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Robustness of Principal Component Analysis with Spearman’s Rank Matrix
This paper is concerned with robust principal component analysis (PCA) based on spatial sign and spatial rank vectors. The most common PC approach is...
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Bounds on Multivariate Kendall’s Tau and Spearman’s Rho for Zero-Inflated Continuous Variables and their Application to Insurance
In this note, we derive upper bounds on Kendall’s tau and Spearman’s rho for multivariate zero-inflated continuous variables often encountered in...
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Rank Correlation
This chapter discusses the rank correlation and its extensions. The rank vector is introduced in section 1. This is followed by a discussion of...
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Measures of Ordinal Association I
Chapter 9 is the first of two chapters describing connections, equivalencies, and relationships relating to...
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New copula families and mixing properties
We characterize absolutely continuous symmetric copulas with square integrable densities in this paper. This characterization is used to create new...
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On a bivariate copula for modeling negative dependence: application to New York air quality data
In many practical scenarios, including finance, environmental sciences, system reliability, etc., it is often of interest to study the various notion...
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Bias in Rank Correlation Under Mixture Models
This study investigates the behavior of two prominent measures of rank correlation—Kendall’s tau and Spearman’s rho—under mixture models,...
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Measures of Interval Association
Chapter 8 describes connections, equivalencies, and relationships relating to bivariate linear correlation and...
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Dependence Orders
Dependence among random variables is one of the most widely studied topics in the literature with lots of applications in diverse areas. Pearson’s...
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Correlation Coefficients of Bivariate Normal Distributions
This lecture deals with the relationship between Pearson’s product-moment correlation coefficient and Spearman’s rank correlation coefficient under...
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Correlation, Association, Regression, Likelihood, and Prediction
The purpose of this lesson on correlation, association, regression, likelihood, and prediction is to provide guidance on how R can be used to first...
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Different Coefficients for Studying Dependence
Through computer simulations, we research several different measures of dependence, including Pearson’s and Spearman’s correlation coefficients, the...
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Correlation and Association
In this chapter presents exact and Monte Carlo permutation statistical methods for measures of linear correlation and association. Also presented in...
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Understanding relationships with the Aggregate Zonal Imbalance using copulas
In the Italian electricity market, we analyze the Aggregate Zonal Imbalance, which is the algebraic sum, changed in sign, of the amount of energy...
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Copulas
In today’s data-driven world, the analysis of multiple variables and their joint behavior has become increasingly important. Copulas offer a...
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Measures of Association
This chapter starts with a discussion on the historical development of correlation coefficients. It then discusses the population and sample...
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Marginals Matrix Under a Generalized Mallows Model Based on the Power Divergence
In rank data modeling, the classical distance-based approach has been extended by many authors in order to capture certain ranking features. Here, we...
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Analysis of Correlation and Regression
It is quite often that one is interested to quantify the dependence (positive or negative) between two or more random variables. The basic role of...
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Measures of Association
This chapter deals with measures of association, how inferences about these measures of association might be made, plus methods for comparing...