plmisot

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R code for the simulation study in:

Rodríguez, D., Valdora, M., and Vena, P. (2022). Robust estimation in partially linear regression models with monotonicity constraints. Communications in Statistics - Simulation and Computation. DOI: 10.1080/03610918.2019.1691732

This is the working implementation the authors used to produce the simulation results in the paper. It is not the supplementary material formally submitted to the journal.

Model

The paper studies the partially linear model

y = x' beta + g(t) + epsilon

with g monotone, in the presence of outliers in the response and the carriers. The repo implements two robust estimators and the simulation study used to compare them.

Estimators

• Alv-Yoh (type = "nos"): the proposal of the paper. Combines a robust semiparametric step (Bianco-Boente style) with the monotone M-estimator of Álvarez and Yohai (2012) for isotonic regression.
• Lu-Du (type = "splines"): the spline-based competitor following Lu (2010), fit by constrained optimization with a choice of loss (ls, huber, tukey, l1).

Repo layout

corridas.R          driver: runs the paper simulations
procesamos.R        driver: builds summary tables and plots from outputs
graficos-paper.R    driver: produces the figures included in the paper
src/
  simular.R         simulation wrappers (Alv-Yoh and Lu-Du)
  generar.R         data generation and contamination schemes (C0, C13, C15, C210, C215, C3)
  mpl.R             Alv-Yoh estimator (partially linear, monotone)
  minimizar.R       constrained optimization for the Lu-Du estimator
  procesar.R        post-processing of simulation outputs
  helpers.R         small utilities
  plotear.R         plotting helpers

Dependencies

R packages: alabama, fda, robustbase, Hmisc, xtable.

install.packages(c("alabama", "fda", "robustbase", "Hmisc", "xtable"))

Usage

Run from the repo root so the relative source('src/...') paths resolve.

Alv-Yoh estimator (estimate$type = "nos", ven is the kernel bandwidth):

source("src/simular.R")
simular(datos = "revision",
        nn = 100,
        estimate = list(type = "nos", ven = c(0.15, 0.45, 0.6, 0.3)),
        cont = "C215",
        poda = 0,
        from = 1, to = 5,
        carpeta = "toy-example")

Lu-Du estimator (estimate$type = "splines", spl is the number of B-spline basis functions):

source("src/simular.R")
simular(datos = "revision",
        nn = 100,
        estimate = list(type = "splines", initial = "cl", fLoss = "huber", spl = 4:13),
        cont = "C215",
        poda = 0,
        from = 1, to = 5,
        carpeta = "toy-example")

initial is the starting point for the optimization ("cl" classical, "rb" robust, "ay" Alv-Yoh).

Reproducing the paper

corridas.R runs the full simulation study (1000 replications per contamination scheme, four bandwidths). The same script also has a smaller toy example. Outputs go to a folder named by the carpeta argument; procesamos.R and graficos-paper.R consume those folders to produce the tables and figures.

Each replication seeds the RNG with its iteration index, so results are reproducible.

References

• Álvarez, E.E. and Yohai, V.J. (2012). M-estimators for isotonic regression. Journal of Statistical Planning and Inference, 142(8), 2351-2368. doi:10.1016/j.jspi.2012.02.051
• Lu, M. (2010). Spline-based sieve maximum likelihood estimation in the partly linear model under monotonicity constraints. Journal of Multivariate Analysis, 101(10), 2528-2542. doi:10.1016/j.jmva.2010.07.002
• Rodríguez, D., Valdora, M. and Vena, P. (2022). Robust estimation in partially linear regression models with monotonicity constraints. Communications in Statistics - Simulation and Computation. doi:10.1080/03610918.2019.1691732

Citation

If you use this code, please cite the paper.