Giuseppe Cavaliere, University of Bologna

"Bootstrap Diagnostic Tests"

Abstract

Violations of the assumptions underlying classical asymptotic theory frequently lead to unreliable statistical inference. This paper proposes a novel bootstrap-based diagnostic procedure to detect such violations. The suggested approach (i) focuses on the distance between the conditional distribution of a bootstrap statistic and the (limiting) Gaussian distribution, and (ii) proposes a method to assess whether this distance is large enough to indicate the invalidity of the asymptotic approximation. The method, which is computationally straightforward, involves applying standard normality tests to a set of bootstrap repetitions to assess significant deviations from the Gaussian distribution. Importantly, these diagnostics do not induce any pre-testing bias, thus improving the reliability of statistical inference. To demonstrate the practical relevance and broad applicability of our diagnostic procedure, we discuss five scenarios where the asymptotic Gaussian approximation fails: (i) detecting infinite variance innovations in a location model for i.i.d. data; (ii) identifying non-stationary behavior in autoregressive time series; (iii) parameters near or at the boundary of the parameter space; (iv) invalidity of the delta method due to (near-)rank deficiency in the implied Jacobian matrix; and (v) weak instruments in instrumental variable regression.

Joint with Luca Fanelli – University of Bologna

Contact person: Anders Rahbek