Search results for " normal distribution"
showing 10 items of 57 documents
Parameter optimization for amplify-and-forward relaying with imperfect channel estimation
2009
Cooperative diversity is a promising technology for future wireless networks. In this paper, we consider a cooperative communication system operating in an amplify-and-forward (AF) mode with an imperfectly-known relay fading channel. It is assumed that a pilot symbol assisted modulation (PSAM) scheme with linear minimum mean square estimator (LMMSE) is used for the channel estimation. A simple and easy-to-evaluate asymptotical upper bound (AUB) of the symbol-error-rate (SER) is derived for uncoded AF cooperative systems with quadrature amplitude modulation (QAM) constellations. Based on the AUB, we propose a criterion for the choice of parameters in the PSAM scheme, i.e., the pilot spacing …
Comparing Correlation Matrix Estimators Via Kullback-Leibler Divergence
2011
We use a self-averaging measure called Kullback-Leibler divergence to evaluate the performance of four different correlation estimators: Fourier, Pearson, Maximum Likelihood and Hayashi-Yoshida estimator. The study uses simulated transaction prices for a large number of stocks and different data generating mechanisms, including synchronous and non-synchronous transactions, homogeneous and heterogeneous inter-transaction time. Different distributions of stock returns, i.e. multivariate Normal and multivariate Student's t-distribution, are also considered. We show that Fourier and Pearson estimators are equivalent proxies of the `true' correlation matrix within all the settings under analysis…
COMPARATIVE ASSESSMENT OF SEVERAL MULTI-CRITERIA DECISION ANALYSIS TOOLS FOR MANAGEMENT OF CONTAMINATED SEDIMENTS
2007
Over the past several decades, environmental decision-making strategies have evolved into increasingly more sophisticated, information-intensive, and complexapproaches including expert judgment, cost-benefit analysis, toxicological risk assessment, comparative risk assessment, and a number of methods forincorporating public and stakeholder values. This evolution has led to an improved array of decision-making aids, including the development of Multi-CriteriaDecision Analysis (MCDA) tools that offer a scientifically sound decision analytical framework. The existence of different MCDA methods and the availability of corresponding software contribute to the possibility of practical implementat…
Multivariate nonparametric tests in a randomized complete block design
2003
AbstractIn this paper multivariate extensions of the Friedman and Page tests for the comparison of several treatments are introduced. Related unadjusted and adjusted treatment effect estimates for the multivariate response variable are also found and their properties discussed. The test statistics and estimates are analogous to the traditional univariate methods. In test constructions, the univariate ranks are replaced by multivariate spatial ranks (J. Nonparam. Statist. 5 (1995) 201). Asymptotic theory is developed to provide approximations for the limiting distributions of the test statistics and estimates. Limiting efficiencies of the tests and treatment effect estimates are found in the…
Second-order interaction in a Trivariate Generalized Gamma Distribution
2004
The concept of second- (and higher-) order interaction is widely used in categorical data analysis, where it proves useful for explaining the interdependence among three (or more) variables. Its use seems to be less common for continuous multivariate distributions, most likely owing to the predominant role of the Multivariate Normal distribution, for which any interaction involving more than two variables is necessarily zero. In this paper we explore the usefulness of a second-order interaction measure for studying the interdependence among three continuous random variables, by applying it to a trivariate Generalized Gamma distribution proposed by Bologna(2000).
On Mardia’s Tests of Multinormality
2004
Classical multivariate analysis is based on the assumption that the data come from a multivariate normal distribution. The tests of multinormality have therefore received very much attention. Several tests for assessing multinormality, among them Mardia’s popular multivariate skewness and kurtosis statistics, are based on standardized third and fourth moments. In Mardia’s construction of the affine invariant test statistics, the data vectors are first standardized using the sample mean vector and the sample covariance matrix. In this paper we investigate whether, in the test construction, it is advantageous to replace the regular sample mean vector and sample covariance matrix by their affi…
Statistical Techniques for Validation of Simulation and Analytic Stochastic Models
2014
In this paper, we consider the problem of statistical validation of multivariate stationary response simulation and analytic stochastic models of observed systems (say, transportation or service systems), which have p response variables. The problem is reduced to testing the equality of the mean vectors for two multivariate normal populations. Without assuming equality of the covariance matrices, it is referred to as the Behrens–Fisher problem. The main purpose of this paper is to bring to the attention of applied researchers the satisfactory tests that can be used for testing the equality of two normal mean vectors when the population covariance matrices are unknown and arbitrary. To illus…
Adaptive independent vector analysis for multi-subject complex-valued fMRI data.
2017
Abstract Background Complex-valued fMRI data can provide additional insights beyond magnitude-only data. However, independent vector analysis (IVA), which has exhibited great potential for group analysis of magnitude-only fMRI data, has rarely been applied to complex-valued fMRI data. The main challenges in this application include the extremely noisy nature and large variability of the source component vector (SCV) distribution. New method To address these challenges, we propose an adaptive fixed-point IVA algorithm for analyzing multiple-subject complex-valued fMRI data. We exploited a multivariate generalized Gaussian distribution (MGGD)- based nonlinear function to match varying SCV dis…
Elliptically Symmetric Distributions: A Review of Achieved Results and Open Issues
2005
The spherically and elliptically symmetrical distributions are used in different statistical areas for different purposes such as the description of multivariate data, in order to find alternatives to the normal distribution in multinormality tests and in the creation of statistical models in which the usual assumption of normality is not realistic. Some achieved results, open issues and some proposals for their use in applications, especially in the financial area, are here presented.
A Synthetic Approach to Multivariate Normal Clustering
1982
Two methods have been suggested for grouping together observations originated from the same multivariate normal distributions, both based on a maximum-likelihood (ML) estimation, but leading to different conclusions. In this paper we compare the use of Day’s approach and that of Scott and Symons in clustering procedures from the theoretical and computational point of view. Based on this comparison, we suggest an approach unifying those approaches. The workability of the approach will be verified by numerical experiments.