Random vectors and covariance matrices - theory

2013 ◽  
pp. 139-171
Keyword(s):  
Covariance Matrices ◽  
Random Vectors

scholarly journals Supermodular ordering of Poisson and binomial random vectors by tree-based correlations

2018 ◽  
Vol 38 (2) ◽  
pp. 385-405
Author(s):  
Nicolas Privault ◽  
Bünyamin Kizildemir
Keyword(s):  
Random Variables ◽  
Covariance Matrices ◽  
Binary Trees ◽  
Independent Random Variables ◽  
Dependence Structure ◽  
Random Vectors ◽  
Partially Ordered ◽  
Ordered Trees ◽  
Lévy Measures ◽  
Inversion Techniques

We construct a dependence structure for binomial, Poisson and Gaussian random vectors, based on partially ordered binary trees and sums of independent random variables. Using this construction, we characterize the supermodular ordering of such random vectors via the componentwise ordering of their covariance matrices. For this, we apply Möbius inversion techniques on partially ordered trees, which allow us to connect the Lévy measures of Poisson random vectors on the discrete d-dimensional hypercube to their covariance matrices.

Quadratic Discriminant Analysis of Spatially Correlated Data

2001 ◽  
Vol 6 (2) ◽  
pp. 15-28 ◽  
Author(s):  
K. Dučinskas ◽  
J. Šaltytė
Keyword(s):  
Discriminant Function ◽  
Error Rate ◽  
Gaussian Random Field ◽  
Correlated Data ◽  
Covariance Matrices ◽  
Classification Rule ◽  
Spatial Correlations ◽  
Linear Quadratic ◽  
Spatial Correlation Function ◽  
Spatially Correlated

The problem of classification of the realisation of the stationary univariate Gaussian random field into one of two populations with different means and different factorised covariance matrices is considered. In such a case optimal classification rule in the sense of minimum probability of misclassification is associated with non-linear (quadratic) discriminant function. Unknown means and the covariance matrices of the feature vector components are estimated from spatially correlated training samples using the maximum likelihood approach and assuming spatial correlations to be known. Explicit formula of Bayes error rate and the first-order asymptotic expansion of the expected error rate associated with quadratic plug-in discriminant function are presented. A set of numerical calculations for the spherical spatial correlation function is performed and two different spatial sampling designs are compared.

Pemberian Umpan Balik Dalam Meningkatkan Hasil Belajar dan Minat Belajar Mahasiswa

2015 ◽  
Vol 4 (3) ◽  
Author(s):  
Seruni Seruni ◽  
Nurul Hikmah
Keyword(s):  
Information Technology ◽  
Learning Outcomes ◽  
Test Data ◽  
Random Sampling ◽  
Covariance Matrices ◽  
Test Results ◽  
Immediate Feedback ◽  
Statistics Course ◽  
Independent Variable ◽  
Descriptive Statistical Analysis

<p>The purpose of this study is to find and analyze the effect of feedback on <br />learning outcomes in mathematics and an interest in basic statistics course. The <br />population in this study are affordable Information Technology Student cademic Year 2012/2013 Semester II Indraprasta PGRI University of South Jakarta. Sample The study sample was obtained through random sampling. This study used an experimental method to the analysis using the MANOVA test. This study has three variables, consisting of: one independent variable, namely the provision of feedback (immediate and delayed), and two dependent variable is the result of interest in the study of mathematics and basic statistics course. The data was collected for the test results to learn mathematics, and a questionnaire for the interest in basic statistics course. Collected data were analyzed using the MANOVA test. Before the data were analyzed, first performed descriptive statistical analysis and test data analysis requirements (test data normality and homogeneity of covariance matrices). The results show that the learning outcomes of interest in mathematics and basic statistics course for students who are given immediate feedback higher than students given feedback delayed. <br /><br /></p>

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