Last updated: 2018-10-13

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This is a broad list of literature on smoothing Gaussian/non-Gaussian data.

Nonparametric methods

KNN

Kernel smootihng methods: Chapter 6 of ESL.

Local regression(linear & higher order): Loader, C. (2006). Local regression and likelihood. Springer Science & Business Media.

Note: Local regression makes no global assumptions about the function but assume that locally it can be well approximated with a member of a simple class of parametric function. Only observations in certain window are used.

Splines: regression splines, smoothing splines; More generally, reproducing kernel Hilbert space: Chapter 5 of ESL

Locally adaptive estimators: wavelet( Mallat, S. (1999). A wavelet tour of signal processing. Elsevier ), Locally adaptive regression splines(A varaiant of smooting splines achieves better local adaptivity. Mammen, E., & van de Geer, S. (1997). Locally adaptive regression splines. The Annals of Statistics, 25(1), 387-413.), Trend filtering( Kim, S. J., Koh, K., Boyd, S., & Gorinevsky, D. (2009). l_1 Trend Filtering. SIAM review, 51(2), 339-360. ).

Additive models: Sparse additive models, Generalized additive mixed models.

More on trend filtering and additive models:

Trend filtering:

Wang, Y. X., Sharpnack, J., Smola, A. J., & Tibshirani, R. J. (2016). Trend filtering on graphs. The Journal of Machine Learning Research, 17(1), 3651-3691.

Ramdas, A., & Tibshirani, R. J. (2016). Fast and flexible ADMM algorithms for trend filtering. Journal of Computational and Graphical Statistics, 25(3), 839-858. The R package for this algo is glmgen.

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

Additive models:

Sadhanala, V., & Tibshirani, R. J. (2017). Additive Models with Trend Filtering. arXiv preprint arXiv:1702.05037.

Petersen, A., Witten, D., & Simon, N. (2016). Fused lasso additive model. Journal of Computational and Graphical Statistics, 25(4), 1005-1025.

Yin Lou, Jacob Bien, Rich Caruana & Johannes Gehrke (2016) Sparse Partially Linear Additive Models, Journal of Computational and Graphical Statistics, 25:4, 1126-1140

Generalized Sparse Additive Models

Chouldechova, A., & Hastie, T. (2015). Generalized additive model selection. arXiv preprint arXiv:1506.03850.

Binomial

Marchand, P., & Marmet, L. (1983). Binomial smoothing filter: A way to avoid some pitfalls of least‐squares polynomial smoothing. Review of scientific instruments, 54(8), 1034-1041.

Hansen, K. D., Langmead, B., & Irizarry, R. A. (2012). BSmooth: from whole genome bisulfite sequencing reads to differentially methylated regions. Genome biology, 13(10), R83.

Note: It actually uses local likelihood moother and assumes \(logit(\pi)\) is approximated by a second degree polynomial. They assume that data follow a binomial distribution and the parameters defining the polynomial are estimated by fitting a weighted generalized linear model to the data inside the genomic window.

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