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Thegmwmx2R package implements the Generalized Method of Wavelet Moments with Exogenous Inputs estimator (GMWMX) presented inVoirol, L., Xu, H., Zhang, Y., Insolia, L., Molinari, R. and Guerrier, S. (2024).The GMWMX estimator is a computationally efficient estimator to estimate large scale regression problems with complex dependence structure in presence of missing data.Thegmwmx2R package allows to estimate (i) functional/structural parameters, (ii) stochastic parameters describing the dependence structure and (iii) nuisance parameters of the missingness process of large regression models with dependent observations and missing data.To illustrate the capability of the GMWMX estimator, thegmwmx2R package provides functions to download an plot Global Navigation Satellite System (GNSS) position time series from theNevada Geodetic Laboratory and allow to estimate linear model with a specific dependence structure modeled by composite stochastic processes, allowing to estimate tectonic velocities and crustal uplift from GNSS position time series.

Find vignettes with detailed examples as well as the user's manual at thepackage website.

Below are instructions on how to install and make use of thegmwmx2 package.

Thegmwmx2 package is available on both CRAN and GitHub. The CRANversion is considered stable while the GitHub version is subject tomodifications/updates which may lead to installation problems or brokenfunctions. You can install the stable version of thegmwmx2 packagewith:

install.packages("gmwmx2")

For users who are interested in having the latest developments, theGitHub version is ideal although more dependencies are required to run astable version of the package. Most importantly, usersmust have a(C++) compiler installed on their machine that is compatible withR(e.g.Clang).

# Install dependenciesinstall.packages(c("devtools"))# Install/Update the package from GitHubdevtools::install_github("SMAC-Group/gmwmx2")# Install the package with Vignettes/User Guidesdevtools::install_github("SMAC-Group/gmwmx2",build_vignettes=TRUE)

Thegmwmx2 package relies on a limited number of external libraries, but notably onRcpp andRcppArmadillo which require aC++ compiler for installation, such as for examplegcc.

The originalgmwmx package was designed to compare estimated parameters obtained from the GMWMX with the ones obtained with the Maximum Likelihood Estimator (MLE) implemented inHector.This allowed for the replication of examples and simulations discussed inCucci, D. A., Voirol, L., Kermarrec, G., Montillet, J. P., and Guerrier, S. (2022).However, as we advanced in the methodological and computational development of the GMWMX method, we sought a standalone implementation that did not includeHector.Additionally, many of the new computational techniques and structural improvements would have been challenging to incorporate into the previousgmwmx package.Therefore, we will now exclusively support and develop thegmwmx2 package.

Thegmwmx2 package is currently in the early stages of development. While the supported features are stable, we have numerous additional methods and computational enhancements planned for gradual integration. These include:

• Computational optimization to improve speed
• Support for a wider range of stochastic models to describe the error term
• Support for a wider range of stochastic models to describe the missingness process
• A computationally efficient model selection criterion for stochastic models

This source code is released under is the GNU AFFERO GENERAL PUBLIC LICENSE (AGPL) v3.0.

Voirol, L., Xu, H., Zhang, Y., Insolia, L., Molinari, R., and Guerrier, S. (2024). Inference for Large Scale Regression Models with Dependent Errors.doi:10.48550/arXiv.2409.05160.

Guerrier, S., Skaloud, J., Stebler, Y. and Victoria-Feser, M.P., 2013. Wavelet-variance-based estimation for composite stochastic processes. Journal of the American Statistical Association, 108(503), pp.1021-1030.doi:10.1080/01621459.2013.799920