1,721,050 research outputs found
On quantile regression models for multivariate data
Full text linkThe goal of this thesis is to bridge the gap between univariate and multivariate quantiles by extending the study of univariate quantile regression and its generalizations to multivariate responses. The statistical analysis focuses on a multivariate framework where we consider vector-valued quantile functions associated with multivariate distributions, providing inferential procedures and establishing the asymptotic properties of the proposed estimators. We illustrate their applicability in a wide variety of scientific settings, including time series, longitudinal and clustered data. The dissertation is divided into four chapters, each of them focusing on various aspects of multivariate analysis and different data types and structures. The methodologies we propose are supported by theoretical results and illustrated using simulation studies and real-world data
Multivariate Mixed Hidden Markov Model for joint estimation of multiple quantiles
No full textThis paper develops a Mixed Hidden Markov Model for joint estimation of multiple quantiles in a multivariate linear regression for longitudinal data. This method accounts for association among multiple responses and study how the relationship between dependent and explanatory variables may vary across different quantile levels of the conditional distribution of the multivariate response variable. Unobserved heterogeneity sources and serial dependence are jointly modeled through the introduction of individual-specific, time-constant random coefficients and time-varying parameters that evolve over time with a Markovian structure, respectively. Estimation is carried out via a suitable EM algorithm without parametric assumptions on the random effects distribution. We assess the empirical behaviour of the proposed methodology through the analysis of the Millennium Cohort Study data
Quantile and expectile copula-based hidden Markov regression models for the analysis of the cryptocurrency market
No full textThe role of cryptocurrencies within the financial systems has been expanding rapidly in recent
years among investors and institutions. It is therefore crucial to investigate this phenomenon and develop
statistical methods able to capture their interrelationships, the links with other global systems and,
at the same time, the serial heterogeneity. Here we introduce 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
Directional M-quantile regression for multivariate dependent outcomes
No full textIn the present work we generalize the univariate M-quantile regression to the analysis of multivariate dependent outcomes. Extending the notion of directional quantiles, we introduce directional M-quantiles which are obtained as projections of the original data on a specified unit norm direction. In order to take into consideration the correlation within grouped measurements and to increase efficiency, we develop a marginal M-Quantile regression model extending the well known generalized estimating equations approach. We build M-quantile regions and contours which allow us to investigate the effect of the covariates on the location, spread and shape of the distribution of the responses. To identify potential outliers and provide a simple visual representation of the variability of the M quantile contours estimator, we construct confidence envelope via nonparametric bootstrap. The validity of our method is analyzed through the study of the wages data from the National Longitudinal Survey of Youth
Expectile hidden Markov regression models for analyzing cryptocurrency returns
Full text linkIn this paper we develop a linear expectile hidden Markov model for the
analysis of cryptocurrency time series in a risk management framework. The
methodology proposed allows to focus on extreme returns and describe their
temporal evolution by introducing in the model time-dependent coefficients
evolving according to a latent discrete homogeneous Markov chain. As it is
often used in the expectile literature, estimation of the model parameters is
based on the asymmetric normal distribution. Maximum likelihood estimates are
obtained via an Expectation-Maximization algorithm using efficient M-step
update formulas for all parameters. We evaluate the introduced method with both
artificial data under several experimental settings and real data investigating
the relationship between daily Bitcoin returns and major world market indices
Vacuum Alignment in SUSY A4 Models
No full textIn this note we discuss the vacuum alignment in supersymmetric models with spontaneously broken flavour symmetries in the presence of soft supersymmetry (SUSY) breaking terms. We show that the inclusion of soft SUSY breaking terms can give rise to non-vanishing vacuum expectation values (VEVs) for the auxiliary components of the flavon fields. These non-zero VEVs can have an important impact on the phenomenology of this class of models, since they can induce an additional flavour violating contribution to the sfermion soft mass matrix of right-left (RL) type. We carry out an explicit computation in a class of SUSY A4 models predicting tri-bimaximal mixing in the lepton sector. The flavour symmetry breaking sector is described in terms of flavon and driving supermultiplets. We find non-vanishing VEVs for the auxiliary components of the flavon fields and for the scalar components of the driving fields which are of order m_{SUSY} x and m_{SUSY}, respectively. Thereby, m_{SUSY} is the generic soft SUSY breaking scale which is expected to be around 1 TeV and is the VEV of scalar components of the flavon fields. Another effect of these VEVs can be the generation of a mu term
Quantile mixed hidden Markov models for multivariate longitudinal data: an application to children's Strengths and Difficulties Questionnaire scores
Full text linkThe identification of factors associated with mental and behavioural disorders in early childhood is critical both for psychopathology research and the support of primary health care practices. Motivated by the Millennium Cohort Study, in this paper we study the effect of a comprehensive set of covariates on children's emotional and behavioural trajectories in England. To this end, we develop a quantile mixed hidden Markov model for joint estimation of multiple quantiles in a linear regression setting for multivariate longitudinal data. The novelty of the proposed approach is based on the multivariate asymmetric Laplace distribution which allows to jointly estimate the quantiles of the univariate conditional distributions of a multivariate response, accounting for possible correlation between the outcomes. Sources of unobserved heterogeneity and serial dependency due to repeated measures are modelled through the introduction of individual-specific, time-constant random coefficients and time-varying parameters evolving over time with a Markovian structure respectively. The inferential approach is carried out through the construction of a suitable expectation–maximization algorithm without parametric assumptions on the random effects distribution.</p
Lepton Flavour Violation in Models with A(4) Flavour Symmetry
No full textWe analyze lepton flavour violating transitions, leptonic magnetic dipole moments (MDMs) and electric dipole moments (EDMs) in a class of models characterized by the flavour symmetry A4×Z3×UFN(1), whose choice is motivated by the approximate tri-bimaximal mixing observed in neutrino oscillations. We construct the relevant low-energy effective Lagrangian where these effects are dominated by dimension six operators, suppressed by the scale M of new physics. All the flavour breaking effects are universally described by the vacuum expectation values 〈Φ〉 of a set of spurions. We separately analyze both a supersymmetric and a general case. While the observed discrepancy δaμ in the anomalous MDM of the muon suggests M of order of a few TeV, several data require M above 10 TeV, in particular the limit on EDM of the electron. In the general case also the present limit on BR(μ→eγ) requires M>10 TeV, at least. The branching ratios for μ→eγ, τ→μγ and τ→eγ are all expected to be of the same order. In the supersymmetric case the constraint from μ→eγ is softened and it can be satisfied by a smaller scale M. In this case both the observed δaμ and the current bound on BR(μ→eγ) can be satisfied, at the price of a rather small value for |〈Φ〉|, of the order of a few percents, that reflects on a similar value for θ13
A two-part finite mixture quantile regression model for semi-continuous longitudinal data
No full textThis paper develops a two-part finite mixture quantile regression model for semi-continuous longitudinal data. The components of the finite mixture are associated
with homogeneous individuals in the population sharing common values of the model parameters. The proposed methodology allows heterogeneity sources that influence the first level decision process, that is, the model for the binary response variable, to influence also the distribution of the positive outcomes. Estimation is carried out through an EM algorithm without parametric assumptions on the random effects distribution. A penalized version of the EM algorithm is also presented to tackle the problem of variable selection. The suggested modelling framework has been discussed using the extensively investigated RAND Health Insurance Experiment dataset in the random intercept cas
Forecasting Multiple VaR and ES Using a Dynamic Joint Quantile Regression with an Application to Portfolio Optimization
No full textAn accurate assessment of tail dependencies of financial returns is key for risk management and portfolio allocation. The use of quantitative risk measures has become an essential tool providing support for financial and asset management decisions. Extending (Taylor in J Bus Econ Stat 37(1):121–133, 2019, [10]), we propose a novel multivariate framework to simultaneously estimate Value at Risk (VaR) and Expected Shortfall (ES) of multiple financial assets, by jointly modelling their marginal quantiles taking into account for their dependence structure. We generalize the joint quantile regression approach by specifying a Conditional Autoregressive Value at Risk (CAViaR) structure in the dynamics of each marginal quantile and modelling the ES of each asset in a time-varying setting. In addition, we propose a new method for portfolio construction, based on the multivariate structure of the problem. We apply our approach to weekly stock market returns, to illustrate the practical applicability of the proposed method and its efficiency gain compared to the univariate approach
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