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Asymptotic normal inference in linear inverse problems
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Carrasco, Marine, Florens, Jean-Pierre and Renault, Eric (2014) Asymptotic normal inference in linear inverse problems. In: Racine, Jeffrey S. and Su, Liangjun and Ullah, Aman, (eds.) The Oxford Handbook of Applied Nonparametric and Semiparametric Econometrics and Statistics. Oxford University Press. ISBN 9780199857944
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Official URL: http://dx.doi.org/10.1093/oxfordhb/9780199857944.0...
Abstract
This chapter studies the estimation of φ in linear inverse problems Tφ = r, where r is only observed with error and T may be given or estimated. The unknown element φ belongs to a Hilbert space E. Four examples are relevant for econometrics: the density estimation, the deconvolution problem, the linear regression with an infinite number of possibly endogenous explanatory variables, and the nonparametric instrumental variables estimation. In the first two cases T is given, whereas it is estimated in the two other cases, respectively at a parametric or nonparametric rate. This chapter will recall the main results on these models: concepts of degree of ill-posedness, regularity of φ, regularized estimation, and the rates of convergence usually obtained. The main contributions are, moreover, related to the asymptotic normality of the regularized solution φ obtained with a regularization parameter α. If α → 0, we particularly consider the asymptotic normality of inner products <φ, ϕ>, where ϕ is an element of E. These results can be used to construct (asymptotic) tests on φ.
| Item Type: | Book Item | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Social Sciences > Economics | ||||
| Publisher: | Oxford University Press | ||||
| ISBN: | 9780199857944 | ||||
| Book Title: | The Oxford Handbook of Applied Nonparametric and Semiparametric Econometrics and Statistics | ||||
| Editor: | Racine, Jeffrey S. and Su, Liangjun and Ullah, Aman | ||||
| Official Date: | February 2014 | ||||
| Dates: |
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| DOI: | 10.1093/oxfordhb/9780199857944.013.003 | ||||
| Status: | Not Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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