Empirical Processes in M-Estimation

By S. Jammalamadaka. 2001

765 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability, Statistical Learning Theory

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Statistics and Probability

In Statistical Learning Theory

Citations in the corpus

Generalized Sparse Additive Models (2019, background): “Then all γ ∈ R n and ρ > 0 , in particular if γ i = 1 /n then we have Lemma F.2 (Corollary 8.3 of van de Geer [2000]) .”
Optimal Rates for Random Fourier Features (2015, background): “We also propose a RFF approximation to derivatives of a kernel with a theoretical study on its approximation quality.”
Density Estimation in Infinite Dimensional Exponential Families (2013, background): “On the other hand, MLE is statistically well-understood, with consistency and convergence rates established in general for the problem of density estimation [39] and in particular for the problem at hand [14].”
Estimating Divergence Functionals and the Likelihood Ratio by Convex Risk Minimization (2008, neutral): “08 53”
On the mathematical foundations of learning (2001, methodology): “For a C ∞ Mercer kernel K we may thus consider I K (B R ) as a hypothesis space.”
Divide and conquer kernel ridge regression: a distributed algorithm with minimax optimal rates (2013, background): “For any f ∈ H, by defining the basis coefficients θj = 〈f, φj〉L2(P) for j = 1, 2, . . ., we can expand the function in terms of these coefficients as f = ∑∞ j=1 θjφj , and simple calculations show that ‖f‖22 = ∫ X f2(x)dP(x) = ∞∑ j=1 θ2j , and ‖f‖2H = 〈f, f〉 = ∞∑ j=1 θ2j µj .”
Mutual Information Neural Estimation (2018, background): “For the second problem, classical consistency theorems for extremum estimators apply (Van de Geer, 2000) under mild conditions on the parameter space.”
High-dimensional additive modeling (2008, background): “Moreover, one then has α = 3 / 4 (see, e.g., [29], Lemma 3.9).”
Time Series Modelling With Semiparametric Factor Dynamics (2009, methodology): “11 in Van de Geer (2000) that treats rates of convergence for least squares estimators on sieves.”
Regularized Policy Iteration with Nonparametric Function Spaces (2016, methodology): “The boundedness of the rewards is a reasonable assumption that can be replaced by a more relaxed condition such as its sub-Gaussianity (Vershynin, 2012; van de Geer, 2000).”
Iterative Value-Aware Model Learning (2018, result): “…the behaviour of the metric entropy is p log( 1 ε ) , which can be seen as having α → 0 with a certain rate, For many examples of the covering number and metric entropy results, refer to van de Geer [2000], Györﬁ et al. [2002], Zhou [2003], Steinwart and Christmann [2008], Giné and Nickl [2015].”
Divide and Conquer Kernel Ridge Regression (2013, neutral): “Past work has established bounds on the estimation error for RKHS-based methods (e.g., Zhang Duchi Wainwright Koltchinskii, 2006; Mendelson, 2002; van de Geer, 2000; Zhang, 2005), which have been refined and extended in more recent work (e.g., Steinwart et al., 2009).”
Estimation of high-dimensional low-rank matrices (2009, background): “The bound is essentially stated in van de Geer (2000) as Lemma 3.2 [further referred to as VG(00)].”