Characterizations of Bivariate Models Using Some Dynamic Conditional Information Divergence Measures

In this article, we study some relevant information divergence measures viz. Renyi divergence and Kerridge’s inaccuracy measures. These measures are extended to conditionally specifiedmodels and they are used to characterize some bivariate distributions using the concepts of weighted and proportional hazard rate models. Moreover, some bounds are obtained for these measures using the likelihood ratio order

Autoregressive conditional kurtosis

This article proposes a new model for autoregressive conditional heteroscedasticity and kurtosis. Via a time-varying degrees of freedom parameter, the conditional variance and conditional kurtosis are permitted to evolve separately. The model uses only the standard Student’s t-density and consequently can be estimated simply using maximum likelihood. The method is applied to a set of four daily financial asset return series comprising U.S. and U.K. stocks and bonds, and significant evidence in favor of the presence of autoregressive conditional kurtosis is observed. Various extensions to the basic model are proposed, and we show that the response of kurtosis to good and bad news is not significantly asymmetric.

Conditional mean functions of non-linear models of US output

We compare a number of models of post War US output growth in terms of the degree and pattern of non-linearity they impart to the conditional mean, where we condition on either the previous period's growth rate, or the previous two periods' growth rates. The conditional means are estimated non-parametrically using a nearest-neighbour technique on data simulated from the models. In this way, we condense the complex, dynamic, responses that may be present in to graphical displays of the implied conditional mean.

Threshold autoregressive and Markov switching models: an application to commercial real estate

Although financial theory rests heavily upon the assumption that asset returns are normally distributed, value indices of commercial real estate display significant departures from normality. In this paper, we apply and compare the properties of two recently proposed regime switching models for value indices of commercial real estate in the US and the UK, both of which relax the assumption that observations are drawn from a single distribution with constant mean and variance. Statistical tests of the models' specification indicate that the Markov switching model is better able to capture the non-stationary features of the data than the threshold autoregressive model, although both represent superior descriptions of the data than the models that allow for only one state. Our results have several implications for theoretical models and empirical research in finance.

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.

Tests of conditional asset pricing models in the brazilian stock market

In this paper, we test a version of the conditional CAPM with respect to a local market portfolio, proxied by the Brazilian stock index during the period 1976-1992. We also test a conditional APT modeI by using the difference between the 3-day rate (Cdb) and the overnight rate as a second factor in addition to the market portfolio in order to capture the large inflation risk present during this period. The conditional CAPM and APT models are estimated by the Generalized Method of Moments (GMM) and tested on a set of size portfolios created from individual securities exchanged on the Brazilian markets. The inclusion of this second factor proves to be important for the appropriate pricing of the portfolios.

A conditional likelihood ratio test for structural models

This paper develops a general method for constructing similar tests based on the conditional distribution of nonpivotal statistics in a simultaneous equations model with normal errors and known reducedform covariance matrix. The test based on the likelihood ratio statistic is particularly simple and has good power properties. When identification is strong, the power curve of this conditional likelihood ratio test is essentially equal to the power envelope for similar tests. Monte Carlo simulations also suggest that this test dominates the Anderson- Rubin test and the score test. Dropping the restrictive assumption of disturbances normally distributed with known covariance matrix, approximate conditional tests are found that behave well in small samples even when identification is weak.

Critical points on growth curves in autoregressive and mixed models

Adjusting autoregressive and mixed models to growth data fits discontinuous functions, which makes it difficult to determine critical points. In this study we propose a new approach to determine the critical stability point of cattle growth using a first-order autoregressive model and a mixed model with random asymptote, using the deterministic portion of the models. Three functions were compared: logistic, Gompertz, and Richards. The Richards autoregressive model yielded the best fit, but the critical growth values were adjusted very early, and for this purpose the Gompertz model was more appropriate.

Computational tools for comparing asymmetric GARCH models via Bayes factors

In this paper we use Markov chain Monte Carlo (MCMC) methods in order to estimate and compare GARCH models from a Bayesian perspective. We allow for possibly heavy tailed and asymmetric distributions in the error term. We use a general method proposed in the literature to introduce skewness into a continuous unimodal and symmetric distribution. For each model we compute an approximation to the marginal likelihood, based on the MCMC output. From these approximations we compute Bayes factors and posterior model probabilities. (C) 2012 IMACS. Published by Elsevier B.V. All rights reserved.

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.

Conditional and transgenic mouse models as tools to study the role of TGFbeta, BMP signaling in skeletal development

Die TGFbeta/BMP Signaltransduktionskaskade ist wichtig für viele Entwicklungsprozesse fast aller embryonaler sowie extraembryonaler Gewebe und sie ist ebenso essentiell bei der Aufrechterhaltung der Homöostase im adulten Organismus. In vielen Mausmodellen und Zellkulturversuchen wurde gezeigt, dass Liganden dieses Signalweges in verschiedene Stadien der Knorpel- und Knochenentwicklung involviert sind. BMPs sind beispielsweise maßgeblich an der frühen Kondensation und Bildung des Knorpels und später an Proliferation und Hypertrophie der Chondrozyten beteiligt. BMPs können ektopisch Knochenbildung auslösen und das Expressionsmuster der Liganden und spezifischen Rezeptoren in der Wachstumsfuge lässt auf eine wichtige Rolle der BMPs in der Wachstumsfuge schließen. Der gezielte knock out der BMP-Rezeptoren Bmpr1a und Bmpr1b in proliferierenden Chondrozyten führt zur Ausbildung einer generellen Chondrodysplasie. Smad1, Smad5 und Smad8 sind die Mediatoren der BMP-Signalkaskade. Im Rahmen der vorliegenden Arbeit sollte die Rolle und Funktion der Smad1- und Smad5-Proteine in der Wachstumsfuge untersucht werden. Hierzu wurden konditionale Smad1-knock out-Mäuse mit einer transgenen Mauslinie gekreuzt, die die Cre-Rekombinase spezifisch in proliferierenden Chondrozyten exprimiert. Diese Mäuse wurden mit und ohne heterozygotem Smad5-Hintergrund charakterisiert. Bei einem knock out von Smad1 allein konnte ein leichte Verkürzung der Wachstumsfuge beobachtet werden, wobei prähypertrophe und hypertrophe Zone gleichermaßen betroffen waren. Dieser Phänotyp war verstärkt in Mäusen mit zusätzlichem heterozygotem Smad5-Hintergrund. Eine Verringerung der Proliferationsrate konnte zusammen mit einer verminderten Ihh-Expression nachgewiesen werden. Zusätzlich konnte anhand von Röntgenaufnahmen eine Dysorganisation der nasalen Region und ein fehlendes nasales Septum beobachtet werden. Produktion und Mineralisation der extrazellulären Matrix waren nicht beeinträchtigt. Um die Rolle der BMP- und TGFbeta-Signalkaskaden während der endochondralen Ossifikation zu vergleichen, wurden transgene Mäuse generiert, in denen die TGFbeta-Signalkaskade spezifisch in proliferierenden Chondrozyten gestört war. Zwei Mauslinien, die ähnliche Phänotypen zeigten, wurden untersucht. Esl1 ist ein TGFbeta-bindendes Protein, von dem man annimmt, dass es die TGFbeta-Signalkaskade inhibieren kann. Esl1-knock out-Mäuse sind kleiner als Wildtypmäuse und die Überexpression von Esl1 in proliferierenden Chondrozyten führt zu einer Verlängerung der Wachstumsfuge und einer verstärkten Proliferationsrate. Knorpelmarker, wie Col2a1 und Sox9 sind in diesen Mäusen herunterreguliert, während Col10a1 und Ihh als Marker für die hypertrophe und prähypertrophe Zone herunterreguliert waren. Dies führt zu der Annahme, dass mehr Zellen in die terminale Differenzierung eintreten. Bei transgenen Mäusen, in denen ein dominant-negativer (dn) TGFbeta-Rezeptor in proliferierenden Chondrozyten überexprimiert wurde, konnte eine verlängerte prähypertrophe Zone, eine erhöhte Ihh-Expression, sowie eine verstärkte Proliferationsrate beobachtet werden. Zusätzlich konnte in homozygoten Tieren ein craniofacialer Phänotyp beschrieben werden, der zu Problemen bei der Nahrungsaufnahme und damit zu einer starken Wachstumsbeeinträchtigung führte. Die BMP- und TGFbeta-Signalkaskaden haben möglicherweise antagonistische Effekte in der Wachstumsfuge. Während der Ausfall von BMP in proliferierenden Chondrozyten aufgrund einer gesunkenen Proliferationsrate zu einer Verkürzung der Wachstumsfuge führte, kann man in Mäusen mit einer Störung der TGFbeta-Signalkaskade eine verstärkte Proliferation in einer daher verlängerten Wachstumsfuge beobachten. Ein weiteres Ziel dieser Arbeit war die Generation einer transgenen Mauslinie, die die Cre-Rekombinase spezifisch in hypertrophen Chondrozyten exprimiert. Promoterstudien mit transgenen Mäusen weisen darauf hin, dass ein putatives AP1-Element, etwa 4 kb vor dem ersten Exon des Col10a1 gelegen, wichtig für die spezifische Expression in hypertrophen Chondrozyten ist. Ein Konstrukt, dass vier Kopien dieses Elements und den basalen Promoter enthält, wurde benutzt, um die Cre-Rekombinase spezifisch zu exprimieren. Diese Mauslinie befindet sich in der Testphase und erste Daten deuten auf eine spezifische Expression der Cre-Rekombinase in hypertrophen Chondrozyten hin.

On the Behaviour of Marginal and Conditional Akaike Information Criteria in Linear Mixed Models

In linear mixed models, model selection frequently includes the selection of random effects. Two versions of the Akaike information criterion (AIC) have been used, based either on the marginal or on the conditional distribution. We show that the marginal AIC is no longer an asymptotically unbiased estimator of the Akaike information, and in fact favours smaller models without random effects. For the conditional AIC, we show that ignoring estimation uncertainty in the random effects covariance matrix, as is common practice, induces a bias that leads to the selection of any random effect not predicted to be exactly zero. We derive an analytic representation of a corrected version of the conditional AIC, which avoids the high computational cost and imprecision of available numerical approximations. An implementation in an R package is provided. All theoretical results are illustrated in simulation studies, and their impact in practice is investigated in an analysis of childhood malnutrition in Zambia.