinear mixed-effects elliptical models

This paper provides general matrix formulas for computing the score function, the (expected and observed) Fisher information and the A matrices (required for the assessment of local influence) for a quite general model which includes the one proposed by Russo et al. (2009). Additionally, we also present an expression for the generalized leverage on fixed and random effects. The matrix formulation has notational advantages, since despite the complexity of the postulated model, all general formulas are compact, clear and have nice forms. (C) 2010 Elsevier B.V. All rights reserved.

Assessment of variance components in nonlinear mixed-effects elliptical models

The issue of assessing variance components is essential in deciding on the inclusion of random effects in the context of mixed models. In this work we discuss this problem by supposing nonlinear elliptical models for correlated data by using the score-type test proposed in Silvapulle and Silvapulle (1995). Being asymptotically equivalent to the likelihood ratio test and only requiring the estimation under the null hypothesis, this test provides a fairly easy computable alternative for assessing one-sided hypotheses in the context of the marginal model. Taking into account the possible non-normal distribution, we assume that the joint distribution of the response variable and the random effects lies in the elliptical class, which includes light-tailed and heavy-tailed distributions such as Student-t, power exponential, logistic, generalized Student-t, generalized logistic, contaminated normal, and the normal itself, among others. We compare the sensitivity of the score-type test under normal, Student-t and power exponential models for the kinetics data set discussed in Vonesh and Carter (1992) and fitted using the model presented in Russo et al. (2009). Also, a simulation study is performed to analyze the consequences of the kurtosis misspecification.

Influence diagnostics in heteroscedastic and/or autoregressive nonlinear elliptical models for correlated data

In this paper, we propose nonlinear elliptical models for correlated data with heteroscedastic and/or autoregressive structures. Our aim is to extend the models proposed by Russo et al. [22] by considering a more sophisticated scale structure to deal with variations in data dispersion and/or a possible autocorrelation among measurements taken throughout the same experimental unit. Moreover, to avoid the possible influence of outlying observations or to take into account the non-normal symmetric tails of the data, we assume elliptical contours for the joint distribution of random effects and errors, which allows us to attribute different weights to the observations. We propose an iterative algorithm to obtain the maximum-likelihood estimates for the parameters and derive the local influence curvatures for some specific perturbation schemes. The motivation for this work comes from a pharmacokinetic indomethacin data set, which was analysed previously by Bocheng and Xuping [1] under normality.

A modified signed likelihood ratio test in elliptical structural models

In this paper we deal with the issue of performing accurate testing inference on a scalar parameter of interest in structural errors-in-variables models. The error terms are allowed to follow a multivariate distribution in the class of the elliptical distributions, which has the multivariate normal distribution as special case. We derive a modified signed likelihood ratio statistic that follows a standard normal distribution with a high degree of accuracy. Our Monte Carlo results show that the modified test is much less size distorted than its unmodified counterpart. An application is presented.

Bayesian estimation of regression parameters in elliptical measurement error models

The main object of this paper is to discuss the Bayes estimation of the regression coefficients in the elliptically distributed simple regression model with measurement errors. The posterior distribution for the line parameters is obtained in a closed form, considering the following: the ratio of the error variances is known, informative prior distribution for the error variance, and non-informative prior distributions for the regression coefficients and for the incidental parameters. We proved that the posterior distribution of the regression coefficients has at most two real modes. Situations with a single mode are more likely than those with two modes, especially in large samples. The precision of the modal estimators is studied by deriving the Hessian matrix, which although complicated can be computed numerically. The posterior mean is estimated by using the Gibbs sampling algorithm and approximations by normal distributions. The results are applied to a real data set and connections with results in the literature are reported. (C) 2011 Elsevier B.V. All rights reserved.

Influence diagnostics for linear models with first-order autoregressive elliptical errors

We introduce in this paper the class of linear models with first-order autoregressive elliptical errors. The score functions and the Fisher information matrices are derived for the parameters of interest and an iterative process is proposed for the parameter estimation. Some robustness aspects of the maximum likelihood estimates are discussed. The normal curvatures of local influence are also derived for some usual perturbation schemes whereas diagnostic graphics to assess the sensitivity of the maximum likelihood estimates are proposed. The methodology is applied to analyse the daily log excess return on the Microsoft whose empirical distributions appear to have AR(1) and heavy-tailed errors. (C) 2008 Elsevier B.V. All rights reserved.

Teaching elliptical excision skills to novice medical students: a randomized controlled study comparing low- and high-fidelity bench models

Background: The search for alternative and effective forms of training simulation is needed due to ethical and medico-legal aspects involved in training surgical skills on living patients, human cadavers and living animals. Aims : To evaluate if the bench model fidelity interferes in the acquisition of elliptical excision skills by novice medical students. Materials and Methods: Forty novice medical students were randomly assigned to 5 practice conditions with instructor-directed elliptical excision skills' training (n = 8): didactic materials (control); organic bench model (low-fidelity); ethylene-vinyl acetate bench model (low-fidelity); chicken legs' skin bench model (high-fidelity); or pig foot skin bench model (high-fidelity). Pre- and post-tests were applied. Global rating scale, effect size, and self-perceived confidence based on Likert scale were used to evaluate all elliptical excision performances. Results : The analysis showed that after training, the students practicing on bench models had better performance based on Global rating scale (all P < 0.0000) and felt more confident to perform elliptical excision skills (all P < 0.0000) when compared to the control. There was no significant difference (all P > 0.05) between the groups that trained on bench models. The magnitude of the effect (basic cutaneous surgery skills' training) was considered large (>0.80) in all measurements. Conclusion : The acquisition of elliptical excision skills after instructor-directed training on low-fidelity bench models was similar to the training on high-fidelity bench models; and there was a more substantial increase in elliptical excision performances of students that trained on all simulators compared to the learning on didactic materials.

Influence diagnostics for elliptical semiparametric mixed models

In this paper we extend semiparametric mixed linear models with normal errors to elliptical errors in order to permit distributions with heavier and lighter tails than the normal ones. Penalized likelihood equations are applied to derive the maximum penalized likelihood estimates (MPLEs) which appear to be robust against outlying observations in the sense of the Mahalanobis distance. A reweighed iterative process based on the back-fitting method is proposed for the parameter estimation and the local influence curvatures are derived under some usual perturbation schemes to study the sensitivity of the MPLEs. Two motivating examples preliminarily analyzed under normal errors are reanalyzed considering some appropriate elliptical errors. The local influence approach is used to compare the sensitivity of the model estimates.

Extremal properties of certain risk models

Cette thèse s'intéresse à étudier les propriétés extrémales de certains modèles de risque d'intérêt dans diverses applications de l'assurance, de la finance et des statistiques. Cette thèse se développe selon deux axes principaux, à savoir: Dans la première partie, nous nous concentrons sur deux modèles de risques univariés, c'est-à- dire, un modèle de risque de déflation et un modèle de risque de réassurance. Nous étudions le développement des queues de distribution sous certaines conditions des risques commun¬s. Les principaux résultats sont ainsi illustrés par des exemples typiques et des simulations numériques. Enfin, les résultats sont appliqués aux domaines des assurances, par exemple, les approximations de Value-at-Risk, d'espérance conditionnelle unilatérale etc. La deuxième partie de cette thèse est consacrée à trois modèles à deux variables: Le premier modèle concerne la censure à deux variables des événements extrême. Pour ce modèle, nous proposons tout d'abord une classe d'estimateurs pour les coefficients de dépendance et la probabilité des queues de distributions. Ces estimateurs sont flexibles en raison d'un paramètre de réglage. Leurs distributions asymptotiques sont obtenues sous certaines condi¬tions lentes bivariées de second ordre. Ensuite, nous donnons quelques exemples et présentons une petite étude de simulations de Monte Carlo, suivie par une application sur un ensemble de données réelles d'assurance. L'objectif de notre deuxième modèle de risque à deux variables est l'étude de coefficients de dépendance des queues de distributions obliques et asymétriques à deux variables. Ces distri¬butions obliques et asymétriques sont largement utiles dans les applications statistiques. Elles sont générées principalement par le mélange moyenne-variance de lois normales et le mélange de lois normales asymétriques d'échelles, qui distinguent la structure de dépendance de queue comme indiqué par nos principaux résultats. Le troisième modèle de risque à deux variables concerne le rapprochement des maxima de séries triangulaires elliptiques obliques. Les résultats théoriques sont fondés sur certaines hypothèses concernant le périmètre aléatoire sous-jacent des queues de distributions. -- This thesis aims to investigate the extremal properties of certain risk models of interest in vari¬ous applications from insurance, finance and statistics. This thesis develops along two principal lines, namely: In the first part, we focus on two univariate risk models, i.e., deflated risk and reinsurance risk models. Therein we investigate their tail expansions under certain tail conditions of the common risks. Our main results are illustrated by some typical examples and numerical simu¬lations as well. Finally, the findings are formulated into some applications in insurance fields, for instance, the approximations of Value-at-Risk, conditional tail expectations etc. The second part of this thesis is devoted to the following three bivariate models: The first model is concerned with bivariate censoring of extreme events. For this model, we first propose a class of estimators for both tail dependence coefficient and tail probability. These estimators are flexible due to a tuning parameter and their asymptotic distributions are obtained under some second order bivariate slowly varying conditions of the model. Then, we give some examples and present a small Monte Carlo simulation study followed by an application on a real-data set from insurance. The objective of our second bivariate risk model is the investigation of tail dependence coefficient of bivariate skew slash distributions. Such skew slash distributions are extensively useful in statistical applications and they are generated mainly by normal mean-variance mixture and scaled skew-normal mixture, which distinguish the tail dependence structure as shown by our principle results. The third bivariate risk model is concerned with the approximation of the component-wise maxima of skew elliptical triangular arrays. The theoretical results are based on certain tail assumptions on the underlying random radius.

The gravity wave momentum flux in hydrostatic flow with directional shear over elliptical mountains

Semi-analytical expressions for the momentum flux associated with orographic internal gravity waves, and closed analytical expressions for its divergence, are derived for inviscid, stationary, hydrostatic, directionally-sheared flow over mountains with an elliptical horizontal cross-section. These calculations, obtained using linear theory conjugated with a third-order WKB approximation, are valid for relatively slowly-varying, but otherwise generic wind profiles, and given in a form that is straightforward to implement in drag parametrization schemes. When normalized by the surface drag in the absence of shear, a quantity that is calculated routinely in existing drag parametrizations, the momentum flux becomes independent of the detailed shape of the orography. Unlike linear theory in the Ri → ∞ limit, the present calculations account for shear-induced amplification or reduction of the surface drag, and partial absorption of the wave momentum flux at critical levels. Profiles of the normalized momentum fluxes obtained using this model and a linear numerical model without the WKB approximation are evaluated and compared for two idealized wind profiles with directional shear, for different Richardson numbers (Ri). Agreement is found to be excellent for the first wind profile (where one of the wind components varies linearly) down to Ri = 0.5, while not so satisfactory, but still showing a large improvement relative to the Ri → ∞ limit, for the second wind profile (where the wind turns with height at a constant rate keeping a constant magnitude). These results are complementary, in the Ri > O(1) parameter range, to Broad’s generalization of the Eliassen–Palm theorem to 3D flow. They should contribute to improve drag parametrizations used in global weather and climate prediction models.

Constraining H-0 in general dark energy models from Sunyaev-Zeldovich/X-ray technique and complementary probes

In accelerating dark energy models, the estimates of the Hubble constant, Ho, from Sunyaev-Zerdovich effect (SZE) and X-ray surface brightness of galaxy clusters may depend on the matter content (Omega(M)), the curvature (Omega(K)) and the equation of state parameter GO. In this article, by using a sample of 25 angular diameter distances of galaxy clusters described by the elliptical beta model obtained through the SZE/X-ray technique, we constrain Ho in the framework of a general ACDM model (arbitrary curvature) and a flat XCDM model with a constant equation of state parameter omega = p(x)/rho(x). In order to avoid the use of priors in the cosmological parameters, we apply a joint analysis involving the baryon acoustic oscillations (BA()) and the (MB Shift Parameter signature. By taking into account the statistical and systematic errors of the SZE/X-ray technique we obtain for nonflat ACDM model H-0 = 74(-4.0)(+5.0) km s(-1) Mpc(-1) (1 sigma) whereas for a fiat universe with constant equation of state parameter we find H-0 = 72(-4.0)(+5.5) km s(-1) Mpc(-1)(1 sigma). By assuming that galaxy clusters are described by a spherical beta model these results change to H-0 = 6(-7.0)(+8.0) and H-0 = 59(-6.0)(+9.0) km s(-1) Mpc(-1)(1 sigma), respectively. The results from elliptical description are in good agreement with independent studies from the Hubble Space Telescope key project and recent estimates based on the Wilkinson Microwave Anisotropy Probe, thereby suggesting that the combination of these three independent phenomena provides an interesting method to constrain the Bubble constant. As an extra bonus, the adoption of the elliptical description is revealed to be a quite realistic assumption. Finally, by comparing these results with a recent determination for a, flat ACDM model using only the SZE/X-ray technique and BAO, we see that the geometry has a very weak influence on H-0 estimates for this combination of data.

Analysis and validation of CFD wind farm models in complex terrain. Effects induced by topography and wind turbines

Wind farms have been extensively simulated through engineering models for the estimation of wind speed and power deficits inside wind farms. These models were designed initially for a few wind turbines located in flat terrain. Other models based on the parabolic approximation of Navier Stokes equations were developed, making more realistic and feasible the operational resolution of big wind farms in flat terrain and offshore sites. These models have demonstrated to be accurate enough when solving wake effects for this type of environments. Nevertheless, few analyses exist on how complex terrain can affect the behaviour of wind farm wake flow. Recent numerical studies have demonstrated that topographical wakes induce a significant effect on wind turbines wakes, compared to that on flat terrain. This circumstance has recommended the development of elliptic CFD models which allow global simulation of wind turbine wakes in complex terrain. An accurate simplification for the analysis of wind turbine wakes is the actuator disk technique. Coupling this technique with CFD wind models enables the estimation of wind farm wakes preserving the extraction of axial momentum present inside wind farms. This paper describes the analysis and validation of the elliptical wake model CFDWake 1.0 against experimental data from an operating wind farm located in complex terrain. The analysis also reports whether it is possible or not to superimpose linearly the effect of terrain and wind turbine wakes. It also represents one of the first attempts to observe the performance of engineering models compares in large complex terrain wind farms.