trendfilteringSupp-package: Optimal one-dimensional data analysis with trend filtering

In capolitsch/trendfilteringSupp: Optimal one-dimensional data analysis with trend filtering

Description

This package serves as a software supplement to Politsch et al. (2020a) and Politsch et al. (2020b). We provide a variety of statistical tools for one-dimensional data analyses with trend filtering (Tibshirani 2014). This package contains user-friendly functionality for optimizing a trend

Author(s)

Collin A. Politsch

Maintainer: Collin A. Politsch <[e-mail]>

References

Main references

1. Politsch et al. (2020a). Trend filtering – I. A modern statistical tool for time-domain astronomy and astronomical spectroscopy. Monthly Notices of the Royal Astronomical Society, 492(3), p. 4005-4018. [Link]
   

2. Politsch et al. (2020b). Trend Filtering – II. Denoising astronomical signals with varying degrees of smoothness. Monthly Notices of the Royal Astronomical Society, 492(3), p. 4019-4032. [Link]
   
   

Trend filtering theory

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

Trend filtering convex optimization algorithm

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

2. Arnold, Sadhanala, and Tibshirani (2014). Fast algorithms for generalized lasso problems. R package glmgen. Version 0.0.3. [Link] (Software implementation of Ramdas and Tibshirani algorithm)
   
   

Effect 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. [Link]

Stein's unbiased risk estimate

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

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

3. Stein (1981). Estimation of the Mean of a Multivariate Normal Distribution. The Annals of Statistics. 9(6), p. 1135-1151. [Link]
   

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. [Link]
   

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

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

Cross validation

1. Hastie, Tibshirani, and Friedman (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. 2nd edition. Springer Series in Statistics. [Online print #12]. (See Sections 7.10 and 7.12)
   

2. James, Witten, Hastie, and Tibshirani (2013). An Introduction to Statistical Learning : with Applications in R. Springer. [Most recent online print] (See Section 5.1). Less technical than the above reference.
   

3. Tibshirani (2013). Model selection and validation 2: Model assessment, more cross-validation. 36-462: Data Mining course notes (Carnegie Mellon). [Link]

capolitsch/trendfilteringSupp documentation built on Oct. 15, 2021, 11:04 a.m.