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Efficient and Adaptive Estimation for Semiparametric Models
TLDR
Asymptotic Inference for (Finite-Dimensional) Parametric Models as mentioned in this paper has been studied in the context of infinite-dimensional parametric models, where information bounds for Euclidean parameters in infinite-dimensional models have been derived.Abstract:
Introduction.- Asymptotic Inference for (Finite-Dimensional) Parametric Models.- Information Bounds for Euclidean Parameters in Infinite-Dimensional Models.- Euclidean Parameters: Further Examples.- Information Bounds for Infinite-Dimensional Parameters.- Infinite-Dimensional Parameters: Further Examples: Construction of Examples.read more
Citations
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Journal ArticleDOI
A tutorial on support vector regression
TL;DR: This tutorial gives an overview of the basic ideas underlying Support Vector (SV) machines for function estimation, and includes a summary of currently used algorithms for training SV machines, covering both the quadratic programming part and advanced methods for dealing with large datasets.
Journal ArticleDOI
Kernel independent component analysis
Francis Bach,Michael I. Jordan +1 more
TL;DR: A class of algorithms for independent component analysis which use contrast functions based on canonical correlations in a reproducing kernel Hilbert space is presented, showing that these algorithms outperform many of the presently known algorithms.
ReportDOI
Double/debiased machine learning for treatment and structural parameters
Victor Chernozhukov,Denis Chetverikov,Mert Demirer,Esther Duflo,Christian Hansen,Whitney K. Newey,James M. Robins +6 more
TL;DR: In this article, the authors show that the impact of regularization bias and overfitting on estimation of the parameter of interest θ0 can be removed by using two simple, yet critical, ingredients: (1) using Neyman-orthogonal moments/scores that have reduced sensitivity with respect to nuisance parameters, and (2) making use of cross-fitting, which provides an efficient form of data-splitting.
BookDOI
Introduction to empirical processes and semiparametric inference
TL;DR: Semi-parametric Inference as mentioned in this paper is a well-known technique in empirical process analysis, and it has been used in many applications, e.g., for finite-dimensional and infinite-dimensional parameters.
Journal ArticleDOI
Adjusting for Nonignorable Drop-Out Using Semiparametric Nonresponse Models
TL;DR: In this article, the conditional hazard of dropout is modeled semiparametrically and no restrictions are placed on the joint distribution of the outcome and other measured variables, and it is shown how to make inferences about the marginal mean μ0 when the continuous dropout time Q is modeled semi-parameterically.
References
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Journal ArticleDOI
On convergence of stochastic processes
TL;DR: In this paper, it is shown that certain known invariance principles can under some hypotheses be improved by enlarging the class of functions for which (2) holds by considering spaces S other than the customary ones.
Journal ArticleDOI
On Adaptive Estimation
TL;DR: In this paper, the authors simplify a general heuristic necessary condition of Stein's for adaptive estimation of a Euclidean parameter in the presence of an infinite dimensional shape nuisance parameter and other non-Gaussian nuisance parameters.
Journal ArticleDOI
Information and Asymptotic Efficiency in Parametric-Nonparametric Models
TL;DR: In this article, lower bounds for estimation of the parameters of models with both parametric and nonparametric components are given in the form of representation theorems (for regular estimates) and asymptotic minimax bounds.
Book
Contributions to a General Asymptotic Statistical Theory
Johann Pfanzagl,W. Wefelmeyer +1 more
TL;DR: In this article, the authors present a unified asymptotic theory for probability measures and show that it can be expressed in terms of a set of families of probability measures, which they call parametric families.
Journal ArticleDOI
New Ways to Prove Central Limit Theorems
TL;DR: In this article, a combination of recent results from the theory of empirical processes and a method of Huber for the study of maximum likelihood estimators under nonstandard conditions is presented.