scholarly journals The multiparameter t’distribution

Filomat ◽  
2019 ◽  
Vol 33 (13) ◽  
pp. 4137-4150 ◽  
Author(s):  
Emna Ghorbel ◽  
Mahdi Louati

This research paper stands for an extension to the multivariate t?distribution introduced in 1954 by Cornish, Dunnett and Sobel, namely the multiparameter t?distribution. This distribution is expressed in two different ways. The first way invests the mixture of a normal vector with a natural extension to the Wishart distribution, that is the Riesz distribution on symmetric matrices. The second one rests upon the Cholesky decomposition of the Riesz matrix. An algorithm for generating this distribution is investigated using the Riesz distribution arising obtained through not only the distribution of the empirical normal covariance matrix for samples with monotone missing data but also through Cholesky decomposition. In addition, Some fundamentals properties of the multiparameter t?distribution such as the infinite divisibility are identified. Besides, the Expectation Maximization algorithm is used to estimate its parameters. Finally, the performance of these estimators is assessed by means of the Mean Squared Error between the true and the estimated parameters.

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Boris Kargoll ◽  
Alexander Dorndorf ◽  
Mohammad Omidalizarandi ◽  
Jens-André Paffenholz ◽  
Hamza Alkhatib

Abstract In this contribution, a vector-autoregressive (VAR) process with multivariate t-distributed random deviations is incorporated into the Gauss-Helmert model (GHM), resulting in an innovative adjustment model. This model is versatile since it allows for a wide range of functional models, unknown forms of auto- and cross-correlations, and outlier patterns. Subsequently, a computationally convenient iteratively reweighted least squares method based on an expectation maximization algorithm is derived in order to estimate the parameters of the functional model, the unknown coefficients of the VAR process, the cofactor matrix, and the degree of freedom of the t-distribution. The proposed method is validated in terms of its estimation bias and convergence behavior by means of a Monte Carlo simulation based on a GHM of a circle in two dimensions. The methodology is applied in two different fields of application within engineering geodesy: In the first scenario, the offset and linear drift of a noisy accelerometer are estimated based on a Gauss-Markov model with VAR and multivariate t-distributed errors, as a special case of the proposed GHM. In the second scenario real laser tracker measurements with outliers are adjusted to estimate the parameters of a sphere employing the proposed GHM with VAR and multivariate t-distributed errors. For both scenarios the estimated parameters of the fitted VAR model and multivariate t-distribution are analyzed for evidence of auto- or cross-correlations and deviation from a normal distribution regarding the measurement noise.


2017 ◽  
Vol 18 (2) ◽  
pp. 308-326 ◽  
Author(s):  
Amare Wubishet Ayele ◽  
Emmanuel Gabreyohannes ◽  
Yohannes Yebabe Tesfay

Modelling and forecasting of commodity price volatility has important applications for asset management, portfolio analysis and risk assessment due to the simple fact that volatility has informational content and contains signals of the market information flow. This article models and forecasts the gold price volatility using the exponentially weighted moving average (EWMA) and the generalized autoregressive conditional heteroscedasticity (GARCH) models for the period from 1998 to 2014. The gold series shows the classical characteristics of financial time series, such as leptokurtic distributions, data dependence and strong serial correlation in squared returns. Hence, the series can be modelled using both EWMA and GARCH-type models. Among the GARCH-type models, GARCH-M(2,2) with Student’s t distribution for the residuals was found to be the best-fit model. Moreover, the manuscript finds that interest rates, exchange rates and crude oil prices have a significant impact on gold volatility. The risk premium effect is found to be positive and statistically significant, suggesting increased volatility is followed by a higher mean. Finally, a comparison is made between the GARCH and the EWMA models. Using the relative mean squared error and mean absolute error measures, the empirical result suggests that GARCH models with explanatory variables are superior for volatility forecasting.


Author(s):  
I. BOUTOURIA ◽  
A. HASSAIRI ◽  
H. MASSAM

The Wishart distribution on a homogeneous cone is a generalization of the Riesz distribution on a symmetric cone which corresponds to a given graph. The paper extends to this distribution, the famous Olkin and Rubin characterization of the ordinary Wishart distribution on symmetric matrices.


2015 ◽  
Vol 15 (03) ◽  
pp. 1550033 ◽  
Author(s):  
XIANWEN WANG ◽  
FENG CHEN ◽  
ZHI CHENG ◽  
YAOHUA DU ◽  
TAIHU WU

A major component of flow cytometry (FCM) data analysis involves gating, which is the process of identifying homogeneous groups of cells. With the rapid development of the portable flow cytometer, manual gating techniques have been unable to meet the demand for accurate and rapid analysis of samples. To provide a practical application for portable devices, we propose a flexible, statistical model-based clustering approach for identifying cell populations in FCM data. This approach, which mimics the manual gating process, employs a finite mixture model with a density function of skew t distribution and estimates parameters via an expectation maximization algorithm. Data analysis from an experiment on a patient’s peripheral blood samples have proven that the proposed methodology yields better results in terms of robustness against outliers than current state-of-the-art automated gating methods, has more flexibility in clustering symmetric data and leads to lower misclassification rates (misclassification rates of skew t method is 0.06442) when handling highly asymmetric data. The method we proposed will improve data analysis of portable flow cytometers, especially when the users have no professional training.


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