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We study trend filtering, a relatively recent method for univariate nonparametric regression.
[author] Rockafellar, R. T.R. T. (1970). Convex Analysis. Princeton Univ. Press, Princeton, New Jersey
1970
Earlier work this paper cites.
[author] Mangasarian, Olvi LO. L. and Schumaker, Larry LL. L. (1971). Discrete splines via mathematical programming. SIAM Journal on Control 9 174–183
1971
Earlier work this paper cites.
[author] Gohberg, II. and Semencul, AA. (1972). On the inversion of finite Toeplitz matrices and their continuous analogs. Mat. issled 2 201–233
1972
Earlier work this paper cites.
[author] Breiman, LeoL., Friedman, Jerome H.J. H., Olshen, Richard A.R. A. and Stone, Charles J.C. J. (1984). Classification and regression trees. Wadsworth Statistics/Probability Series. Wadsworth Advanced Books and Software, Belmont, CA. 726392
1984
Earlier work this paper cites.
[author] Schrijver, AlexanderA. (1986). Theory of linear and integer programming. Wiley-Interscience Series in Discrete Mathematics. John Wiley & Sons, Ltd., Chichester A Wiley-Interscience Publication. 874114 (88m:90090)
1986
Earlier work this paper cites.
[author] Müller, Hans-GeorgH.-G. and Stadtmüller, UlrichU. (1987). Variable bandwidth kernel estimators of regression curves. Ann. Statist. 15 182–201. 10.1214/aos/1176350260 885731
1987
Earlier work this paper cites.
[author] Pollard, D.D. (1990). Empirical Processes: Theory and Applications. NSF-CBMS Regional Conference Series in Probability and Statistics 2. Institute of Mathematical Statistics, Hayward, CA
1990
Earlier work this paper cites.
[author] Friedman, Jerome H.J. H. (1991). Multivariate adaptive regression splines. Ann. Statist. 19 1–141. With discussion and a rejoinder by the author. 10.1214/aos/1176347963 1091842
1991
Earlier work this paper cites.
[author] Rudin, Leonid IL. I., Osher, StanleyS. and Fatemi, EmadE. (1992). Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena 60 259–268
1992
Earlier work this paper cites.
[author] Brockmann, MichaelM., Gasser, TheoT. and Herrmann, EvaE. (1993). Locally adaptive bandwidth choice for kernel regression estimators. J. Amer. Statist. Assoc. 88 1302–1309. 1245363
1993
Earlier work this paper cites.
1993
Earlier work this paper cites.
[author] Donoho, David LD. L. and Johnstone, Jain MJ. M. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika 81 425–455
1994
Earlier work this paper cites.
[author] Tibshirani, RobertR. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B (Methodological) 267–288
1996
Earlier work this paper cites.
[author] Van der Vaart, AadA. and Wellner, Jon A.J. A. (1996). Weak Convergence and Empirical Process: With Applications to Statistics. Springer-Verlag
1996
Earlier work this paper cites.
[author] Goldenshluger, A.A. and Nemirovski, A.A. (1997). On spatially adaptive estimation of nonparametric regression. Math. Methods Statist. 6 135–170. 1466625
1997
Earlier work this paper cites.
[author] Lepski, O. V.O. V., Mammen, E.E. and Spokoiny, V. G.V. G. (1997). Optimal spatial adaptation to inhomogeneous smoothness: an approach based on kernel estimates with variable bandwidth selectors. Ann. Statist. 25 929–947. 10.1214/aos/1069362731 1447734
1997
Earlier work this paper cites.
[author] Mammen, EnnoE. and van de Geer, SaraS. (1997). Locally adaptive regression splines. The Annals of Statistics 25 387–413
1997
Earlier work this paper cites.
[author] Donoho, David L.D. L. and Johnstone, Iain M.I. M. (1998). Minimax estimation via wavelet shrinkage. Annals of Statistics 26 879–921
1998
Earlier work this paper cites.
[author] Laurent, BeatriceB. and Massart, PascalP. (2000). Adaptive estimation of a quadratic functional by model selection. Annals of Statistics 1302–1338
2000
Cited alongside, same era.
[author] Van de Geer, S.S. (2000). Applications of Empirical Process Theory. Cambridge University Press
2000
Cited alongside, same era.
[author] Zhou, ShanggangS. and Shen, XiaotongX. (2001). Spatially adaptive regression splines and accurate knot selection schemes. J. Amer. Statist. Assoc. 96 247–259. 10.1198/016214501750332820 1952735
2001
Cited alongside, same era.
[author] Winkler, GerhardG. and Liebscher, VolkmarV. (2002). Smoothers for discontinuous signals. Journal of Nonparametric Statistics 14 203–222
2002
Cited alongside, same era.
[author] Pintore, AlexandreA., Speckman, PaulP. and Holmes, Chris C.C. C. (2006). Spatially adaptive smoothing splines. Biometrika 93 113–125. 10.1093/biomet/93.1.113 2277744
[author] Foygel, RinaR. and Mackey, LesterL. (2014). Corrupted sensing: Novel guarantees for separating structured signals. IEEE Transactions on Information Theory 60 1223–1247
2014
Later among the works it cites.
[author] Groeneboom, PietP. and Jongbloed, GeurtG. (2014). Nonparametric Estimation under Shape Constraints: Estimators, Algorithms and Asymptotics 38. Cambridge University Press
2014
Later among the works it cites.
[author] Tibshirani, Ryan JR. J. (2014). Adaptive piecewise polynomial estimation via trend filtering. The Annals of Statistics 42 285–323
2014
Later among the works it cites.
Wang, Y.-X
2014
Later among the works it cites.
[author] Johnstone, Iain MI. M. (2015). Gaussian estimation: Sequence and wavelet models. Available at http://statweb.stanford.edu/~imj/GE09-08-15.pdf
2015
Later among the works it cites.
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2006
Cited alongside, same era.
[author] Rudelson, MarkM. and Vershynin, RomanR. (2006). Combinatorics of random processes and sections of convex bodies. Annals of Mathematics 603–648
2006
Cited alongside, same era.
[author] Steidl, GabrieleG., Didas, StephanS. and Neumann, JuliaJ. (2006). Splines in higher order TV regularization. International journal of computer vision 70 241–255
2006
Cited alongside, same era.
Lévy-Leduc, C
2008
Cited alongside, same era.
[author] Kim, Seung-JeanS.-J., Koh, KwangmooK., Boyd, StephenS. and Gorinevsky, DimitryD. (2009). l 1 l_{1} trend filtering. SIAM Rev. 51 339–360. 10.1137/070690274 2505584
2009
Cited alongside, same era.
[author] Kuczma, MarekM. (2009). An introduction to the theory of functional equations and inequalities: Cauchy’s equation and Jensen’s inequality. Springer Science & Business Media
2009
Cited alongside, same era.
[author] Rockafellar, R TyrrellR. T. and Wets, Roger J-BR. J.-B. (2009). Variational analysis 317. Springer Science & Business Media
2009
Cited alongside, same era.
[author] Bühlmann, PeterP. and van de Geer, SaraS. (2011). Statistics for high-dimensional data. Springer Series in Statistics. Springer, Heidelberg Methods, theory and applications. 10.1007/978-3-642-20192-9 2807761
2011
Cited alongside, same era.
2015
Later among the works it cites.
[author] Arnold, Taylor BT. B. and Tibshirani, Ryan JR. J. (2016). Efficient implementations of the generalized lasso dual path algorithm. Journal of Computational and Graphical Statistics 25 1–27
2016
Later among the works it cites.
2016
Later among the works it cites.
[author] Oymak, SametS. and Hassibi, BabakB. (2016). Sharp mse bounds for proximal denoising. Foundations of Computational Mathematics 16 965–1029
2016
Later among the works it cites.
[author] Wang, Yu-XiangY.-X., Sharpnack, JamesJ., Smola, Alexander JA. J. and Tibshirani, Ryan JR. J. (2016). Trend filtering on graphs. The Journal of Machine Learning Research 17 1–41
2016
Later among the works it cites.
[author] Dalalyan, ArnakA., Hebiri, MohamedM. and Lederer, JohannesJ. (2017). On the prediction performance of the Lasso. Bernoulli 23 552–581
2017
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2017
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2017
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2017
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[author] Bellec, Pierre C.P. C. (2018). Sharp oracle inequalities for Least Squares estimators in shape restricted regression. Ann. Statist. 46 745–780. 10.1214/17-AOS1566 3782383
2018
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2018
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