Related papers: A New Multiple Correlation Coefficient without Spe…
Understanding and developing a correlation measure that can detect general dependencies is not only imperative to statistics and machine learning, but also crucial to general scientific discovery in the big data age. In this paper, we…
One of the central objectives of modern risk management is to find a set of risks where the probability of multiple simultaneous catastrophic events is negligible. That is, risks are taken only when their joint behavior seems sufficiently…
We proposed a new statistical dependency measure called Copula Dependency Coefficient(CDC) for two sets of variables based on copula. It is robust to outliers, easy to implement, powerful and appropriate to high-dimensional variables. These…
Identifying how dependence relationships vary across different conditions plays a significant role in many scientific investigations. For example, it is important for the comparison of biological systems to see if relationships between…
We take a different look at the problem of testing the independence of two metric-space-valued random variables using the distance correlation. Instead of testing if the distance correlation vanishes exactly, we are interested in the…
Linear regression is a frequently used tool in statistics, however, its validity and interpretability relies on strong model assumptions. While robust estimates of the coefficients' covariance extend the validity of hypothesis tests and…
Besides the classical distinction of correlation and dependence, many dependence measures bear further pitfalls in their application and interpretation. The aim of this paper is to raise and recall awareness of some of these limitations by…
In the present paper we consider the varying coefficient model which represents a useful tool for exploring dynamic patterns in many applications. Existing methods typically provide asymptotic evaluation of precision of estimation…
Recently, the concept of tail dependence has been discussed in financial applications related to market or credit risk. The multivariate extreme value theory is a proper tool to measure and model dependence, for example, of large loss…
The coefficient of variation is a useful indicator for comparing the spread of values between dataset with different units or widely different means. In this paper we address the problem of investigating the equality of the coefficients of…
We describe an algorithm to quantify dependence in a multivariate data set. The algorithm is able to identify any linear and non-linear dependence in the data set by performing a hypothesis test for two variables being independent. As a…
Classification problems are essential statistical tasks that form the foundation of decision-making across various fields, including patient prognosis and treatment strategies for critical conditions. Consequently, evaluating the…
This paper deals with asymptotics for multiple-set linear canonical analysis (MSLCA). A definition of this analysis, that adapts the classical one to the context of Euclidean random variables, is given and properties of the related…
Multivariate correlation analysis plays a key role in various fields such as statistics and big data analytics. In this paper, it is presented a new non-parametric association measure between more than two variables based on the concept of…
In this article, we consider the problem of testing the independence between two random variables. Our primary objective is to develop tests that are highly effective at detecting associations arising from explicit or implicit functional…
This paper proposes a new statistic to test independence between two high dimensional random vectors ${\mathbf{X}}:p_1\times1$ and ${\mathbf{Y}}:p_2\times1$. The proposed statistic is based on the sum of regularized sample canonical…
In this paper we propose an extension of the classical Sobol' estimator for the estimation of variance based sensitivity indices. The approach assumes a linear correlation model between the input variables which is used to decompose the…
Accurately estimating the proportion of true signals among a large number of variables is crucial for enhancing the precision and reliability of scientific research. Traditional signal proportion estimators often assume independence among…
We propose a coefficient that measures dependence in paired samples of functions. It has properties similar to the Pearson correlation, but differs in significant ways: (i) it is designed to measure dependence between curves, (ii) it…
Identifying dependency in multivariate data is a common inference task that arises in numerous applications. However, existing nonparametric independence tests typically require computation that scales at least quadratically with the sample…