Exp_Map_Barycenter_Method_pw

This function implements the Exponential map to calculate \(\hat{F}_t(u)\) for a fixed \(u\)

internal

Implementation of the methodologies described in 1) Alexander Petersen, Xi Liu and Afshin A. Divani (2021) <doi:10.1214/20-aos1971>, 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) <doi:10.1111/jtsa.12590>, including estimation, prediction, and inference of the Wasserstein autoregressive models.

Xi Liu

Wasserstein Regression and Inference

Chao Zhang

Matthew Coleman

Alexander Petersen

Exp_Map_Barycenter_Method_pw function

<dl><dt>u</dt>
<dd>The value where the cdf \(\hat{F}\) is evaluated</dd>
<dt>forecast</dt>
<dd>A vector that contains the WAR(p) model forecast result</dd>
<dt>cdf</dt>
<dd>The quantile grid used in forecasting</dd></dl>

Arguments

Numerical implementation of the pointwise Exponential map — Exp_Map_Barycenter_Method_pw

<dl>

<dt>u</dt>
<dd>The value where the cdf \(\hat{F}\) is evaluated</dd>


<dt>forecast</dt>
<dd>A vector that contains the WAR(p) model forecast result</dd>


<dt>cdf</dt>
<dd>The quantile grid used in forecasting</dd>

</dl>

Exp_Map_Barycenter_Method_pw: Numerical implementation of the pointwise Exponential map

Description

Usage

Value

Arguments

References