Simulation (Ours vs GY)

This repository also includes a simulation framework to compare:

• Ours: split + Hoeffding-adjusted tolerance intervals
• GY: Guo–Young-style spline-based tolerance intervals (full-sample; no split)

Setup

All simulation code is under:

• R/sim/ : core functions (data generation, truth content, fitting, intervals, replication runner)
• scripts/ : runnable entry scripts

Key files:

• R/sim/data_generate.R : generate_data(model_id, n) for simulation models
• R/sim/truth_content.R : content_function(model_id, lower, upper, x) for true conditional content
• R/sim/one_replication_ours.R : one replication for Ours
• R/sim/one_replication_gy.R : one replication for GY
• R/sim/run_one_setting.R : runs M replications and returns pointwise summaries for both methods
• scripts/run_simulation_grid.R : runs a grid over models and sample sizes and saves results

Parameters and notation

• content : target content level (e.g., 0.90)
• mis = 1 - content : miscoverage level
• alpha : confidence error level (confidence is 1 - alpha)
• n : sample size per replication
• M : number of Monte Carlo replications per (model, n)

How to run

Run Simulation (CP)

From the project root:

Rscript scripts/run_simulation_grid.R

Make a plot

Rscript scripts/make_plot.R

Outputs

pointwise CSV with columns:

• x : evaluation grid point
• coverage : proportion of replicatioin with `true_content(x) >= content
• mean_width : mean interval with at x
• na_proportion : proportion of replications with NA/failed parameters
• model : model id
• n : sample size
• Method : "Ours" or "GY"

Notes

• The evaluation grid is `x = seq(0, 10, length.out = n). For reproducibility, seed are managed inside the replication loop.
• Results (results/, *.csv, *.png) are excluded.

References

• Guo, Y. and Young, D. S. (2024).
  Approximate tolerance intervals for nonparametric regression models.
  Journal of Nonparametric Statistics, 36(1), 212–239.
  DOI: https://doi.org/10.1080/10485252.2023.2277260