DES - Working Papers. Statistics and Econometrics. WS
http://hdl.handle.net/10016/14
2015-04-27T09:08:10ZBayesian Linear Regression with Conditional Heteroskedasticity
http://hdl.handle.net/10016/20436
Bayesian Linear Regression with Conditional Heteroskedasticity
Zhao, Yanyun
In this paper we consider adaptive Bayesian semiparametric analysis of the linear regression model in the presence of conditional heteroskedasticity. The distribution of the error term on predictors are modelled by a normal distribution with covariate-dependent variance. We show that a rate-adaptive procedure for all smoothness levels of this standard deviation function is performed if the prior is properly chosen. More specifically, we derive adaptive posterior distribution rate up to a logarithm factor for the conditional standard deviation based on a transformation of hierarchical Gaussian spline prior and log-spline prior respectively.
2015-04-01T00:00:00ZTwo-sample Hotelling's T² statistics based on the functional Mahalanobis semi-distance
http://hdl.handle.net/10016/20253
Two-sample Hotelling's T² statistics based on the functional Mahalanobis semi-distance
Joseph, Esdras; Galeano, Pedro; Lillo, Rosa E.
Universidad Carlos III de Madrid. Departamento de Estadística
The comparison of the means of two independent samples is one of the most popular problems in real-world data analysis. In the multivariate context, two-sample Hotelling's T² frequently used to test the equality of means of two independent Gaussian random samples assuming either the same or a different covariance matrix. In this paper, we derive two-sample Hotelling's T² from two functional distributions. The statistics that we propose are based on the functional Mahalanobis semi-distance and, under certain conditions, their asymptotic distributions are chisquared, regardless the distribution of the functional random samples. Additionally, we provide the link between the two-sample Hotelling's T² semi-distance and statistics based on the functional principal components semi-distance. A Monte Carlo study indicates that the twosample Hotelling's T² of power those based on the functional principal components semidistance. We analyze a data set of daily temperature records of 35 Canadian weather stations over a year with the goal of testing whether or not the mean temperature functions of the stations in the Eastern and Western Canada regions are equal. The results appear to indicate differences between both regions that are not found with statistics based on the functional principal components semi-distance.
2015-03-01T00:00:00ZSmall versus big-data factor extraction in Dynamic Factor Models: An empirical assessment
http://hdl.handle.net/10016/20103
Small versus big-data factor extraction in Dynamic Factor Models: An empirical assessment
Ruiz, Esther; Poncela, Pilar
Universidad Carlos III de Madrid. Departamento de Estadística
In the context of Dynamic Factor Models (DFM), we compare point and interval estimates of the underlying unobserved factors extracted using small and big-data procedures. Our paper differs from previous works in the related literature in several ways. First, we focus on factor extraction rather than on prediction of a given variable in the system. Second, the comparisons are carried out by implementing the procedures considered to the same data. Third, we are interested not only on point estimates but also on confidence intervals for the factors. Based on a simulated system and the macroeconomic data set popularized by Stock and Watson (2012), we show that, for a given procedure, factor estimates based on different cross-sectional dimensions are highly correlated. On the other hand, given the cross-sectional dimension, the Maximum Likelihood Kalman filter and smoother (KFS) factor estimates are highly correlated with those obtained using hybrid Principal Components (PC) and KFS procedures. The PC estimates are somehow less correlated. Finally, the PC intervals based on asymptotic approximations are unrealistically tiny.
2015-01-01T00:00:00ZA Directional Multivariate Value at Risk
http://hdl.handle.net/10016/20088
A Directional Multivariate Value at Risk
Torres, Raúl; Lillo, Rosa E.; Laniado, Henry
Universidad Carlos III de Madrid. Departamento de Estadística
In economics, insurance and finance, value at risk (VaR) is a widely used measure of the risk of loss on a specific portfolio of financial assets. For a given portfolio, time horizon, and probability alfa, the 100alfa% VaR is defined as a threshold loss value, such that the probability that the loss on the portfolio over the given time horizon exceeds this value is alfa. That is to say, it is a quantile of the distribution of the losses, which has both good analytic properties and easy interpretation as a risk measure. However, its extension to the multivariate framework is not unique because a unique definition of multivariate quantile does not exist. In the current literature, the multivariate quantiles are related to a specific partial order considered in Rn, or to a property of the univariate quantile that is desirable to be extended to Rn. In this work, we introduce a multivariate value at risk as a vector-valued directional risk measure, based on a directional multivariate quantile, which has recently been introduced in the literature. The directional approach allows the manager to consider external information or risk preferences in her/his analysis. We have derived some properties of the risk measure and we have compared the univariate VaR over the marginals with the components of the directional multivariate VaR. We have also analyzed the relationship between some families of copulas, for which it is possible to obtain closed forms of the multivariate VaR that we propose. Finally, comparisons with other alternative multivariate VaR given in the literature, are provided in terms of robustness.
2015-01-01T00:00:00Z