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.

Bayesian Analysis for Nonlinear Regression Model Under Skewed Errors, with Application in Growth Curves

We have considered a Bayesian approach for the nonlinear regression model by replacing the normal distribution on the error term by some skewed distributions, which account for both skewness and heavy tails or skewness alone. The type of data considered in this paper concerns repeated measurements taken in time on a set of individuals. Such multiple observations on the same individual generally produce serially correlated outcomes. Thus, additionally, our model does allow for a correlation between observations made from the same individual. We have illustrated the procedure using a data set to study the growth curves of a clinic measurement of a group of pregnant women from an obstetrics clinic in Santiago, Chile. Parameter estimation and prediction were carried out using appropriate posterior simulation schemes based in Markov Chain Monte Carlo methods. Besides the deviance information criterion (DIC) and the conditional predictive ordinate (CPO), we suggest the use of proper scoring rules based on the posterior predictive distribution for comparing models. For our data set, all these criteria chose the skew-t model as the best model for the errors. These DIC and CPO criteria are also validated, for the model proposed here, through a simulation study. As a conclusion of this study, the DIC criterion is not trustful for this kind of complex model.

Do higher moments really matter in portfolio choice?

We present explicit formulas for evaluating the difference between Markowitz weights and those from optimal portfolios, with the same given return, considering either asymmetry or kurtosis. We prove that, whenever the higher moment constraint is not binding, the weights are never the same. If, due to special features of the first and second moments, the difference might be negligible, in quite many cases it will be very significant. An appealing illustration, when the designer wants to incorporate an asset with quite heavy tails, but wants to moderate this effect, further supports the argument.

Effect of nonnormal random components on level and power in group-randomized trials

The use of group-randomized trials is particularly widespread in the evaluation of health care, educational, and screening strategies. Group-randomized trials represent a subset of a larger class of designs often labeled nested, hierarchical, or multilevel and are characterized by the randomization of intact social units or groups, rather than individuals. The application of random effects models to group-randomized trials requires the specification of fixed and random components of the model. The underlying assumption is usually that these random components are normally distributed. This research is intended to determine if the Type I error rate and power are affected when the assumption of normality for the random component representing the group effect is violated. ^ In this study, simulated data are used to examine the Type I error rate, power, bias and mean squared error of the estimates of the fixed effect and the observed intraclass correlation coefficient (ICC) when the random component representing the group effect possess distributions with non-normal characteristics, such as heavy tails or severe skewness. The simulated data are generated with various characteristics (e.g. number of schools per condition, number of students per school, and several within school ICCs) observed in most small, school-based, group-randomized trials. The analysis is carried out using SAS PROC MIXED, Version 6.12, with random effects specified in a random statement and restricted maximum likelihood (REML) estimation specified. The results from the non-normally distributed data are compared to the results obtained from the analysis of data with similar design characteristics but normally distributed random effects. ^ The results suggest that the violation of the normality assumption for the group component by a skewed or heavy-tailed distribution does not appear to influence the estimation of the fixed effect, Type I error, and power. Negative biases were detected when estimating the sample ICC and dramatically increased in magnitude as the true ICC increased. These biases were not as pronounced when the true ICC was within the range observed in most group-randomized trials (i.e. 0.00 to 0.05). The normally distributed group effect also resulted in bias ICC estimates when the true ICC was greater than 0.05. However, this may be a result of higher correlation within the data. ^

Empirical Analysis of Credit Risk Regime Switching and Temporal Conditional Default Correlation in Credit Default Swap Valuation: The Market liquidity effect

In this paper, we extend the debate concerning Credit Default Swap valuation to include time varying correlation and co-variances. Traditional multi-variate techniques treat the correlations between covariates as constant over time; however, this view is not supported by the data. Secondly, since financial data does not follow a normal distribution because of its heavy tails, modeling the data using a Generalized Linear model (GLM) incorporating copulas emerge as a more robust technique over traditional approaches. This paper also includes an empirical analysis of the regime switching dynamics of credit risk in the presence of liquidity by following the general practice of assuming that credit and market risk follow a Markov process. The study was based on Credit Default Swap data obtained from Bloomberg that spanned the period January 1st 2004 to August 08th 2006. The empirical examination of the regime switching tendencies provided quantitative support to the anecdotal view that liquidity decreases as credit quality deteriorates. The analysis also examined the joint probability distribution of the credit risk determinants across credit quality through the use of a copula function which disaggregates the behavior embedded in the marginal gamma distributions, so as to isolate the level of dependence which is captured in the copula function. The results suggest that the time varying joint correlation matrix performed far superior as compared to the constant correlation matrix; the centerpiece of linear regression models.

Portfolio efficiency tests with conditioning information using empirical likelihood estimation

We evaluate the use of Generalized Empirical Likelihood (GEL) estimators in portfolios efficiency tests for asset pricing models in the presence of conditional information. Estimators from GEL family presents some optimal statistical properties, such as robustness to misspecification and better properties in finite samples. Unlike GMM, the bias for GEL estimators do not increase as more moment conditions are included, which is expected in conditional efficiency analysis. We found some evidences that estimators from GEL class really performs differently in small samples, where efficiency tests using GEL generate lower estimates compared to tests using the standard approach with GMM. With Monte Carlo experiments we see that GEL has better performance when distortions are present in data, especially under heavy tails and Gaussian shocks.

Weak Convergence to the Tangent Process of the Linear Multifractional Stable Motion

2000 Mathematics Subject Classification: 60G18, 60E07

Geometrical Methods in Multivariate Risk Management: Algorithms and Applications

This thesis builds a framework for evaluating downside risk from multivariate data via a special class of risk measures (RM). The peculiarity of the analysis lies in getting rid of strong data distributional assumptions and in orientation towards the most critical data in risk management: those with asymmetries and heavy tails. At the same time, under typical assumptions, such as the ellipticity of the data probability distribution, the conformity with classical methods is shown. The constructed class of RM is a multivariate generalization of the coherent distortion RM, which possess valuable properties for a risk manager. The design of the framework is twofold. The first part contains new computational geometry methods for the high-dimensional data. The developed algorithms demonstrate computability of geometrical concepts used for constructing the RM. These concepts bring visuality and simplify interpretation of the RM. The second part develops models for applying the framework to actual problems. The spectrum of applications varies from robust portfolio selection up to broader spheres, such as stochastic conic optimization with risk constraints or supervised machine learning.

A new family of multivariate heavy-tailed distributions with variable marginal amounts of tailweight: Application to robust clustering

We propose a family of multivariate heavy-tailed distributions that allow variable marginal amounts of tailweight. The originality comes from introducing multidimensional instead of univariate scale variables for the mixture of scaled Gaussian family of distributions. In contrast to most existing approaches, the derived distributions can account for a variety of shapes and have a simple tractable form with a closed-form probability density function whatever the dimension. We examine a number of properties of these distributions and illustrate them in the particular case of Pearson type VII and t tails. For these latter cases, we provide maximum likelihood estimation of the parameters and illustrate their modelling flexibility on simulated and real data clustering examples.

A candidate gene approach to identify DNA markers associated with meat quality and production traits: investigation of several cathepsin genes in Italian heavy pigs.

The cathepsin enzymes represent an important family of lysosomal proteinases with a broad spectrum of functions in many, if not in all, tissues and cell types. In addition to their primary role during the normal protein turnover, they possess highly specific proteolytic activities, including antigen processing in the immune response and a direct role in the development of obesity and tumours. In pigs, the involvement of cathepsin enzymes in proteolytic processes have important effects during the conversion of muscle to meat, due to their influence on meat texture and sensory characteristics, mainly in seasoned products. Their contribution is fundamental in flavour development of dry-curing hams. However, several authors have demonstrated that high cathepsin activity, in particular of cathepsin B, is correlated to defects of these products, such as an excessive meat softness together with abnormal free tyrosine content, astringent or metallic aftertastes and formation of a white film on the cut surface. Thus, investigation of their genetic variability could be useful to identify DNA markers associated with these dry cured hams parameters, but also with meat quality, production and carcass traits in Italian heavy pigs. Unfortunately, no association has been found between cathepsin markers and meat quality traits so far, in particular with cathepsin B activity, suggesting that other genes, besides these, affect meat quality parameters. Nevertheless, significant associations were observed with several carcass and production traits in pigs. A recent study has demonstrated that different single nucleotide polymorphisms (SNPs) localized in cathepsin D (CTSD), F (CTSF), H and Z genes were highly associated with growth, fat deposition and production traits in an Italian Large White pig population. The aim of this thesis was to confirm some of these results in other pig populations and identify new cathepsin markers in order to evaluate their effects on cathepsin activity and other production traits. Furthermore, starting from the data obtained in previous studies on CTSD gene, we also analyzed the known polymorphism located in the insulin-like growth factor 2 gene (IGF2 intron3-g.3072G>A). This marker is considered the causative mutation for the quantitative trait loci (QTL) affecting muscle mass and fat deposition in pigs. Since IGF2 maps very close to CTSD on porcine chromosome (SSC) 2, we wanted to clarify if the effects of the CTSD marker were due to linkage disequilibrium with the IGF2 intron3-g.3072G>A mutation or not. In the first chapter, we reported the results from these two SSC2 gene markers. First of all, we evaluated the effects of the IGF2 intron3-g.3072G>A polymorphism in the Italian Large White breed, for which no previous studies have analysed this marker. Highly significant associations were identified with all estimated breeding values for production and carcass traits (P<0.00001), while no effects were observed for meat quality traits. Instead, the IGF2 intron3-g.3072G>A mutation did not show any associations with the analyzed traits in the Italian Duroc pigs, probably due to the low level of variability at this polymorphic site for this breed. In the same Duroc pig population, significant associations were obtained for the CTSD marker for all production and carcass traits (P < 0.001), after excluding possible confounding effects of the IGF2 mutation. The effects of the CTSD g.70G>A polymorphism were also confirmed in a group of Italian Large White pigs homozygous for the IGF2 intron3-g.3072G allele G (IGF2 intron3-g.3072GG) and by haplotype analysis between the markers of the two considered genes. Taken together, all these data indicated that the IGF2 intron3-g.3072G>A mutation is not the only polymorphism affecting fatness and muscle deposition in pigs. In the second chapter, we reported the analysis of two new SNPs identified in cathepsin L (CTSL) and cathepsin S (CTSS) genes and the association results with meat quality parameters (including cathepsin B activity) and several production traits in an Italian Large White pig population. Allele frequencies of these two markers were evaluated in 7 different pig breeds. Furthermore, we mapped using a radiation hybrid panel the CTSS gene on SSC4. Association studies with several production traits, carried out in 268 Italian Large White pigs, indicated positive effects of the CTSL polymorphism on average daily gain, weight of lean cuts and backfat thickness (P<0.05). The results for these latter traits were also confirmed using a selective genotype approach in other Italian Large White pigs (P<0.01). In the 268 pig group, the CTSS polymorphism was associated with feed:gain ratio and average daily gain (P<0.05). Instead, no association was observed between the analysed markers and meat quality parameters. Finally, we wanted to verify if the positive results obtained for the cathepsin L and S markers and for other previous identified SNPs (cathepsin F, cathepsin Z and their inhibitor cystatin B) were confirmed in the Italian Duroc pig breed (third chapter). We analysed them in two groups of Duroc pigs: the first group was made of 218 performance-tested pigs not selected by any phenotypic criteria, the second group was made of 100 Italian Duroc pigs extreme and divergent for visible intermuscular fat trait. In the first group, the CTSL polymorphism was associated with weight of lean cuts (P<0.05), while suggestive associations were obtained for average daily gain and backfat thickness (P<0.10). Allele frequencies of the CTSL gene marker also differed positively among the visible intermuscular extreme tails. Instead, no positive effects were observed for the other DNA markers on the analysed traits. In conclusion, in agreement with the present data and for the biological role of these enzymes, the porcine CTSD and CTSL markers: a) may have a direct effect in the biological mechanisms involved in determining fat and lean meat content in pigs, or b) these markers could be very close to the putative functional mutation(s) present in other genes. These findings have important practical applications, in particular the CTSD and CTSL mutations could be applied in a marker assisted selection (MAS) both in the Italian Large White and Italian Duroc breeds. Marker assisted selection could also increase in efficiency by adding information from the cathepsin S genotype, but only in the Italian Large White breed.

Of tails and Tempests : Feminine sexuality and Shakespearean children's texts

This paper reads a range of nineteenth-century texts for children that retell either Shakespeare's The Tempest or mermaid narratives, considering the models of feminine subjectivity and sexuality that they construct. It then moves on to two key contemporary texts — Disney's film adaptation of The Little Mermaid (Clements and Musker 1989) and Penni Russon's Undine (2004) — that combine the Shakespearean heroine with the mermaid, and reads them against the nineteenth-century models. Ultimately, the essay determines that, while these texts seem to perform a progressive appropriation of the two traditions, they actually combine the most conservative aspects of both The Tempest and mermaid stories to produce authoritative (and dangerously persuasive) ideals of passive feminine sexuality that confine girls within patriarchally-dictated familial positions. The new figure for adolescent female subjectivity, the mermaid-Miranda, becomes in turn a model of identification and aspiration for the implied juvenile consumer.