Functional Linear Regression of CDFs

This repository is the official implementation of the numerical experiments in the paper "Functional Linear Regression of Cumulative Distribution Functions".

Requirements

Python version we used: Python 3.6.9.

R version we used: R version 4.1.2.

To install requirements for the synthetic data experiments:

pip3 install -r requirements.txt

To install R packages used in the real data experiments:

# Run the following R codes in R.
install.packages('hdm')
install.packages('stats')
install.packages('quadprog')

Synthetic data experiments

Estimation errors against sample size (Figure 2a)

To obtain the $\ell^2$ errors and KS distances under different sample sizes with the simulated sample and generate Figure 1a, run this command:

python3 simulation.py

Estimation errors against dimension (Figure 2b)

To obtain the $\ell^2$ errors and KS distances under different dimensions with the simulated sample and generate Figure 1b, run this command:

python3 sim_dim.py

Real data experiments

Estimation errors of the estimator and the projected estimator (Figure 2c)

To obtain the $\ell^2$ errors of the estimator and the projected estimator in the real data experiments, run:

Rscript exp_real_data.R

To plot Figure 1c, run

python3 plot_real_data.py

Results

After running the above commands, our codes

• save the estimation errors under different sample sizes in the simulation studies in 'sample_size.npz',

• generate Figure 2a in 'sim_sample_size.pdf',

• save the estimation errors under different dimensions in the simulation studies in 'dimension.npz',

• generate Figure 2b in 'sim_dimension.pdf',

• save the $\ell^2$ errors of the estimator and the projected estimator in the real data experiments in 'l2error_mat.txt' and 'l2error_proj_mat.txt' respectively,

• generate Figure 2c in 'exp_real_data.pdf'.