fsemipar-package {fsemipar}

Estimation, Variable Selection and Prediction for Functional Semiparametric Models

Description

This package is dedicated to the estimation and simultaneous estimation and variable selection in several functional semiparametric models with scalar response. These include the functional single-index model, the semi-functional partial linear model, and the semi-functional partial linear single-index model. Additionally, it encompasses algorithms for addressing estimation and variable selection in linear models and bi-functional partial linear models when the scalar covariates with linear effects are derived from the discretisation of a curve. Furthermore, the package offers routines for kernel- and kNN-based estimation using Nadaraya-Watson weights in models with a nonparametric or semiparametric component. It also includes S3 methods (predict, plot, print, summary) to facilitate statistical analysis across all the considered models and estimation procedures.

Details

The package can be divided into several thematic sections:

1. Estimation of the functional single-index model.

   • projec.

   • semimetric.projec.

   • fsim.kernel.fit and fsim.kNN.fit.

   • fsim.kernel.fit.optim and fsim.kNN.fit.optim

   • fsim.kernel.test and fsim.kNN.test.

   • predict, plot, summary and print methods for fsim.kernel and fsim.kNN classes.

2. Simultaneous estimation and variable selection in linear and semi-functional partial linear models.

   1. Linear model

      • lm.pels.fit.

      • predict, summary, plot and print methods for lm.pels class.

   2. Semi-functional partial linear model.

      • sfpl.kernel.fit and sfpl.kNN.fit.

      • predict, summary, plot and print methods for sfpl.kernel and sfpl.kNN classes.

   3. Semi-functional partial linear single-index model.

      • sfplsim.kernel.fit and sfplsim.kNN.fit.

      • predict, summary, plot and print methods for sfplsim.kernel and sfplsim.kNN classes.

3. Algorithms for impact point selection in models with covariates derived from the discretisation of a curve.

   1. Linear model

      • PVS.fit.

      • predict, summary, plot and print methods for PVS class.

   2. Bi-functional partial linear model.

      • PVS.kernel.fit and PVS.kNN.fit.

      • predict, summary, plot and print methods for PVS.kernel and PVS.kNN classes.

   3. Bi-functional partial linear single-index model.

      • FASSMR.kernel.fit and FASSMR.kNN.fit.

      • IASSMR.kernel.fit and IASSMR.kNN.fit.

      • predict, summary, plot and print methods for FASSMR.kernel, FASSMR.kNN, IASSMR.kernel and IASSMR.kNN classes.

4. Two datasets: Tecator and Sugar.

Author(s)

German Aneiros [aut], Silvia Novo [aut, cre]

Maintainer: Silvia Novo <[e-mail]>

References

Aneiros, G. and Vieu, P., (2014) Variable selection in infinite-dimensional problems, Statistics and Probability Letters, 94, 12–20. doi:10.1016/j.spl.2014.06.025.

Aneiros, G., Ferraty, F., and Vieu, P., (2015) Variable selection in partial linear regression with functional covariate, Statistics, 49 1322–1347, doi:10.1080/02331888.2014.998675.

Aneiros, G., and Vieu, P., (2015) Partial linear modelling with multi-functional covariates. Computational Statistics, 30, 647–671. doi:10.1007/s00180-015-0568-8.

Novo S., Aneiros, G., and Vieu, P., (2019) Automatic and location-adaptive estimation in functional single-index regression, Journal of Nonparametric Statistics, 31(2), 364–392, doi:10.1080/10485252.2019.1567726.

Novo, S., Aneiros, G., and Vieu, P., (2021) Sparse semiparametric regression when predictors are mixture of functional and high-dimensional variables, TEST, 30, 481–504, doi:10.1007/s11749-020-00728-w.

Novo, S., Aneiros, G., and Vieu, P., (2021) A kNN procedure in semiparametric functional data analysis, Statistics and Probability Letters, 171, 109028, doi:10.1016/j.spl.2020.109028.

Novo, S., Vieu, P., and Aneiros, G., (2021) Fast and efficient algorithms for sparse semiparametric bi-functional regression, Australian and New Zealand Journal of Statistics, 63, 606–638, doi:10.1111/anzs.12355.