Related papers: The Fr\'echet correlation coefficient for heteroge…
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…
We describe a method for unmixing mixtures of freely independent random variables in a manner analogous to the independent component analysis (ICA) based method for unmixing independent random variables from their additive mixtures. Random…
Graphical structure learning is an effective way to assess and visualize cross-biomarker dependencies in biomedical settings. Standard approaches to estimating graphs rely on conditional independence tests that may not be sensitive to…
Quantile regression provides a framework for modeling statistical quantities of interest other than the conditional mean. The regression methodology is well developed for linear models, but less so for nonparametric models. We consider…
Accurate estimation for extent of cross{sectional dependence in large panel data analysis is paramount to further statistical analysis on the data under study. Grouping more data with weak relations (cross{sectional dependence) together…
The complexity of semiparametric models poses new challenges to statistical inference and model selection that frequently arise from real applications. In this work, we propose new estimation and variable selection procedures for the…
This work introduces a novel methodology for assessing catastrophic forgetting (CF) in continual learning. We propose a new conformal prediction (CP)-based metric, termed the Conformal Prediction Confidence Factor (CPCF), to quantify and…
In high dimensional analysis, effects of explanatory variables on responses sometimes rely on certain exposure variables, such as time or environmental factors. In this paper, to characterize the importance of each predictor, we utilize its…
Identifying systemic risk patterns in geopolitical, economic, financial, environmental, transportation, epidemiological systems and their impacts is the key to risk management. This paper proposes a new nonlinear time series model:…
This paper advances a variable screening approach to enhance conditional quantile forecasts using high-dimensional predictors. We have refined and augmented the quantile partial correlation (QPC)-based variable screening proposed by Ma et…
This paper introduces FlexCodeTS, a new conditional density estimator for time series. FlexCodeTS is a flexible nonparametric conditional density estimator, which can be based on an arbitrary regression method. It is shown that FlexCodeTS…
Many scientific and industrial processes produce data that is best analysed as vectors of relative values, often called compositions or proportions. The Dirichlet distribution is a natural distribution to use for composition or proportion…
This paper proposes probabilistic conformal prediction (PCP), a predictive inference algorithm that estimates a target variable by a discontinuous predictive set. Given inputs, PCP construct the predictive set based on random samples from…
Heteroskedastic errors can lead to inaccurate statistical conclusions if they are not properly handled. We introduce a test for heteroskedasticity for the nonparametric regression model with multiple covariates. It is based on a suitable…
In order to address complex systems, apply pattern recongnition on their evolution could play an key role to understand their dynamics. Global patterns are required to detect emergent concepts and trends, some of them with qualitative…
Using first principles from inference, we design a set of functionals for the purposes of \textit{ranking} joint probability distributions with respect to their correlations. Starting with a general functional, we impose its desired…
Signal averaging is the process that consists in computing a mean shape from a set of noisy signals. In the presence of geometric variability in time in the data, the usual Euclidean mean of the raw data yields a mean pattern that does not…
The present paper solves the problem of local linear approximation of the Fr\'echet conditional mean in an extrinsic and intrinsic way from time correlated bivariate curve data evaluated in a manifold (see Torres et al, 2025, on global…
We show that the stochastic independence of real-valued random variables is equivalent to the conditional uncorrelation, where the conditioning takes place over the Cartesian products of intervals. Next, we express the mutual independence…
Formal concept analysis (FCA) is a useful mathematical tool for obtaining information from relational datasets. One of the most interesting research goals in FCA is the selection of the most representative variables of the dataset, which is…