Model selection for regression on a random design

By Y. Baraud. 2002

149 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/66050598c99b487f901bd5f46b0f1248448692e4

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Citations in the corpus

Parametric or nonparametric? A parametricness index for model selection (2011, background): “Publications of work in this direction include [3–6, 10, 13, 15, 22–24, 42, 69], to name a few.”
Penalized nonparametric mean square estimation of the coefficients of diffusion processes (2007, methodology): “Proof of Lemma 6.1 Using Baraud et al. (2001a), we prove that, for all n and ∆ > 0, where C 0 is a constant depending on π 0 , π 1 , q n is an integer such that q n < n and L n ( φ ) is a quantity depending on the basis of the largest nesting space S n of the collection and is deﬁned below.”
Model selection via testing: an alternative to (penalized) maximum likelihood estimators (2006, methodology): “Further limitations of the classical methods for model selection are connected with the choice of the models which have to share some special properties: they should, for instance, be finite dimensional linear spaces generated by special bases, as in Baraud [3] or be uniformly bounded as in Yang ([6”
Consistent covariate selection and post model selection inference in semiparametric regression (2004, background): “The previous proposition and Assumptions 2.1–2.4 verify that Theorem 2.1 of Baraud (2002) can be invoked.”
Aggregation for Gaussian regression (2007, background): “4) in regression problems have been obtained by many authors mainly for the model selection case; see, for example, [4, 5, 7, 8, 9, 10, 11, 12, 15, 23, 28, 30, 32, 42] and the references cited in these works.”
High-dimensional additive modeling (2008, unknown): “Other approaches are based on wavelets [27] or can adapt to the unknown smoothness of the underlying functions [2].”
Finite-Dimensional Projection for Classification and Statistical Learning (2008, unknown): “This theorem therefore should be seen essentially as a theoretical guarantee that using this form of penalty is well-founded from a statistical point of view, and will have suitable convergence properties as the sample size n grows large.”
Sparsity oracle inequalities for the Lasso (2007, methodology): “For an overview of these methods in random design regression we refer to [3], to the book [13] and to more recent papers [4, 15] where some other methods are suggested.”
SLOPE is Adaptive to Unknown Sparsity and Asymptotically Minimax (2015, background): “An incomplete list of works working with Gaussian designs would include [19, 5, 12, 20, 55, 7, 30].”
A simple nonparametric approach to estimating the distribution of random coefficients in structural models (2016, unknown): “Then, following Lemma 5.2 in Baraud (2002), we have Pr sup µ∈G\{0} ∥µ∥2L2 ∥µ∥2L2,N > c”
Data-Driven Rate-Optimal Specification Testing in Regression Models (2005, methodology): “This approach is used for testing the white noise model with normal errors by Fan (1996) and for testing a linear regression model with normal errors by Fan and Huang (2001) and Baraud, Huet and Laurent (2003), who extend the maximum approach. Further work on the linear model includes Spokoiny (2001”
Rejoinder: Local Rademacher complexities and oracle inequalities in risk minimization (2006, background): “ers by Birg´e and Massart [8], Barron, Birg´e and Massart [3] and Massart [36], we refer the reader to a book by van de Geer [46], a book by Gy¨orﬁ, Kohler, Krzyzak and Walk [22] and papers by Baraud [2] and Kohler [25]. Our goal here is only to outline the connection of regression problems to a mor”
Model Selection (2018, background): “The case of random design is studied by Baraud (2002), Wegkamp (2003), and Birgé (2004), based on the results of Barron, Birgé and Massart (1999).”