arXiv 9 Nov 2016 · Mathematics — Statistics Theory · 4 citations (OpenAlex)
arXiv:1611.03015 · PDF · DOI · OpenAlex · Extracted main text
This paper develops inferential methods for a very general class of ill-posed models in econometrics encompassing the nonparametric instrumental variable regression, various functional regressions, and the density deconvolution. We focus on uniform confidence sets for the parameter of interest estimated with Tikhonov regularization, as in Darolles, Fan, Florens, and Renault (2011). Since it is impossible to have inferential methods based on the central limit theorem, we develop two alternative approaches relying on the concentration inequality and bootstrap approximations. We show that expected diameters and coverage properties of resulting sets have uniform validity over a large class of models, i.e., constructed confidence sets are honest. Monte Carlo experiments illustrate that introduced confidence sets have reasonable width and coverage properties. Using U.S. data, we provide uniform confidence sets for Engel curves for various commodities.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | V. Chernozhukov, D. Chetverikov, and K. Kato (2016) Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related gaussian couplings | 1.000 | 6 | 4 | 100% |
| 2 | A. Babii and J.-P. Florens (2020) Is completeness necessary? estimation in nonidentified linear models | 1.000 | 6 | 3 | 100% |
| 3 | S. Darolles, Y. Fan, J. Florens, and E. Renault Nonparametric instrumental regression | 1.000 | 6 | 3 | 100% |
| 4 | V. Chernozhukov, D. Chetverikov, and K. Kato Gaussian approximation of suprema of empirical processes | 1.000 | 5 | 3 | 100% |
| 5 | S. Boucheron, G. Lugosi, and P. Massart (2013) Concentration Inequalities | 0.843 | 3 | 3 | 100% |
| 6 | R. Blundell, X. Chen, and D. Kristensen (2007) Semi-nonparametric iv estimation of shape-invariant engel curves | 0.811 | 4 | 2 | 100% |
| 7 | M. Carrasco, J.-P. Florens, and E. Renault (2007) Chapter 77: Linear inverse problems in structural econometrics estimation based on spectral decomposition and regularization | 0.811 | 4 | 2 | 100% |
| 8 | A. B. Tsybakov (2009) Introduction to nonparametric estimation | 0.811 | 4 | 2 | 100% |
| 9 | A. Babii (2020) High-dimensional mixed-frequency iv regression | 0.737 | 3 | 2 | 100% |
| 10 | R. M. Dudley (2016) V.n. sudakov's work on expected suprema of gaussian processes | 0.737 | 3 | 2 | 100% |
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