Related papers: Varying-Coefficient Fr\'echet Regression
This paper provides a new methodology to analyze unobserved heterogeneity when observed characteristics are modeled nonlinearly. The proposed model builds on varying random coefficients (VRC) that are determined by nonlinear functions of…
Quantile regression has been successfully used to study heterogeneous and heavy-tailed data. Varying-coefficient models are frequently used to capture changes in the effect of input variables on the response as a function of an index or…
The varying coefficient model has received broad attention from researchers as it is a powerful dimension reduction tool for non-parametric modeling. Most existing varying coefficient models fitted with polynomial spline assume equidistant…
Mixed effect modeling for longitudinal data is challenging when the observed data are random objects, which are complex data taking values in a general metric space without linear structure. In such settings the classical additive error…
In this paper, we propose a varying coefficient panel data model with unobservable multiple interactive fixed effects that are correlated with the regressors. We approximate each coefficient function by B-spline, and propose a robust…
Time-varying non-Euclidean random objects are playing a growing role in modern data analysis, and periodicity is a fundamental characteristic of time-varying data. However, quantifying periodicity in general non-Euclidean random objects…
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…
Linear regression is widely used to model relationships between responses and predictors. In modern applications, one encounters data where the responses are non-Euclidean random objects situated in a metric space, paired with Euclidean…
Fr\'echet mean and variance provide a way of obtaining mean and variance for general metric space valued random variables and can be used for statistical analysis of data objects that lie in abstract spaces devoid of algebraic structure and…
We introduce an improved variational autoencoder (VAE) for text modeling with topic information explicitly modeled as a Dirichlet latent variable. By providing the proposed model topic awareness, it is more superior at reconstructing input…
The quantile varying coefficient (VC) model can flexibly capture dynamical patterns of regression coefficients. In addition, due to the quantile check loss function, it is robust against outliers and heavy-tailed distributions of the…
This paper proposes a new high dimensional regression method by merging Gaussian process regression into a variational autoencoder framework. In contrast to other regression methods, the proposed method focuses on the case where output…
We in this paper consider Fr\'echet sufficient dimension reduction with responses being complex random objects in a metric space and high dimension Euclidean predictors. We propose a novel approach called weighted inverse regression…
To consider model uncertainty in global Fr\'{e}chet regression and improve density response prediction, we propose a frequentist model averaging method. The weights are chosen by minimizing a cross-validation criterion based on Wasserstein…
Human migration exhibits complex spatiotemporal dependence driven by environmental and socioeconomic forces. Modeling such patterns at scale requires methods that accommodate many random effects while remaining feasible when raw data or…
The existing Fr\'echet regression is actually defined within a linear framework, since the weight function in the Fr\'echet objective function is linearly defined, and the resulting Fr\'echet regression function is identified to be a linear…
It is well known, that Fr\'echet means on non-Euclidean spaces may exhibit nonstandard asymptotic rates depending on curvature. Even for distributions featuring standard asymptotic rates, there are non-Euclidean effects, altering finite…
The linear varying coefficient models posits a linear relationship between an outcome and covariates in which the covariate effects are modeled as functions of additional effect modifiers. Despite a long history of study and use in…
Empirical regression discontinuity (RD) studies often include covariates in their specifications to increase the precision of their estimates. In this paper, we propose a novel class of estimators that use such covariate information more…
We develop IV Fr\'echet regression (IVFR), an instrumental-variable (IV) method for settings where the outcome is an entire distribution. Framing the problem as an IV regression in 2-Wasserstein space, IVFR extends global Fr\'echet…