Wasserstein Regression and Inference

Implementation of the methodologies described in 1) Alexander Petersen, Xi Liu and Afshin A. Divani (2021) , including global F tests, partial F tests, intrinsic Wasserstein-infinity bands and Wasserstein density bands, and 2) Chao Zhang, Piotr Kokoszka and Alexander Petersen (2022) , including estimation, prediction, and inference of the Wasserstein autoregressive models.

WRI

An R package for the paper “Wasserstein F-tests and confidence bands for the Frechet regression of density response curves”.

Installation

You can install the released version of WRI from CRAN with:

install.packages("WRI")

Example

This is a basic example which shows you how to solve a common problem:

library(WRI)
data(strokeCTdensity)
predictor = strokeCTdensity$predictors
dSup = strokeCTdensity$densitySupport
densityCurves = strokeCTdensity$densityCurve
xpred = predictor[3, ]

res = wass_regress(rightside_formula = ~., Xfit_df = predictor,
Ytype = 'density', Ymat = densityCurves, Sup = dSup)
# compute the density band for the third observation
confidence_Band1 = confidenceBands(res, Xpred_df = xpred, type = 'density')

Main components

• strokeCTdensity: clinical, radiological scalar variables and density curves of the hematoma of 393 stroke patients
• wass_regress: perform Frechet Regression with the Wasserstein Distance
• wass_R2: compute Wasserstein coefficient of determination
• globalFtest: perform global F test for Wasserstein regression
• partialFtest: perform partial F test for Wasserstein regression
• summary.WRI: provide summary information of Wasserstein regression
• confidenceBands: compute intrinsic confidence bands and density bands