Quantile Non‑parametric Additive Models
DOI:
https://doi.org/10.18778/0208-6018.345.07Keywords:
Quantile regression, nonparametric regression, additive modelAbstract
Quantile regression allows us to assess different possible impacts of covariates on different quantiles of a response variable. Additive models for quantile functions provide an attractive framework for non‑parametric regression applications focused on functions of the response instead of its central tendency. Total variation smoothing penalties can be used to control the smoothness of additive components. We write down a general approach to estimation and inference for additive models of this type. Quantile regression as a risk measure has been applied in sector portfolio analysis for a data set from the Warsaw Stock Exchange.
Downloads
References
Breiman L., Friedman J. (1985), Estimating optimal transformations for multiple regression and correlation, “Journal of the American Statistical Association”, vol. 80, no. 391, pp. 580–598.
Google Scholar
Hastie T., Tibshirani R. (1986), Generalized Additive Models, “Statistical Science”, no. 1, pp. 297–310.
Google Scholar
Hastie T., Tibshirani R. (1990), Generalized Additive Models, Chapman Hall, New York.
Google Scholar
https://mfasiolo.github.io/qgam/articles/qgam.html (accessed: 5.11.2018).
Google Scholar
Koenker R., Mizera I. (2004), Penalized triograms: total variation regularization for bivariate smoothing, “Journal of the Royal Statistical Society” (B), no. 66, pp. 145–163.
Google Scholar
Koenker R., Ng P. (2005), A Frisch Newton Algorithm for Sparse Quantile Regression, “Mathematicae Applicatae Sinica”, no. 21, pp. 225–236.
Google Scholar
Koenker R., Ng P., Portnoy S. (1994), Quantile smoothing splines, “Biometrika”, no. 81, pp. 673–680.
Google Scholar
Lindsey J. K. (1997), Applying Generalized Linear Model, Springer, Berlin.
Google Scholar
Wood S. (2006), Generalized Additive Models: An Introduction with R., Chapman Hall, New York.
Google Scholar
Wood S. (2010), Mixed GAM Computation Vehicle with Automatic Smoothness Estimation, https://cran.r-project.org/web/packages/mgcv/mgcv.pdf (accessed: 12.12.2019).
Google Scholar
Wood S. N. (2017). Generalized additive models: an introduction with R, CRC press, New York.
Google Scholar
Wood S. N., Pya N., Säfken B. (2016), Smoothing parameter and model selection for general smooth models, “Journal of the American Statistical Association”, vol. 111(516), pp. 1548–1575.
Google Scholar