134 research outputs found
Bayesian binary quantile regression for the analysis of Bachelor-Master transition
The multi-cycle organization of modern university systems stimulates the
interest in studying the progression to higher level degree courses during the
academic career. In particular, after the achievement of the first level
qualification (Bachelor degree), students have to decide whether to continue
their university studies, by enrolling in a second level (Master) programme, or
to conclude their training experience. In this work we propose a binary
quantile regression approach to analyze the Bachelor-Master transition
phenomenon with the adoption of the Bayesian inferential perspective. In
addition to the traditional predictors of academic outcomes, such as the
personal characteristics and the field of study, different aspects of the
student's performance are considered. Moreover, a new contextual variable,
indicating the type of university regulations, is taken into account in the
model specification. The utility of the Bayesian binary quantile regression to
characterize the non-continuation decision after the first cycle studies is
illustrated with an application to administrative data of Bachelor graduates at
the School of Economics of Sapienza University of Rome and compared with a more
conventional logistic regression approach.Comment: 24 pages, 7 figures and 3 table
On the Lp-quantiles for the Student t distribution
L_p-quantiles represent an important class of generalised quantiles and are
defined as the minimisers of an expected asymmetric power function, see Chen
(1996). For p=1 and p=2 they correspond respectively to the quantiles and the
expectiles. In his paper Koenker (1993) showed that the tau quantile and the
tau expectile coincide for every tau in (0,1) for a class of rescaled Student t
distributions with two degrees of freedom. Here, we extend this result proving
that for the Student t distribution with p degrees of freedom, the tau quantile
and the tau L_p-quantile coincide for every tau in (0,1) and the same holds for
any affine transformation. Furthermore, we investigate the properties of
L_p-quantiles and provide recursive equations for the truncated moments of the
Student t distribution
Large deviations for risk measures in finite mixture models
Due to their heterogeneity, insurance risks can be properly described as a
mixture of different fixed models, where the weights assigned to each model may
be estimated empirically from a sample of available data. If a risk measure is
evaluated on the estimated mixture instead of the (unknown) true one, then it
is important to investigate the committed error. In this paper we study the
asymptotic behaviour of estimated risk measures, as the data sample size tends
to infinity, in the fashion of large deviations. We obtain large deviation
results by applying the contraction principle, and the rate functions are given
by a suitable variational formula; explicit expressions are available for
mixtures of two models. Finally, our results are applied to the most common
risk measures, namely the quantiles, the Expected Shortfall and the shortfall
risk measures
Bayesian inference for CoVaR
Recent financial disasters emphasised the need to investigate the consequence
associated with the tail co-movements among institutions; episodes of contagion
are frequently observed and increase the probability of large losses affecting
market participants' risk capital. Commonly used risk management tools fail to
account for potential spillover effects among institutions because they provide
individual risk assessment. We contribute to analyse the interdependence
effects of extreme events providing an estimation tool for evaluating the
Conditional Value-at-Risk (CoVaR) defined as the Value-at-Risk of an
institution conditioned on another institution being under distress. In
particular, our approach relies on Bayesian quantile regression framework. We
propose a Markov chain Monte Carlo algorithm exploiting the Asymmetric Laplace
distribution and its representation as a location-scale mixture of Normals.
Moreover, since risk measures are usually evaluated on time series data and
returns typically change over time, we extend the CoVaR model to account for
the dynamics of the tail behaviour. Application on U.S. companies belonging to
different sectors of the Standard and Poor's Composite Index (S&P500) is
considered to evaluate the marginal contribution to the overall systemic risk
of each individual institutio
Joint estimation of conditional quantiles in multivariate linear regression models. An application to financial distress
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
Quantile and expectile copula-based hidden Markov regression models for the analysis of the cryptocurrency market
The role of cryptocurrencies within the financial systems has been expanding
rapidly in recent years among investors and institutions. It is therefore
crucial to investigate the phenomena and develop statistical methods able to
capture their interrelationships, the links with other global systems, and, at
the same time, the serial heterogeneity. For these reasons, this paper
introduces hidden Markov regression models for jointly estimating quantiles and
expectiles of cryptocurrency returns using regime-switching copulas. The
proposed approach allows us to focus on extreme returns and describe their
temporal evolution by introducing time-dependent coefficients evolving
according to a latent Markov chain. Moreover to model their time-varying
dependence structure, we consider elliptical copula functions defined by
state-specific parameters. Maximum likelihood estimates are obtained via an
Expectation-Maximization algorithm. The empirical analysis investigates the
relationship between daily returns of five cryptocurrencies and major world
market indices.Comment: 35 pages, 6 figures. arXiv admin note: text overlap with
arXiv:2301.0972
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