Andrii Babii, Jean-Pierre Florens
arXiv 11 Sep 2017 · Mathematics — Statistics Theory
arXiv:1709.03473 · PDF · Extracted main text
Modern data analysis depends increasingly on estimating models via flexible high-dimensional or nonparametric machine learning methods, where the identification of structural parameters is often challenging and untestable. In linear settings, this identification hinges on the completeness condition, which requires the nonsingularity of a high-dimensional matrix or operator and may fail for finite samples or even at the population level. Regularized estimators provide a solution by enabling consistent estimation of structural or average structural functions, sometimes even under identification failure. We show that the asymptotic distribution in these cases can be nonstandard. We develop a comprehensive theory of regularized estimators, which include methods such as high-dimensional ridge regularization, gradient descent, and principal component analysis (PCA). The results are illustrated for high-dimensional and nonparametric instrumental variable regressions and are supported through simulation experiments.
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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 | A. Babii (2020) Honest confidence sets in nonparametric iv regression and other ill-posed models | 1.000 | 6 | 4 | 100% |
| 2 | E. Giné and R. Nickl (2016) Mathematical foundations of infinite-dimensional statistical models | 1.000 | 5 | 3 | 100% |
| 3 | M. Carrasco, J.-P. Florens, and E. Renault (2007) Linear inverse problems in structural econometrics estimation based on spectral decomposition and regularization | 0.928 | 4 | 4 | 100% |
| 4 | A. Babii (2022) High-dimensional mixed-frequency iv regression | 0.928 | 4 | 3 | 100% |
| 5 | J. Freyberger (2017) On completeness and consistency in nonparametric instrumental variable models | 0.874 | 5 | 2 | 100% |
| 6 | V. S. Korolyuk and Y. V. Borovskich (1994) Theory of U-statistics | 0.843 | 3 | 3 | 100% |
| 7 | J.-P. Florens, J. Johannes, and S. Van Bellegem (2011) Identification and estimation by penalization in nonparametric instrumental regression self | 0.811 | 4 | 2 | 100% |
| 8 | X. Chen and T. M. Christensen (2018) Optimal sup-norm rates and uniform inference on nonlinear functionals of nonparametric iv regression | 0.644 | 2 | 2 | 100% |
| 9 | H. W. Engl, M. Hanke, and A. Neubauer (1996) Regularization of inverse problems | 0.644 | 2 | 2 | 100% |
| 10 | G. G. Gregory (1977) Large sample theory for u-statistics and tests of fit | 0.644 | 2 | 2 | 100% |
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