104 research outputs found
Dispersion Models for Extremes
We propose extreme value analogues of natural exponential families and
exponential dispersion models, and introduce the slope function as an analogue
of the variance function. The set of quadratic and power slope functions
characterize well-known families such as the Rayleigh, Gumbel, power, Pareto,
logistic, negative exponential, Weibull and Fr\'echet. We show a convergence
theorem for slope functions, by which we may express the classical extreme
value convergence results in terms of asymptotics for extreme dispersion
models. The main idea is to explore the parallels between location families and
natural exponential families, and between the convolution and minimum
operations.Comment: 23 pages. Abstract submitted to the 56th Session of the ISI, Lisboa,
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Distributional Properties of means of Random Probability Measures
The present paper provides a review of the results concerning distributional properties of means of random probability measures. Our interest in this topic has originated from inferential problems in Bayesian Nonparametrics. Nonetheless, it is worth noting that these random quantities play an important role in seemingly unrelated areas of research. In fact, there is a wealth of contributions both in the statistics and in the probability literature that we try to summarize in a unified framework. Particular attention is devoted to means of the Dirichlet process given the relevance of the Dirichlet process in Bayesian Nonparametrics. We then present a number of recent contributions concerning means of more general random probability measures and highlight connections with the moment problem, combinatorics, special functions, excursions of stochastic processes and statistical physics.Bayesian Nonparametrics; Completely random measures; Cifarelli–Regazzini identity; Dirichlet process; Functionals of random probability measures; Generalized Stieltjes transform; Neutral to the right processes; Normalized random measures; Posterior distribution; Random means; Random probability measure; Two–parameter Poisson–Dirichlet process.
Distributional properties of means of random probability measures
The present paper provides a review of the results concerning distributional properties of means of random probability measures. Our interest in this topic has originated from inferential problems in Bayesian Nonparametrics. Nonetheless, it is worth noting that these random quantities play an important role in seemingly unrelated areas of research. In fact, there is a wealth of contributions both in the statistics and in the probability literature that we try to summarize in a unified framework. Particular attention is devoted to means of the Dirichlet process given the relevance of the Dirichlet process in Bayesian Nonparametrics. We then present a number of recent contributions concerning means of more general random probability measures and highlight connections with the moment problem, combinatorics, special functions, excursions of stochastic processes and statistical physics.Bayesian Nonparametrics; Completely random measures; Cifarelli-Regazzini identity; Dirichlet process; Functionals of random probability measures; Generalized Stieltjes transform; Neutral to the right processes; Normalized random measures; Posterior distribution; Random means; Random probability measure; Two-parameter Poisson-Dirichlet process
Unit Root Tests in Three-Regime SETAR Models
This paper proposes a simple direct testing procedure to distinguish a linear unit root process from a globally stationary three-regime self-exciting threshold autoregressive process. We derive the asymptotic null distribution of the Wald statistic, and show that it does not depend on unknown fixed threshold values. Monte Carlo evidence clearly indicates that the exponential average of the Wald statistic is more powerful than the Dickey-Fuller test that ignores the threshold nature under the alternative.Self-exciting threshold autoregressive models, Unit roots, Globally stationary processes, Threshold cointegration, Wald tests, Monte Carlo simulations, Real exchange rates
Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-moments
This paper discusses different classes of loss models in non-life insurance
settings. It then overviews the class Tukey transform loss models that have not
yet been widely considered in non-life insurance modelling, but offer
opportunities to produce flexible skewness and kurtosis features often required
in loss modelling. In addition, these loss models admit explicit quantile
specifications which make them directly relevant for quantile based risk
measure calculations. We detail various parameterizations and sub-families of
the Tukey transform based models, such as the g-and-h, g-and-k and g-and-j
models, including their properties of relevance to loss modelling.
One of the challenges with such models is to perform robust estimation for
the loss model parameters that will be amenable to practitioners when fitting
such models. In this paper we develop a novel, efficient and robust estimation
procedure for estimation of model parameters in this family Tukey transform
models, based on L-moments. It is shown to be more robust and efficient than
current state of the art methods of estimation for such families of loss models
and is simple to implement for practical purposes.Comment: 42 page
Closed-form approximations of moments and densities of continuous-time Markov models
This paper develops power series expansions of a general class of moment
functions, including transition densities and option prices, of continuous-time
Markov processes, including jump--diffusions. The proposed expansions extend
the ones in Kristensen and Mele (2011) to cover general Markov processes. We
demonstrate that the class of expansions nests the transition density and
option price expansions developed in Yang, Chen, and Wan (2019) and Wan and
Yang (2021) as special cases, thereby connecting seemingly different ideas in a
unified framework. We show how the general expansion can be implemented for
fully general jump--diffusion models. We provide a new theory for the validity
of the expansions which shows that series expansions are not guaranteed to
converge as more terms are added in general. Thus, these methods should be used
with caution. At the same time, the numerical studies in this paper demonstrate
good performance of the proposed implementation in practice when a small number
of terms are included
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