Bootstrap Diagnostic Tests

Giuseppe Cavaliere, Luca Fanelli () and Iliyan Georgiev

Papers from arXiv.org

Abstract: Violation of the assumptions underlying classical (Gaussian) limit theory frequently leads to unreliable statistical inference. This paper shows the novel result that the bootstrap can detect such violation by means of simple and powerful tests which (a) induce no pre-testing bias, (b) can be performed using the same critical values in a broad range of applications, and (c) are consistent against deviations from asymptotic normality. By focusing on the discrepancy between the conditional distribution of a bootstrap statistic and the (limiting) Gaussian distribution which obtains under valid specification, we show how to assess whether this discrepancy is large enough to indicate specification invalidity. The method, which is computationally straightforward, only requires to measure the discrepancy between the bootstrap and the Gaussian distributions based on a sample of i.i.d. draws of the bootstrap statistic. We derive sufficient conditions for the randomness in the data to mix with the randomness in the bootstrap repetitions in a way such that (a), (b) and (c) above hold. To demonstrate the practical relevance and broad applicability of our diagnostic procedure, we discuss five scenarios where the asymptotic Gaussian approximation may fail: (i) weak instruments in instrumental variable regression; (ii) non-stationarity in autoregressive time series; (iii) parameters near or at the boundary of the parameter space; (iv) infinite variance innovations in a location model for i.i.d. data; (v) invalidity of the delta method due to (near-)rank deficiency in the implied Jacobian matrix. An illustration drawn from the empirical macroeconomic literature concludes.

Date: 2025-09
New Economics Papers: this item is included in nep-ecm and nep-ets
References: Add references at CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2509.01351 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2509.01351

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().