Cumulants of Multivariate Symmetric and Skew Symmetric Distributions

This paper provides a systematic and comprehensive treatment for obtaining general expressions of any order, for the moments and cumulants of spherically and elliptically symmetric multivariate distributions; results for the case of multivariate t-distribution and related skew-t distribution are discussed in some detail.

Effects of Different Anxiety Levels on the Behavioral Patternings Investigated through T-pattern Analysis in Wistar Rats Tested in the Hole-Board Apparatus

The Hole-Board is an ethologically based tool for investigating the anxiety-related behavior of rats following manipulation of the central anxiety level. The present paper aims to assess behavioral patterning following pharmacological manipulation of emotional assets in Wistar rats tested in this experimental apparatus. For this purpose, the behavior of three groups of rats injected with saline, diazepam or FG7142 was evaluated using conventional quantitative and multivariate T-pattern analyses. The results demonstrate that quantitative analyses of individual components of the behavior, disjointed from the comprehensive behavioral structure, are of narrow utility in the understanding of the subject’s emotional condition. Among the components of the behavioral repertoire in rodents tested in the Hole-Board, Edge-Sniff and Head-Dip represent the most significant ones to rate anxiety level. They are characterized by a strong bivariate relationship and are also firmly part of the behavioral architecture, as revealed by the T-pattern analysis (TPA), a multivariate technique able to detect significant relationships among behavioral events over time. Edge-Sniff → Head-Dip sequences, in particular, are greatly influenced by the level of anxiety: barely detectable in control animals, they completely disappear in subjects with a reduced level of anxiety and are present in almost 25% of the total of T-patterns detected in subjects whose anxiety level increased.

Adjustment models for multivariate geodetic time series with vector-autoregressive errors

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.

Theory of best integer equivariant estimation for contaminated normal and multivariate t-distribution with applications

<p>Best integer equivariant (BIE) estimators provide minimum mean squared error (MMSE) solutions to the problem of GNSS carrier-phase ambiguity resolution for a wide range of distributions. The associated BIE estimators are universally optimal in the sense that they have an accuracy which is never poorer than that of any integer estimator and any linear unbiased estimator. Their accuracy is therefore always better or the same as that of Integer Least-Squares (ILS) estimators and Best Linear Unbiased Estimators (BLUEs).</p><p>Current theory is based on using BIE for the multivariate normal distribution. In this contribution this will be generalized to the contaminated normal distribution and the multivariate t-distribution, both of which have heavier tails than the normal. Their computational formulae are presented and discussed in relation to that of the normal distribution. In addition a GNSS real-data based analysis is carried out to demonstrate the universal MMSE properties of the BIE estimators for GNSS-baselines and associated parameters.</p><p> </p><p><strong>Keywords: </strong>Integer equivariant (IE) estimation · Best integer equivariant (BIE) · Integer Least-Squares (ILS) . Best linear unbiased estimation (BLUE) · Multivariate contaminated normal · Multivariate t-distribution . Global Navigation Satellite Systems (GNSSs)</p>

Multivariate analysis of PIXE + XRF and PIXE spectral images

Multivariate t-SNE analysis enables pixel identification with similar X-ray spectra for layer thickness determination and calculation of elemental concentrations.