arXiv 15 Jan 2019 · Econometrics · publishedJournal of Econometrics (2019) · 5 citations (OpenAlex)
arXiv:1901.04861 · PDF · DOI · OpenAlex · Extracted main text
This paper presents a unified second order asymptotic framework for conducting inference on parameters of the form $\phi(\theta_0)$, where $\theta_0$ is unknown but can be estimated by $\hat\theta_n$, and $\phi$ is a known map that admits null first order derivative at $\theta_0$. For a large number of examples in the literature, the second order Delta method reveals a nondegenerate weak limit for the plug-in estimator $\phi(\hat\theta_n)$. We show, however, that the `standard' bootstrap is consistent if and only if the second order derivative $\phi_{\theta_0}”=0$ under regularity conditions, i.e., the standard bootstrap is inconsistent if $\phi_{\theta_0}”\neq 0$, and provides degenerate limits unhelpful for inference otherwise. We thus identify a source of bootstrap failures distinct from that in Fang and Santos (2018) because the problem (of consistently bootstrapping a nondegenerate limit) persists even if $\phi$ is differentiable. We show that the correction procedure in Babu (1984) can be extended to our general setup. Alternatively, a modified bootstrap is proposed when the map is in addition second order nondifferentiable. Both are shown to provide local size control under some conditions. As an illustration, we develop a test of common conditional heteroskedastic (CH) features, a setting with both degeneracy and nondifferentiability -- the latter is because the Jacobian matrix is degenerate at zero and we allow the existence of multiple common CH features.
appendix boundary found by appendix_command · 46% of the source is main text. Read the extracted text to check this.
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 | Babu, G. J (1984) Bootstrapping statistics with linear combinations of Chi-squares as weak limit | 1.000 | 8 | 4 | 100% |
| 2 | Efron, B (1979) Bootstrap methods: Another look at the Jackknife | 1.000 | 7 | 3 | 100% |
| 3 | Hall, P. and Horowitz, J. L (1996) Bootstrap critical values for tests based on Generalized-Method-of-Moments estimators | 1.000 | 5 | 4 | 100% |
| 4 | Dümbgen, L (1993) On nondifferentiable functions and the bootstrap | 1.000 | 5 | 3 | 100% |
| 5 | Andrews, D. W. K. and Soares, G (2010) Inference for parameters defined by moment inequalities using generalized moment selection | 0.941 | 6 | 4 | 83% |
| 6 | Andrews, D. W. K. and Shi, X (2013) Inference based on conditional moment inequalities | 0.941 | 6 | 3 | 83% |
| 7 | Dovonon, P. and Renault, E (2013) Testing for common conditionally heteroskedastic factors | 0.932 | 37 | 6 | 81% |
| 8 | Chernozhukov, V., Hong, H. and Tamer, E (2007) Estimation and confidence regions for parameter sets in econometric models | 0.928 | 5 | 4 | 80% |
| 9 | Linton, O., Song, K. E. and Whang, Y.-J (2010) An improved bootstrap test of stochastic dominance | 0.874 | 6 | 3 | 67% |
| 10 | Fang, Z. and Santos, A (2018) Inference on directionally differentiable functions self | 0.865 | 34 | 9 | 65% |
Showing the top 10 of 88 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Improved Inference on the Rank of a Matrix | 0.909 | 12 | 4 |
| 2 | Unified Inference on Moment Restrictions with Nuisance Parameters | 0.675 | 26 | 4 |
| 3 | Statistical Inference of Optimal Allocations 1: Regularities and their Implications | 0.511 | 2 | 2 |
| 4 | Uniform inference for value functions | 0.405 | 1 | 1 |
| 5 | Inference under First-Order Degeneracy | 0.405 | 1 | 1 |