اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدJoint estimation of conditional quantiles in multivariate linear regression models. An application to financial distress
63
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
This paper proposes a maximum-likelihood approach to jointly estimate marginal conditional quantiles of multivariate response variables in a linear regression framework. We consider a slight reparameterization of the Multivariate Asymmetric Laplace distribution proposed by Kotz et al (2001) and exploit its location-scale mixture representation to implement a new EM algorithm for estimating model parameters. The idea is to extend the link between the Asymmetric Laplace distribution and the well-known univariate quantile regression model to a multivariate context, i.e. when a multivariate dependent variable is concerned. The approach accounts for association among multiple responses and study how the relationship between responses and explanatory variables can vary across different quantiles of the marginal conditional distribution of the responses. A penalized version of the EM algorithm is also presented to tackle the problem of variable selection. The validity of our approach is analyzed in a simulation study, where we also provide evidence on the efficiency gain of the proposed method compared to estimation obtained by separate univariate quantile regressions. A real data application is finally proposed to study the main determinants of financial distress in a sample of Italian firms.
قيم البحث
اقرأ أيضاً
Regression models describing the joint distribution of multivariate response variables conditional on covariate information have become an important aspect of contemporary regression analysis. However, a limitation of such models is that they often r
ely on rather simplistic assumptions, e.g. a constant dependency structure that is not allowed to vary with the covariates or the restriction to linear dependence between the responses only. We propose a general framework for multivariate conditional transformation models that overcomes these limitations and describes the entire distribution in a tractable and interpretable yet flexible way conditional on nonlinear effects of covariates. The framework can be embedded into likelihood-based inference, including results on asymptotic normality, and allows the dependence structure to vary with covariates. In addition, the framework scales well beyond bivariate response situations, which were the main focus of most earlier investigations. We illustrate the application of multivariate conditional transformation models in a trivariate analysis of childhood undernutrition and demonstrate empirically that our approach can be beneficial compared to existing benchmarks such that complex truly multivariate data-generating processes can be inferred from observations.
We propose a multivariate functional responses low rank regression model with possible high dimensional functional responses and scalar covariates. By expanding the slope functions on a set of sieve basis, we reconstruct the basis coefficients as a m
atrix. To estimate these coefficients, we propose an efficient procedure using nuclear norm regularization. We also derive error bounds for our estimates and evaluate our method using simulations. We further apply our method to the Human Connectome Project neuroimaging data to predict cortical surface motor task-evoked functional magnetic resonance imaging signals using various clinical covariates to illustrate the usefulness of our results.
In this paper the method of simulated quantiles (MSQ) of Dominicy and Veredas (2013) and Dominick et al. (2013) is extended to a general multivariate framework (MMSQ) and to provide a sparse estimator of the scale matrix (sparse-MMSQ). The MSQ, like
alternative likelihood-free procedures, is based on the minimisation of the distance between appropriate statistics evaluated on the true and synthetic data simulated from the postulated model. Those statistics are functions of the quantiles providing an effective way to deal with distributions that do not admit moments of any order like the $alpha$-Stable or the Tukey lambda distribution. The lack of a natural ordering represents the major challenge for the extension of the method to the multivariate framework. Here, we rely on the notion of projectional quantile recently introduced by Hallin etal. (2010) and Kong Mizera (2012). We establish consistency and asymptotic normality of the proposed estimator. The smoothly clipped absolute deviation (SCAD) $ell_1$--penalty of Fan and Li (2001) is then introduced into the MMSQ objective function in order to achieve sparse estimation of the scaling matrix which is the major responsible for the curse of dimensionality problem. We extend the asymptotic theory and we show that the sparse-MMSQ estimator enjoys the oracle properties under mild regularity conditions. The method is illustrated and its effectiveness is tested using several synthetic datasets simulated from the Elliptical Stable distribution (ESD) for which alternative methods are recognised to perform poorly. The method is then applied to build a new network-based systemic risk measurement framework. The proposed methodology to build the network relies on a new systemic risk measure and on a parametric test of statistical dominance.
We introduce a new approach to a linear-circular regression problem that relates multiple linear predictors to a circular response. We follow a modeling approach of a wrapped normal distribution that describes angular variables and angular distributi
ons and advances it for a linear-circular regression analysis. Some previous works model a circular variable as projection of a bivariate Gaussian random vector on the unit square, and the statistical inference of the resulting model involves complicated sampling steps. The proposed model treats circular responses as the result of the modulo operation on unobserved linear responses. The resulting model is a mixture of multiple linear-linear regression models. We present two EM algorithms for maximum likelihood estimation of the mixture model, one for a parametric model and another for a non-parametric model. The estimation algorithms provide a great trade-off between computation and estimation accuracy, which was numerically shown using five numerical examples. The proposed approach was applied to a problem of estimating wind directions that typically exhibit complex patterns with large variation and circularity.
The use of quantiles to obtain insights about multivariate data is addressed. It is argued that incisive insights can be obtained by considering directional quantiles, the quantiles of projections. Directional quantile envelopes are proposed as a way
to condense this kind of information; it is demonstrated that they are essentially halfspace (Tukey) depth levels sets, coinciding for elliptic distributions (in particular multivariate normal) with density contours. Relevant questions concerning their indexing, the possibility of the reverse retrieval of directional quantile information, invariance with respect to affine transformations, and approximation/asymptotic properties are studied. It is argued that the analysis in terms of directional quantiles and their envelopes offers a straightforward probabilistic interpretation and thus conveys a concrete quantitative meaning; the directional definition can be adapted to elaborate frameworks, like estimation of extreme quantiles and directional quantile regression, the regression of depth contours on covariates. The latter facilitates the construction of multivariate growth charts---the question that motivated all the development.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
