Trend filtering


Companion references for this package

  1. Politsch et al. (2020a). Trend filtering – I. A modern statistical tool for time-domain astronomy and astronomical spectroscopy. MNRAS, 492(3), p. 4005-4018. [Publisher] [arXiv] [BibTeX].

  2. Politsch et al. (2020b). Trend Filtering – II. Denoising astronomical signals with varying degrees of smoothness. MNRAS, 492(3), p. 4019-4032. [Publisher] [arXiv] [BibTeX].

Trend filtering theory

  1. Tibshirani (2014). Adaptive piecewise polynomial estimation via trend filtering. The Annals of Statistics. 42(1), p. 285-323.

  2. Tibshirani (2020). Divided Differences, Falling Factorials, and Discrete Splines: Another Look at Trend Filtering and Related Problems. arXiv preprint.

Optimization algorithms for trend filtering

  1. Ramdas and Tibshirani (2016). Fast and Flexible ADMM Algorithms for Trend Filtering. Journal of Computational and Graphical Statistics, 25(3), p. 839-858.

  2. Arnold, Sadhanala, and Tibshirani (2014). glmgen: Fast algorithms for generalized lasso problems. R package version 0.0.3.

  3. Taylor B. Arnold and Ryan J. Tibshirani (2020). genlasso: Path Algorithm for Generalized Lasso Problems. R package version 1.5.

Effective degrees of freedom for trend filtering

  1. Tibshirani and Taylor (2012). Degrees of freedom in lasso problems. The Annals of Statistics, 40(2), p. 1198-1232.


Related topics


Stein's unbiased risk estimate

  1. Tibshirani and Wasserman (2015). Stein’s Unbiased Risk Estimate. 36-702: Statistical Machine Learning course notes (Carnegie Mellon University).

  2. Efron (2014). The Estimation of Prediction Error: Covariance Penalties and Cross-Validation. Journal of the American Statistical Association. 99(467), p. 619-632.

Cross validation

  1. Hastie, Tibshirani, and Friedman (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. 2nd edition. Springer Series in Statistics. (See Sections 7.10 and 7.12)

The Bootstrap and variations

  1. Efron and Tibshirani (1986). Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy. Statistical Science, 1(1), p. 54-75.

  2. Mammen (1993). Bootstrap and Wild Bootstrap for High Dimensional Linear Models. The Annals of Statistics, 21(1), p. 255-285.

  3. Efron (1979). Bootstrap Methods: Another Look at the Jackknife. The Annals of Statistics, 7(1), p. 1-26.