README

This repository provides code to reproduce the results of the following paper:

Nikolaos Ignatiadis, Sujayam Saha, Dennis L. Sun & Omkar Muralidharan (2021) Empirical Bayes Mean Estimation With Nonparametric Errors Via Order Statistic Regression on Replicated Data, Journal of the American Statistical Association, DOI: 10.1080/01621459.2021.1967164

The paper is also available on arXiv:

Nikolaos Ignatiadis, Sujayam Saha, Dennis L. Sun & Omkar Muralidharan (2021). Empirical Bayes mean estimation with nonparametric errors via order statistic regression on replicated data. [arXiv]

The main method has been implemented in Julia and is available as the Aurora.jl Julia package.

AuroraR

In the subdirectory AuroraR of this repository we provide a R package that wraps the Julia package and includes code for the different methods and simulations in the paper.

The R package may be installed as follows:

devtools::install_github("nignatiadis/AuroraPaper", subdir="AuroraR")

We note that the R package also wraps the nonparametric maximum likelihood (NPMLE) functionality from the REBayes package. In turn, REBayes requires a working installation of the Mosek convex optimization solver; we used Version 9.2.

Reproduction code

The folder simulation_scripts contains the code for the simulation studies (that calls functions from the AuroraR package above). Concretely:

• simulation_scripts/homoskedastic_simulations.R runs the simulations of Section 6.1. It can be called in the terminal via R homoskedastic_simulations.R arg1 dir, where arg1 can take on values 1,2,.., 6 (corresponding to different combinations of prior/likelihood) and dir is the directory in which Julia is installed.
• simulation_scripts/heteroskedastic_simulations.R runs the simulations of Section 6.2. It can be called in the terminal via R heteroskedastic_simulations.R arg1 dir where arg1 can take values 1,2 or 3 (for the three simulation settings considered) and dir is the Julia directory.
• simulation_scripts/pareto_simulations.R runs the simulations of Section 6.3. (Warning: the case with 100,000 units and 100 replicates is slow and may take >20 hours per Monte Carlo replicate.)

The vignettes folder contains R Markdown files that reproduce the figures from the paper, some of which require files that are generated from the three previous scripts.

• vignettes/motivation.Rmd reproduces Figure 1.
• vignettes/homoskedastic_simulations_plots.Rmd reproduces Figure 2.
• vignettes/location_family_auroral_coefficients.Rmd reproduces Figure 3.
• vignettes/heteroskedastic_simulations_plots.Rmd reproduces Figure 4.
• vignettes/pareto_simulations_plots.Rmd reproduces Figure 5.