Search results for " normal distribution"
showing 10 items of 57 documents
L1-Penalized Censored Gaussian Graphical Model
2018
Graphical lasso is one of the most used estimators for inferring genetic networks. Despite its diffusion, there are several fields in applied research where the limits of detection of modern measurement technologies make the use of this estimator theoretically unfounded, even when the assumption of a multivariate Gaussian distribution is satisfied. Typical examples are data generated by polymerase chain reactions and flow cytometer. The combination of censoring and high-dimensionality make inference of the underlying genetic networks from these data very challenging. In this article, we propose an $\ell_1$-penalized Gaussian graphical model for censored data and derive two EM-like algorithm…
Functional connectivity inference from fMRI data using multivariate information measures
2022
Abstract Shannon’s entropy or an extension of Shannon’s entropy can be used to quantify information transmission between or among variables. Mutual information is the pair-wise information that captures nonlinear relationships between variables. It is more robust than linear correlation methods. Beyond mutual information, two generalizations are defined for multivariate distributions: interaction information or co-information and total correlation or multi-mutual information. In comparison to mutual information, interaction information and total correlation are underutilized and poorly studied in applied neuroscience research. Quantifying information flow between brain regions is not explic…
Bayesian hypothesis testing: A reference approach
2002
Summary For any probability model M={p(x|θ, ω), θeΘ, ωeΩ} assumed to describe the probabilistic behaviour of data xeX, it is argued that testing whether or not the available data are compatible with the hypothesis H0={θ=θ0} is best considered as a formal decision problem on whether to use (a0), or not to use (a0), the simpler probability model (or null model) M0={p(x|θ0, ω), ωeΩ}, where the loss difference L(a0, θ, ω) –L(a0, θ, ω) is proportional to the amount of information δ(θ0, ω), which would be lost if the simplified model M0 were used as a proxy for the assumed model M. For any prior distribution π(θ, ω), the appropriate normative solution is obtained by rejecting the null model M0 wh…
On the Efficiency of Affine Invariant Multivariate Rank Tests
1998
AbstractIn this paper the asymptotic Pitman efficiencies of the affine invariant multivariate analogues of the rank tests based on the generalized median of Oja are considered. Formulae for asymptotic relative efficiencies are found and, under multivariate normal and multivariatetdistributions, relative efficiencies with respect to Hotelling'sT2test are calculated.
On the Computation of Symmetrized M-Estimators of Scatter
2016
This paper focuses on the computational aspects of symmetrized Mestimators of scatter, i.e. the multivariate M-estimators of scatter computed on the pairwise differences of the data. Such estimators do not require a location estimate, and more importantly, they possess the important block and joint independence properties. These properties are needed, for example, when solving the independent component analysis problem. Classical and recently developed algorithms for computing the M-estimators and the symmetrized M-estimators are discussed. The effect of parallelization is considered as well as new computational approach based on using only a subset of pairwise differences. Efficiencies and…
Finding condensed descriptions for multi-dimensional data.
1976
Abstract We describe two programs that may be used to find condensed descriptions for data available in a contingency table or in a covariance matrix in the case that these data follow a multinomial or a multivariate normal distribution, respectively. The programs perform a stepwise model search among multiplicative models by computing appropriate likelihood-ratio test statistics.
Regular Minimality and Thurstonian-type modeling
2009
Abstract A Thurstonian-type model for pairwise comparisons is any model in which the response (e.g., “they are the same” or “they are different”) to two stimuli being compared depends, deterministically or probabilistically, on the realizations of two randomly varying representations (perceptual images) of these stimuli. The two perceptual images in such a model may be stochastically interdependent but each has to be selectively dependent on its stimulus. It has been previously shown that all possible discrimination probability functions for same–different comparisons can be generated by Thurstonian-type models of the simplest variety, with independent percepts and deterministic decision ru…
Weak versus strong dominance of shrinkage estimators
2021
We consider the estimation of the mean of a multivariate normal distribution with known variance. Most studies consider the risk of competing estimators, that is the trace of the mean squared error matrix. In contrast we consider the whole mean squared error matrix, in particular its eigenvalues. We prove that there are only two distinct eigenvalues and apply our findings to the James–Stein and the Thompson class of estimators. It turns out that the famous Stein paradox is no longer a paradox when we consider the whole mean squared error matrix rather than only its trace.
Estimating Engel curves under unit and item nonresponse
2010
SUMMARY This paper estimates food Engel curves using data from the first wave of the Survey on Health, Aging and Retirement in Europe (SHARE). Our statistical model simultaneously takes into account selectivity due to unit and item nonresponse, endogeneity problems, and issues related to flexible specification of the relationship of interest. We estimate both parametric and semiparametric specifications of the model. The parametric specification assumes that the unobservables in the model follow a multivariate Gaussian distribution, while the semiparametric specification avoids distributional assumptions about the unobservables. Copyright © 2011 John Wiley & Sons, Ltd.
Non-Gaussian Distribution for Var Calculation: an Assessment for the Italian Market
2001
Abstract In this paper we compare different approaches to computing VaR (Value-at-Risk) for heavy tailed return series. Using data from the Italian market, we show that almost all the return series present statistically significant skewness and kurtosis. We implement (i) the stable models proposed by Rachev et al . (2000), (ii) an alternative to the Gaussian distributions based on a Generalized Error Distribution and (iii) a non-parametric model proposed by Li (1999). All the models are then submitted to backtest on out-of-sample data in order to assess their forecasting power. We observe that when the percentiles are low, all the models tested produce results that are dominant compared to …