Asymptotic bootstrap validity is usually understood as consistency of the distribution of a bootstrap statistic, conditional on the data, for the unconditional limit distribution of a statistic of interest. From this perspective, randomness of the limit bootstrap measure is regarded as a failure of the bootstrap. We show that such limiting randomness does not necessarily invalidate bootstrap inference if validity is understood as control over the frequency of correct inferences in large samples. We first establish sufficient conditions for asymptotic bootstrap validity in cases where the unconditional limit distribution of a statistic can be obtained by averaging a (random) limiting bootstrap distribution. Further, we provide results ensuring the asymptotic validity of the bootstrap as a tool for conditional inference, the leading case being that where a bootstrap distribution estimates consistently a conditional (and thus, random) limit distribution of a statistic. We apply our framework to several inference problems in econometrics, including linear models with possibly non-stationary regressors, CUSUM statistics, conditional Kolmogorov-Smirnov specification tests and tests for constancy of parameters in dynamic econometric models.
Giuseppe Cavaliere, Iliyan Georgiev (2020). Inference under random limit bootstrap measures. ECONOMETRICA, 88(6), 2547-2574 [10.3982/ECTA16557].
Inference under random limit bootstrap measures
Giuseppe Cavaliere
;Iliyan Georgiev
2020
Abstract
Asymptotic bootstrap validity is usually understood as consistency of the distribution of a bootstrap statistic, conditional on the data, for the unconditional limit distribution of a statistic of interest. From this perspective, randomness of the limit bootstrap measure is regarded as a failure of the bootstrap. We show that such limiting randomness does not necessarily invalidate bootstrap inference if validity is understood as control over the frequency of correct inferences in large samples. We first establish sufficient conditions for asymptotic bootstrap validity in cases where the unconditional limit distribution of a statistic can be obtained by averaging a (random) limiting bootstrap distribution. Further, we provide results ensuring the asymptotic validity of the bootstrap as a tool for conditional inference, the leading case being that where a bootstrap distribution estimates consistently a conditional (and thus, random) limit distribution of a statistic. We apply our framework to several inference problems in econometrics, including linear models with possibly non-stationary regressors, CUSUM statistics, conditional Kolmogorov-Smirnov specification tests and tests for constancy of parameters in dynamic econometric models.File | Dimensione | Formato | |
---|---|---|---|
ECTA16557.pdf
accesso aperto
Tipo:
Versione (PDF) editoriale
Licenza:
Licenza per Accesso Aperto. Creative Commons Attribuzione - Non commerciale - Non opere derivate (CCBYNCND)
Dimensione
740.24 kB
Formato
Adobe PDF
|
740.24 kB | Adobe PDF | Visualizza/Apri |
ECTA16557SUPP.pdf
accesso aperto
Tipo:
File Supplementare
Licenza:
Licenza per Accesso Aperto. Creative Commons Attribuzione - Non commerciale - Non opere derivate (CCBYNCND)
Dimensione
180.83 kB
Formato
Adobe PDF
|
180.83 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.