On the uniform asymptotic validity of subsampling and the bootstrap

By Joseph P. Romano, A. Shaikh. 2012

105 citations recorded by the source corpus.

This paper provides conditions under which subsampling and the bootstrap can be used to construct estimators of the quantiles of the distribution of a root that behave well uniformly over a large class of distributions $\mathbf{P}$. These results are then applied (i) to construct confidence regions that behave well uniformly over $\mathbf{P}$ in the sense that the coverage probability tends to at least the nominal level uniformly over $\mathbf{P}$ and (ii) to construct tests that behave well uniformly over $\mathbf{P}$ in the sense that the size tends to no greater than the nominal level uniformly over $\mathbf{P}$. Without these stronger notions of convergence, the asymptotic approximations to the coverage probability or size may be poor, even in very large samples. Specific applications include the multivariate mean, testing moment inequalities, multiple testing, the empirical process and U-statistics.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9c93301ad78b95b0afc1ba9cd57081eb0ebc6d0b

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Citations in the corpus

Kernel-Based Semiparametric Estimators: Small Bandwidth Asymptotics and Bootstrap Consistency (2018, background): “It would be of interest to develop uniform versions of Theorems 1 and 2 along the lines of Romano and Shaikh (2012) and Einmahl and Mason (2005), respectively.”
Sensitivity analysis of environmental models: A systematic review with practical workflow (2014, unknown): “Technique to address the question without running new model evaluations are subsampling and bootstrapping (Efron and Tibshirani, 1993; Romano and Shaikh, 2012).”
Program evaluation and causal inference with high-dimensional data (2013, result): “These uniformity results build upon and complement those given in Romano and Shaikh (2012) for the empirical bootstrap.”
Instrumental variables and the sign of the average treatment effect (2019, unknown): “By Lemma 11.4.2 of Romano and Shaikh (2012), we therefore have that 1 n ∑ 1≤i≤n XiZi Pn→ 0 .”
Global Sensitivity Analysis of environmental models: Convergence and validation (2016, methodology): “Here, the indices SVBM i and S VBT i are estimated according to the method proposed by Saltelli (2002). First, two independent input samples XA and XB are built (each being a matrix of dimension (n,M)).”
Generic results for establishing the asymptotic size of confidence sets and tests (2020, methodology): “…does not33 seem to be conducive to obtaining results that are uniform over both the AR parameter ρ and the innovation distribution.34 The approach of Romano and Shaikh (2008, 2010, 2012) applies to subsampling and bootstrap methods, but not to35 other methods of constructing critical values.”
Breaking the curse of dimensionality in regression (2017, background): “…|FX(x)− FY (x)| ≤ ε ) + P ( sup x∈R |FX(x)− FY (x)| > ε ) (i) ≤ P ( ‖X‖∞ > F−1X (1− α− ε) ) + P ( sup x∈R |FX(x)− FY (x)| > ε ) = α+ ε+ P ( sup x∈R |FX(x)− FY (x)| > ε ) , (85) where (i) follows from Lemma A.1(i) in Romano and Shaikh (2012) and the last line follows by the definition of FX(·).”
Asymptotically exact inference in conditional moment inequality models (2011, background): “This issue of uniformity in the underlying distribution is often a concern in situations such as the present one, where the asymptotic distribution changes dramatically with the data generating process (see, e.g., Andrews and Guggenberger, 2010; Romano and Shaikh, 2012).”
Program evaluation with high-dimensional data (2013, result): “These uniformity results build upon and complement those given in Romano and Shaikh (2012) for the empirical bootstrap.”