The Experts below are selected from a list of 423294 Experts worldwide ranked by ideXlab platform
Ryan Martin - One of the best experts on this subject based on the ideXlab platform.
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inferential models a framework for prior free posterior probabilistic inference
Journal of the American Statistical Association, 2013Co-Authors: Ryan MartinAbstract:Posterior probabilistic statistical inference without priors is an important but so far elusive goal. Fisher’s fiducial inference, Dempster–Shafer theory of belief functions, and Bayesian inference with default priors are attempts to achieve this goal but, to date, none has given a completely satisfactory picture. This article presents a new framework for probabilistic inference, based on inferential models (IMs), which not only provides data-dependent probabilistic measures of uncertainty about the unknown parameter, but also does so with an automatic Long-Run Frequency-calibration property. The key to this new approach is the identification of an unobservable auxiliary variable associated with observable data and unknown parameter, and the prediction of this auxiliary variable with a random set before conditioning on data. Here we present a three-step IM construction, and prove a Frequency-calibration property of the IM’s belief function under mild conditions. A corresponding optimality theory is develo...
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inferential models a framework for prior free posterior probabilistic inference
arXiv: Statistics Theory, 2012Co-Authors: Ryan Martin, Chuanhai LiuAbstract:Posterior probabilistic statistical inference without priors is an important but so far elusive goal. Fisher's fiducial inference, Dempster-Shafer theory of belief functions, and Bayesian inference with default priors are attempts to achieve this goal but, to date, none has given a completely satisfactory picture. This paper presents a new framework for probabilistic inference, based on inferential models (IMs), which not only provides data-dependent probabilistic measures of uncertainty about the unknown parameter, but does so with an automatic Long-Run Frequency calibration property. The key to this new approach is the identification of an unobservable auxiliary variable associated with observable data and unknown parameter, and the prediction of this auxiliary variable with a random set before conditioning on data. Here we present a three-step IM construction, and prove a Frequency-calibration property of the IM's belief function under mild conditions. A corresponding optimality theory is developed, which helps to resolve the non-uniqueness issue. Several examples are presented to illustrate this new approach.
Franck Moraux - One of the best experts on this subject based on the ideXlab platform.
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A switching self-exciting jump diffusion process for stock prices
Annals of Finance, 2019Co-Authors: Donatien Hainaut, Franck MorauxAbstract:This study proposes a new Markov switching process with clustering effects. In this approach, a hidden Markov chain with a finite number of states modulates the parameters of a self-excited jump process combined to a geometric Brownian motion. Each regime corresponds to a particular economic cycle determining the expected return, the diffusion coefficient and the Long-Run Frequency of clustered jumps. We study first the theoretical properties of this process and we propose a sequential Monte-Carlo method to filter the hidden state variables. We next develop a Markov Chain Monte-Carlo procedure to fit the model to the S&P 500. We find that self-exciting jumps occur mainly during economic recession and nearly disappear in periods of economic growth. Finally, we analyse the impact of such a jump clustering on implied volatilities of European options.
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a switching self exciting jump diffusion process for stock prices
Post-Print, 2019Co-Authors: Donatien Hainaut, Franck MorauxAbstract:This study proposes a new Markov switching process with clustering eects. In this approach, a hidden Markov chain with a nite number of states modulates the parameters of a self-excited jump process combined to a geometric Brownian motion. Each regime corresponds to a particular economic cycle determining the expected return, the diusion coecient and the Long-Run Frequency of clustered jumps. We study rst the theoretical properties of this process and we propose a sequential Monte-Carlo method to lter the hidden state variables. We next develop a Markov Chain Monte-Carlo procedure to t the model to the S&P 500. Finally, we analyse the impact of such a jump clustering on implied volatilities of European options.
Donatien Hainaut - One of the best experts on this subject based on the ideXlab platform.
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A switching self-exciting jump diffusion process for stock prices
Annals of Finance, 2019Co-Authors: Donatien Hainaut, Franck MorauxAbstract:This study proposes a new Markov switching process with clustering effects. In this approach, a hidden Markov chain with a finite number of states modulates the parameters of a self-excited jump process combined to a geometric Brownian motion. Each regime corresponds to a particular economic cycle determining the expected return, the diffusion coefficient and the Long-Run Frequency of clustered jumps. We study first the theoretical properties of this process and we propose a sequential Monte-Carlo method to filter the hidden state variables. We next develop a Markov Chain Monte-Carlo procedure to fit the model to the S&P 500. We find that self-exciting jumps occur mainly during economic recession and nearly disappear in periods of economic growth. Finally, we analyse the impact of such a jump clustering on implied volatilities of European options.
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a switching self exciting jump diffusion process for stock prices
Post-Print, 2019Co-Authors: Donatien Hainaut, Franck MorauxAbstract:This study proposes a new Markov switching process with clustering eects. In this approach, a hidden Markov chain with a nite number of states modulates the parameters of a self-excited jump process combined to a geometric Brownian motion. Each regime corresponds to a particular economic cycle determining the expected return, the diusion coecient and the Long-Run Frequency of clustered jumps. We study rst the theoretical properties of this process and we propose a sequential Monte-Carlo method to lter the hidden state variables. We next develop a Markov Chain Monte-Carlo procedure to t the model to the S&P 500. Finally, we analyse the impact of such a jump clustering on implied volatilities of European options.
Alexander Gammerman - One of the best experts on this subject based on the ideXlab platform.
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on line predictive linear regression
arXiv: Statistics Theory, 2009Co-Authors: Vladimir Vovk, Ilia Nouretdinov, Alexander GammermanAbstract:We consider the on-line predictive version of the standard problem of linear regression; the goal is to predict each consecutive response given the corresponding explanatory variables and all the previous observations. The standard treatment of prediction in linear regression analysis has two drawbacks: (1) the classical prediction intervals guarantee that the probability of error is equal to the nominal significance level $\varepsilon$, but this property per se does not imply that the Long-Run Frequency of error is close to $\varepsilon$; (2) it is not suitable for prediction of complex systems as it assumes that the number of observations exceeds the number of parameters. We state a general result showing that in the on-line protocol the Frequency of error for the classical prediction intervals does equal the nominal significance level, up to statistical fluctuations. We also describe alternative regression models in which informative prediction intervals can be found before the number of observations exceeds the number of parameters. One of these models, which only assumes that the observations are independent and identically distributed, is popular in machine learning but greatly underused in the statistical theory of regression.
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on line predictive linear regression
Annals of Statistics, 2009Co-Authors: Vladimir Vovk, Ilia Nouretdinov, Alexander GammermanAbstract:Gauss linear model; independent identically distributed observations; multivariate analysis; on-line protocol; prequential statistics; regression We consider the on-line predictive version of the standard problem of linear regression; the goal is to predict each consecutive response given the corresponding explanatory variables and all the previous observations. The standard treatment of prediction in linear regression analysis has two drawbacks: (1) the usual prediction intervals guarantee that the probability of error is equal to the nominal significance level ǫ, but this property per se does not imply that the Long-Run Frequency of error is close to ǫ; (2) it is not suitable for prediction of complex systems as it assumes that the number of observations exceeds the number of parameters. We state a general result showing that in the on-line protocol the Frequency of error does equal the nominal significance level, up to statistical fluctuations, and we describe alternative regression models in which informative prediction intervals can be found before the number of observations exceeds the number of parameters. One of these models, which only assumes that the observations are independent and identically distributed, is popular in machine learning but greatly underused in the statistical theory of regression.
Vladimir Vovk - One of the best experts on this subject based on the ideXlab platform.
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on line predictive linear regression
arXiv: Statistics Theory, 2009Co-Authors: Vladimir Vovk, Ilia Nouretdinov, Alexander GammermanAbstract:We consider the on-line predictive version of the standard problem of linear regression; the goal is to predict each consecutive response given the corresponding explanatory variables and all the previous observations. The standard treatment of prediction in linear regression analysis has two drawbacks: (1) the classical prediction intervals guarantee that the probability of error is equal to the nominal significance level $\varepsilon$, but this property per se does not imply that the Long-Run Frequency of error is close to $\varepsilon$; (2) it is not suitable for prediction of complex systems as it assumes that the number of observations exceeds the number of parameters. We state a general result showing that in the on-line protocol the Frequency of error for the classical prediction intervals does equal the nominal significance level, up to statistical fluctuations. We also describe alternative regression models in which informative prediction intervals can be found before the number of observations exceeds the number of parameters. One of these models, which only assumes that the observations are independent and identically distributed, is popular in machine learning but greatly underused in the statistical theory of regression.
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on line predictive linear regression
Annals of Statistics, 2009Co-Authors: Vladimir Vovk, Ilia Nouretdinov, Alexander GammermanAbstract:Gauss linear model; independent identically distributed observations; multivariate analysis; on-line protocol; prequential statistics; regression We consider the on-line predictive version of the standard problem of linear regression; the goal is to predict each consecutive response given the corresponding explanatory variables and all the previous observations. The standard treatment of prediction in linear regression analysis has two drawbacks: (1) the usual prediction intervals guarantee that the probability of error is equal to the nominal significance level ǫ, but this property per se does not imply that the Long-Run Frequency of error is close to ǫ; (2) it is not suitable for prediction of complex systems as it assumes that the number of observations exceeds the number of parameters. We state a general result showing that in the on-line protocol the Frequency of error does equal the nominal significance level, up to statistical fluctuations, and we describe alternative regression models in which informative prediction intervals can be found before the number of observations exceeds the number of parameters. One of these models, which only assumes that the observations are independent and identically distributed, is popular in machine learning but greatly underused in the statistical theory of regression.
