Related papers: Frequentist Model Averaging for Global Fr\'{e}chet…
Model selection strategies have been routinely employed to determine a model for data analysis in statistics, and further study and inference then often proceed as though the selected model were the true model that were known a priori. This…
The Fr\'echet regression is a useful method for modeling random objects in a general metric space given Euclidean covariates. However, the conventional approach could be sensitive to outlying objects in the sense that the distance from the…
Data consisting of samples of probability density functions are increasingly prevalent, necessitating the development of methodologies for their analysis that respect the inherent nonlinearities associated with densities. In many…
A common feature of methods for analyzing samples of probability density functions is that they respect the geometry inherent to the space of densities. Once a metric is specified for this space, the Fr\'echet mean is typically used to…
We study the problem of network regression, where one is interested in how the topology of a network changes as a function of Euclidean covariates. We build upon recent developments in generalized regression models on metric spaces based on…
Model averaging considers the model uncertainty and is an alternative to model selection. In this paper, we propose a frequentist model averaging estimator for composite quantile regressions. In recent years, research on these topics has…
Model averaging has gained significant attention in recent years due to its ability of fusing information from different models. The critical challenge in frequentist model averaging is the choice of weight vector. The bootstrap method,…
In this paper we construct optimal designs for frequentist model averaging estimation. We derive the asymptotic distribution of the model averaging estimate with fixed weights in the case where the competing models are non-nested and none…
We consider the problem of designing experiments for the estimation of a target in regression analysis if there is uncertainty about the parametric form of the regression function. A new optimality criterion is proposed, which minimizes the…
Regression with distribution-valued responses and Euclidean predictors has gained increasing scientific relevance. While methodology for univariate distributional data has advanced rapidly in recent years, multivariate distributions, which…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…
We study nonparametric density estimation problems where error is measured in the Wasserstein distance, a metric on probability distributions popular in many areas of statistics and machine learning. We give the first minimax-optimal rates…
Quantifying model uncertainty is critical for understanding prediction reliability, yet distinguishing between aleatoric and epistemic uncertainty remains challenging. We extend recent work from classification to regression to provide a…
In this article, we consider the problem of estimating the parameters of the Fr\'echet distribution from both frequentist and Bayesian points of view. First we briefly describe different frequentist approaches, namely, maximum likelihood,…
We study the estimation problem of distribution-on-distribution regression, where both predictors and responses are probability measures. Existing approaches typically rely on a global optimal transport map or tangent-space linearization,…
Statistical analysis is increasingly confronted with complex data from metric spaces. Petersen and M\"uller (2019) established a general paradigm of Fr\'echet regression with complex metric space valued responses and Euclidean predictors.…
Model averaging is an important alternative to model selection with attractive prediction accuracy. However, its application to high-dimensional data remains under-explored. We propose a high-dimensional model averaging method via…
Considering two random variables with different laws to which we only have access through finite size iid samples, we address how to reweight the first sample so that its empirical distribution converges towards the true law of the second…
The problem of modeling the relationship between univariate distributions and one or more explanatory variables has found increasing interest. Traditional functional data methods cannot be applied directly to distributional data because of…
Increasingly, statisticians are faced with the task of analyzing complex data that are non-Euclidean and specifically do not lie in a vector space. To address the need for statistical methods for such data, we introduce the concept of…