Code for OGAM

Overview

1. Directory FNS contains the main functions which are called for the simulations and data applications. Specifically,

• FNS_DataGene_Simu1 : function to generate data for simulation setting 1.
• FNS_DataGene_Simu2 : function to generate data for simulation setting 2.
• FNS_SmoBack : functions to conduct smoothbackfitting.
• FNS_SmoBack_credit : differs from FNS_SmoBack only in the stopping criterion.

2. Directory datasets contains the preprocessed datasets credit and flight for data applications. Raw data are available in the following links:

• credit : https://data.mendeley.com/datasets/wb3ndt69gf (P2P_Macro_Data.dta, 3 GB)
• flight : https://community.amstat.org/jointscsg-section/dataexpo/dataexpo2009

3. Directory res contains the analysis results of the simulations and data applications. Specifically,

• sim1: Numerical results of simulation setting 1, including the constants for bandwidths (batch_constants_for_bandwidths.Rdata and online_constants_for_bandwidths.Rdata), the batch estimates (batch_gam_1.Rdata--batch_gam_100.Rdata) and the online estimates (online_gam_L'X'_1.Rdata--online_gam_L'X'_100.Rdata) with different candidate sequence lengths X=3,5,10.

• sim2: Numerical results of simulation setting 2, including the constants for bandwidths (batch_constants_for_bandwidths.Rdata and online_constants_for_bandwidths.Rdata), the batch estimates (batch_gam_1.Rdata--batch_gam_100.Rdata) and the online estimates (online_gam_L'X'_1.Rdata--online_gam_L'X'_100.Rdata) with different candidate sequence lengths X=3,5,10.

• flight: Numerical results of the flight dataset analysis, including the constants for bandwidths (batch_constants_for_bandwidths.Rdata and online_constants_for_bandwidths.Rdata), the batch estimates (flight_full_batch.Rdata) and the online estimates (flight_full_online.Rdata).

• credit: Numerical results of the credit dataset analysis, including the constants for bandwidths (batch_constants_for_bandwidths.Rdata and online_constants_for_bandwidths.Rdata), the batch estimates (credit_batch.Rdata) and the online estimates (credit_online.Rdata).

4. Directory fig contains the figures generated by the numerical experiments. Specificaly,

• theoretical_eff.pdf: The theoretical lower bound for the relative efficiency of the proposed online estimates versus different lengths of candidate bandwidth sequences, which corresponds to Figure 4 in the main context.
• selection_L.pdf: The relationship between the computational cost and the length of candidate bandwidth sequence, which corresponds to Figure 5 in the main context.
• simu_empirical_eff.pdf: The empirical relative efficiency for the simulations that corresponds to Figure 6 in the main context.
• simu_time.pdf: The comparison of computing times for the simulations that corresponds to Figure 7 in the main context.
• flights_betas.pdf: The component function estimates for the flights dataset, which corresponds to Figure 8 in the main context.
• credit_betas.pdf: The component function estimates for the credit dataset, which corresponds to Figure 9 in the main context.
• compare.pdf: The relative efficiencies of the proposed method and other online nonparametric methods in the degenerated one-dimensional case, which corresponds to Figure 1 in the supplement.

5. Directory Compare_Code contains the code for simulation in Section S.2 of the supplement to compare with other online nonparametric methods in the degenerated one-dimensional case. Specifically,

• The sub-directory Common contains functions that will be called by the R script simuscript.R.

• The sub-directory DPSR_results_from Python contains the numerical results of the method of Xue introduced in Section S.2 of the supplement, which was performed by the same synthetic data and by the Python version developed by and obtained through personal communications with the authors (the Python code thus cannot be made publicly here).

• The sub-directory res contains the numerical results of the proposed method as well as the methods of Kong and Quan, as introduced in Section S.2 of the supplement.

• The R script simuscript.R contains the code to perform the simulation.

• The R script figplot.R contains the code to generate Figure 1 of the supplement.

Workflows

Simulation 1 and 2

1. Make sure that the R scripts simulation1.R and simulation2.R are in the same directory as the folder FNS.
2. As the bandwidth selection is not our focus, users can choose to run Section 1 and 2 of supp-bandwidth_selection.R to generate the constants for bandwidths or to load them directly in Step 3 for convenience. If choose to load them, make sure that the following files exist:

• res/sim1/online_constants_for_bandwidths.Rdata
• res/sim1/batch_constants_for_bandwidths.Rdata
• res/sim2/online_constants_for_bandwidths.Rdata
• res/sim2/batch_constants_for_bandwidths.Rdata

3. Run the R scripts simulation1.R and simulation2.R which will load the constants for bandwidths and call functions in the folder FNS to compute the integrated mean square errors of the online and batch estimates as well as computing times. The corresponding results will be stored in the directory res/sim1 and directory res/sim2.
4. Run the R scripts simu_figplot.R to generate Figure 4-7.

Simulation 3 in the supplementary materials

1. Run the R script Compare_Code/simuscript.R which will compute the integrated mean square errors of different online nonparametric methods in the degenerated one-dimensional case.
2. Run the R script Compare_Code/figplot.R to generate Figure 1 of the supplement.

Data application 1: the flight dataset

1. Due to the upload restrictions, we provide the preprocessed data here, which are separated into several parts. Run datasets/flight/flight_merge.R to merge them or download the raw csv data from the link in the Overview to the directory datasets/flight and run datasets/flight/flight_preprocess.R to preprocess the raw csv data.
2. As the bandwidth selection is not our focus, users can choose to run Section 3 of supp-bandwidth_selection.R to generate the constants for bandwidths or to load them directly in Step 3 for convenience. If choose to load them, make sure that the following files exist:

• res/flight/online_constants_for_bandwidths.Rdata
• res/flight/batch_constants_for_bandwidths.Rdata

3. Run the R script flight_main.R which will compute the online and batch estimates as well as computing times. The corresponding results will be stored in the directory res/flight.
4. Run the R script flight_figplot.R to generate table 1 and Figure 8

Data application 2: the credit dataset

1. Run datasets/credit/credit_merge.R to merge the separated preprocessed data or download the raw csv data from the link in the Overview to the directory datasets/credit and run datasets/credit/credit_preprocess.R to preprocess the raw csv data.
2. Run Section 4 of supp-bandwidth_selection.R to generate the constants for bandwidths, or load them directly in Step 3 for convenience. If choose to load them, make sure that the following files exist:

• res/credit/online_constants_for_bandwidths.Rdata
• res/credit/batch_constants_for_bandwidths.Rdata

3. Run the R script credit_main.R which will compute the online and batch estimates as well as computing times. The corresponding results will be stored in the directory res/credit.
4. Run the R script credit_figplot.R to generate table 2 and Figure 9.