Conditional expected likelihood technique for compound Gaussian and Gaussian distributed noise mixtures

Expected likelihood (EL) technique for quality assessment of parameter estimates of signals embedded in Gaussian noise is extended in this paper over the case where useful signals are immersed in a mixture of compound Gaussian and Gaussian distributed noises. The main problem here is that analytical expressions for distributions of such mixtures do not exist in most cases. Moreover, in some cases like $K$-distributed noise only where closed-form expressions for the data distribution are available, the traditional Cram\'{e}r-Rao bound does not exist. This makes EL technique even more important for parameter estimation performance assessment. In this paper, for the so-called conditional model, we introduce test statistics whose distribution for the true (actual) parameters does not depend on these parameters and specifics of texture distribution, which makes them applicable for EL applications. We illustrate the utility of this EL technique by studying and predicting the performance breakdown of some direction of arrival estimators in a mixture of $K$-distributed and Gaussian noise

Pricing and Inference with Mixtures of Conditionally Normal Processes.

We consider the problems of derivative pricing and inference when the stochastic discount factor has an exponential-affine form and the geometric return of the underlying asset has a dynamics characterized by a mixture of conditionally Normal processes. We consider both the static case in which the underlying process is a white noise distributed as a mixture of Gaussian distributions (including extreme risks and jump diffusions) and the dynamic case in which the underlying process is conditionally distributed as a mixture of Gaussian laws. Semi-parametric, non parametric and Switching Regime situations are also considered. In all cases, the risk-neutral processes and explicit pricing formulas are obtained.Derivative Pricing ; Stochastic Discount Factor ; Implied Volatility, Mixture of Normal Distributions ; Mixture of Conditionally Normal Processes ; Nonparametric Kernel Estimation ; Mixed-Normal GARCH Processes ; Switching Regime Models.

Bridging stylized facts in finance and data non-stationarities

Employing a recent technique which allows the representation of nonstationary data by means of a juxtaposition of locally stationary patches of different length, we introduce a comprehensive analysis of the key observables in a financial market: the trading volume and the price fluctuations. From the segmentation procedure we are able to introduce a quantitative description of a group of statistical features (stylizes facts) of the trading volume and price fluctuations, namely the tails of each distribution, the U-shaped profile of the volume in a trading session and the evolution of the trading volume autocorrelation function. The segmentation of the trading volume series provides evidence of slow evolution of the fluctuating parameters of each patch, pointing to the mixing scenario. Assuming that long-term features are the outcome of a statistical mixture of simple local forms, we test and compare different probability density functions to provide the long-term distribution of the trading volume, concluding that the log-normal gives the best agreement with the empirical distribution. Moreover, the segmentation of the magnitude price fluctuations are quite different from the results for the trading volume, indicating that changes in the statistics of price fluctuations occur at a faster scale than in the case of trading volume.Comment: 13 pages, 12 figure

On the Probability Distribution of Economic Growth

Normality is often mechanically and without sufficient reason assumed in econometric models. In this paper three important and significantly heteroscedastic GDP series are studied. Heteroscedasticity is removed and the distributions of the filtered series are then compared to a Normal, a Normal-Mixture and Normal-Asymmetric Laplace (NAL) distributions. NAL represents a reduced and empirical form of the Aghion and Howitt (1992) model for economic growth, based on Schumpeter's idea of creative destruction. Statistical properties of the NAL distributions are provided and it is shown that NAL competes well with the alternatives.The Aghion-Howitt model, asymmetric innovations, mixed normal- asymmetric Laplace distribution, Kernel density estimation, Method of Moments estimation.

Probabilistic partial volume modelling of biomedical tomographic image data

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