Topic
Normal variance-mean mixture
About: Normal variance-mean mixture is a research topic. Over the lifetime, 12 publications have been published within this topic receiving 351 citations.
Papers
1 Jan 1997
TL;DR: In this article, the one and two-dimensional normal inverse Gaussian Levy process is studied in relation to German and Danish financial data and the uniform residuals are calculated by means of an algorithm which simulates random variables from the normal inverse GAussian distribution.
Abstract: The one – and two-dimensional normal inverse Gaussian Levy process is studied in relation to German and Danish financial data. In order to investigate if the normal inverse Gaussian Levy process is a suitable model we calculate the uniform residuals by means of an algorithm which simulates random variables from the normal inverse Gaussian distribution. The algorithm uses the characterization of the normal inverse Gaussian distribution as a normal variance-mean mixture. Finally, an approximation of the process which will make it more tractable from a mathematical finance point of view is provided. Our approximation only relies on the fact that the process is a Levy process with characteristic triplet and therefore the method is general and can be applied to any Levy process
351 citations
TL;DR: In this paper, the authors study the normal variance-mean mixture model from a semiparametric point of view, i.e. they let the mixing distribution belong to a nonparametric family.
Abstract: We study the normal variance-mean mixture model from a semiparametric point of view, i.e. we let the mixing distribution belong to a non-parametric family. The main results are consistency of the non-parametric maximum likelihood estimator and construction of an asymptotically normal and efficient estimator for the Euclidian part of the parameter. We study the model according to the theory outlined in the monograph by Bickel et al. (1993) and apply a general result (based on the theory of empirical processes) for semiparametric models from van der Vaart (1996) to prove asymptotic normality and efficiency of the proposed estimator.
31 citations
TL;DR: EM and generalized EM algorithms are developed for computing regression quantiles of linear and nonlinear regression models and it is shown that the proposed EM algorithm and the MM (Majorization–Minimization) algorithm for quantile regressions are really the same in terms of computation.
Abstract: The three-parameter asymmetric Laplace distribution (ALD) has received increasing attention in the field of quantile regression due to an important feature between its location and asymmetric parameters. On the basis of the representation of the ALD as a normal-variance–mean mixture with an exponential mixing distribution, this article develops EM and generalized EM algorithms, respectively, for computing regression quantiles of linear and nonlinear regression models. It is interesting to show that the proposed EM algorithm and the MM (Majorization–Minimization) algorithm for quantile regressions are really the same in terms of computation, since the updating formula of them are the same. This provides a good example that connects the EM and MM algorithms. Simulation studies show that the EM algorithm can successfully recover the true parameters in quantile regressions.
23 citations
TL;DR: A multiple scaled multivariate skew normal variance-mean mixture distribution to model heavy-tailed and/or skew measurement noises (HTSMN) whose each dimension has different tail and skewness behaviors is proposed.
Abstract: In this brief, we first propose a multiple scaled multivariate skew normal variance-mean mixture (MSMSNVMM) distribution to model heavy-tailed and/or skew measurement noises (HTSMN) whose each dimension has different tail and skewness behaviors. The MSMSNVMM distribution has more flexible tail behaviors and richer skewness features than Gaussian scale mixture (GScM) distribution, generalized Gaussian scale mixture (GGScM) distribution and scale mixtures of skew normal (SMSN) distribution. Furthermore, we derive a robust Kalman filter based on variational Bayesian (VB) method. The superiority of the new filter is demonstrated in a maneuvering target tracking example.
8 citations
TL;DR: In this article, the problem of statistical inference on the parameters of the semiparametric variance-mean mixtures was studied, and the problem was shown to be NP-hard.
Abstract: In this paper we study the problem of statistical inference on the parameters of the semiparametric variance-mean mixtures. This class of mixtures has recently become rather popular in statistical ...
4 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 1 |
| 2018 | 1 |
| 2017 | 1 |
| 2016 | 2 |
| 2015 | 1 |
| 2014 | 2 |