1,721,047 research outputs found
Mixtures of conjugate prior distributions and large deviations for level crossing probabilities
No full textIn this paper we present asymptotic estimates of level crossing probabilities from a Bayesian point of view, based on large deviations. For the Bayesian analysis we choose a finite mixture of conjugate prior distributions to model the uncertainty on the unknown parameters of the two classes of stochastic processes considered: the Brownian motion and the compound Poisson process with upward jumps and negative drift. The estimates of level crossing probabilities are derived as a consequence of large deviation principles for posterior distributions
Bayes factors for Fieller's problem
No full textThis paper considers point null hypothesis testing when the sampling distribution belongs to a particular class, defined in Gleser & Hwang (1987). We discuss the drawbacks of frequentist and likelihood solutions and we show how proper Bayesian analysis encounters relatively similar difficulties. We explore the performance of several noninformative Bayesian approaches to testing, namely asymptotic approximations of Bayes factors and default Bayes factors. We argue that in a default Bayesian analysis of Fieller's problem the choice of the 'correct' prior distribution is crucial. Although standard and default Bayes factors based on Jeffreys' priors show, to a lesser extent, pathologies similar to those arising in a classical framework, default Bayes factors based on reference priors seem to correct the bias and provide sensible results in term of robustness and consistency
Forecasting VaR and ES using a joint quantile regression and its implications in portfolio allocation
Full text linkIn this paper, we propose a multivariate quantile regression framework to forecast Value at Risk (VaR) and Expected Shortfall (ES) of multiple financial assets simultaneously, extending Taylor (2019). We generalize the Multivariate Asymmetric Laplace (MAL) joint quantile regression of Petrella and Raponi (2019) to a time-varying setting, which allows us to specify a dynamic process for the evolution of both the VaR and ES of each asset. The proposed methodology accounts for the dependence structure among asset returns. By exploiting the properties of the MAL distribution, we propose a new portfolio optimization method that minimizes portfolio risk and controls for well-known characteristics of financial data. We evaluate the advantages of the proposed approach on both simulated and real data, using weekly returns on three major stock market indices. We show that our method outperforms other existing models and provides more accurate risk measure forecasts than univariate methods
Unified Bayesian conditional autoregressive risk measures using the skew exponential power distribution
No full textConditional Autoregressive Value-at-Risk and Conditional Autoregressive Expectile have become two popular approaches for direct measurement of market risk. Since their introduction several improvements both in the Bayesian and in the classical framework have been proposed to better account for asymmetry and local non-linearity. Here we propose a unified Bayesian Conditional Autoregressive Risk Measures approach by using the Skew Exponential Power distribution. Further, we extend the proposed models using a semiparametric P-Spline approximation answering for a flexible way to consider the presence of non-linearity. To make the statistical inference we adapt the MCMC algorithm proposed in Bernardi et al. (2018) to our case. The effectiveness of the whole approach is demonstrated using real data on daily return of five stock market indices
Two-part quantile regression models for semi-continuous longitudinal data: A finite mixture approach
Full text linkThis article develops a two-part finite mixture quantile regression model for semi-continuous longitudinal data. The proposed methodology allows heterogeneity sources that influence the model for the binary response variable to also influence the distribution of the positive outcomes. As is common in the quantile regression literature, estimation and inference on the model parameters are based on the asymmetric Laplace distribution. Maximum likelihood estimates are obtained through the EM algorithm without parametric assumptions on the random effects distribution. In addition, a penalized version of the EM algorithm is presented to tackle the problem of variable selection. The proposed statistical method is applied to the well-known RAND Health Insurance Experiment dataset which gives further insights on its empirical behaviour
Censored Exponential Data: Large Deviations for MLEs and Posterior Distributions
No full textIn this article, we consider several statistical models for censored exponential data. We prove a large deviation result for the maximum likelihood estimators (MLEs) of each model, and a unique result for the posterior distributions which works well for all the cases. Finally, comparing the large deviation rate functions for MLEs and posterior distributions, we show that a typical feature fails for one model; moreover, we illustrate the relation between this fact and a well-known result for curved exponential models
Large deviation results on some estimators for stationary Gaussian processes
No full textIn this paper, we present large deviation results for estimators of some unknown parameters concerning
stationary Gaussian processes. We deal with both maximum likelihood estimators and posterior distributions;
moreover, we illustrate the differences between short-range- and long-range-dependent processes. As
a typical feature the rate functions for maximum likelihood estimators and posterior distributions are given
in terms of the same relative entropy and the roles of the two probability measures in the relative entropy
are exchanged. We define a sort of relative entropy with respect to the sampling process which in the i.i.d.
case corresponds to the relative entropy with respect to the common law of each single sample. In view
of potential applications in risk theory we prove large deviation results for estimators of the logarithmic
asymptotic decay rate of the tail of the supremum of a random walk with stationary Gaussian increments.
Finally, we present results for compound renewal processes with stationary Gaussian distributed rewards,
independent of i.i.d.Weibull distributed renewal times
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Bayes factors at work in a challenging class of problems
No full textThis paper considers a Bayesian approach to pint null hypothesis testing when the sampling distribution nelongs to a particular class, defined in Gleser and Hwang (1987). Different approaches to the class have been used in the literature; however, none of them is fully satisfactory.
A Bayesian viewpoint is adopted to analyze the behaviour of several version of the Bayes factor in this context. We first discuss the use of a proper Bayes factor and we show the high sensitivity of conclusions with respect to prior inputs. Also, alternative approaches based on default Bayes factors are considered in the particular context of linear calibration
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