Locally adaptive regression splines

By Enno Mammen, Sara A. van de Geer. 1997

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Citations in the corpus

Fused Lasso Additive Model (2014, methodology): “Tibshirani [2014] showed that 0th order trend ﬁltering is equivalent to 0th order locally adaptive regression splines, proposed by Mammen et al. [1997].”
Nonparametric Regression with Correlated Errors (2001, background): “, [20]), Mammen and van de Geer [48], Goldenshluger and Nemirovski [26], Lepski et al [46], Devroye and Lugosi [18], and others.”
Bayesian inference for generalized additive mixed models based on Markov random field priors (2001, result): “Closeness of xed e ects is in agreement with asymptotic normality results for penal-ized likelihood estimations in semiparametric GLMs by Mammen and van de Geer(1997).”
Splines in Higher Order TV Regularization (2006, background): “For larger m and the continuous setting, an attempt to solve the contact problem is contained in [16].”
Piecewise linear regularized solution paths (2007, methodology): “ty holds for the LASSO, and suggested the LAR–LASSO algorithm which takes advantage of it. Similar algorithmswere suggested forthe LASSOin [14] and for total-variation penalized squared error loss in [13]. We have extended some path-following ideas to versions of the regularized support vector machi”
Estimation of a k-monotone density: limit distribution theory and the Spline connection (2005, methodology): “In the problem of nonparametric regression via splines, Mammen and van de Geer [30] have conjectured that n−1/(2k+1) is the order of the distance between the knot points of their regression spline m̂ under the assumption that the true regression curve m0 satisfies our same working assumptions, but t”
LASSO Isotone for High-Dimensional Additive Isotonic Regression (2010, background): “Later theoretical discussion from Mammen and Yu [2007] outlined some positive properties of this procedure.”
Properties and refinements of the fused lasso (2008, methodology): “…that, in the nonparametric function estimation settings, one can obtain b µ F as a piecewise-constant variable-knot spline function on [0 , 1] [see Mammen and van de Geer (1997), Proposition 8] and that the taut-string algorithm of Davies and Kovac (2001a) solves the constrained version of (2.2).”
Estimating time-varying networks (2008, methodology): “The total variation penalty has been successfully applied in detecting sharp transitions in signal processing, image denoising and nonparametric estimation, e.g Rudin et al. (1992); Mammen and Geer (1997); Davies and Kovac (2001).”
Multiple Change-Point Estimation With a Total Variation Penalty (2010, methodology): “+ 1 and estimate the vector ( u 1 ,... , u n ) by using a criterion based on a total variation penalty as in Mammen and Van De Geer (1997): The following proposition gives the rate of convergence of ˆ u (λ n ) when an upper bound for the number of change points is known and equal to K max .”
Optimal rates of statistical seriation (2016, background): “Such an argument can be found in [14, 3, 69] for the larger class of vectors with bounded total variation (see [54]) but we do not pursue sharp logarithmic terms in this work.”