Inconsistency of the Bootstrap when a Parameter is on the Boundary of the Parameter Space

By Donald W. K. Andrews. 2000

395 citations recorded by the source corpus.

Subfields: Applied Mathematics, Artificial Intelligence, Statistics and Probability

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Citations in the corpus

ASYMPTOTIC SIZE AND A PROBLEM WITH SUBSAMPLING AND WITH THE m OUT OF n BOOTSTRAP (2009, methodology): “…Shao and Wu, 1989; Wu, 1990; Eaton and Tyler, 1991; Politis and Romano, 1994; Shao, 1994, 1996; Beran, 1997; Bickel, Götze, and van Zwet, 1997; Andrews, 1999, 2000; Politis, Romano, and Wolf, 1999 (hereafter PRW); Romano and Wolf, 2001; Guggenberger and Wolf, 2004; and Lehmann and Romano,…”
A Test of Non-Identifying Restrictions and Confidence Regions for Partially Identified Parameters (2009, neutral): “Note that our proposed use of the bootstrap only concerns the empirical process, as in Andrews (2000), so that issues of validity related to bootstrapping the test statistic itself do not arise.”
Inference in Nonparametric Instrumental Variables With Partial Identification (2012, methodology): “The strategy to obtain identiflcation in the linear case is to multiply both sides of the flrst equation in ( 3 ) by Z and take expectations.”
Inference on Directionally Differentiable Functions (2014, methodology): “We refer to the functionals, we know by way of example that the consistency of the standard bootstrap may not (Bickel et al ., 1997; Andrews, 2000).”
A Test for Superior Predictive Ability (2005, methodology): “This can be achieved by increasing B until the results are robust to increments, or more formal methods, such as the three-step method of Andrews and Buchinsky (2000), can be applied.”
Imposing regional monotonicity on translog stochastic production frontiers with a simple three-step procedure (2009, methodology): “…to an inconsistent covariance matrix if the restricted parameters are at the boundary of the feasible parameter space (Andrews 2000; Dhrymes 2006).5 Andrews (2000) suggests alternative methods, e.g. rescaled bootstrapping, that lead to a consistent covariance matrix even in the case of binding…”
Distributional Tests in Multivariate Dynamic Models with Normal and Student-t Innovations (2009, background): “In this regard, it is important to note that Andrews (2000) shows that the size of bootstrap tests remains asymptotically valid when some of the parameters are on the boundary of the parameter space, even though the sampling distribution of the estimators provided by the bootstrap is invalid.”
EL inference for partially identified models: Large deviations optimality and bootstrap validity (2010, methodology): “…the empirical likelihood bootstrap proposed by Brown and Newey (2002) is not asymptotically valid when applied to moment inequality models.3 Then I propose a slight modification of that bootstrap, along the lines of the modified parametric bootstrap in Andrews (2000), that does work asymptotically.”
Bootstrap LR tests of stationarity, common trends and cointegration (2012, neutral): “A recent paper by Morley and Sinclair [13] also deals with the bootstrap stationarity tests, but only for univariate series; their algorithm, however, is not apparently obtained within a state-space framework.1 Note that, as pointed out by Andrews [17], while the standard bootstrap technique may not”
Statistical Inference for Average Treatment Effects Estimated by Synthetic Control Methods (2019, methodology): “F.1 A simple example from Andrews (2000) We consider a simple example as considered in Andrews (2000).”
SHARP BOUNDS ON THE DISTRIBUTION OF TREATMENT EFFECTS AND THEIR STATISTICAL INFERENCE (2009, methodology): “been proposed to rectify the failure of the standard bootstrap, see Andrews (2000), Bickel, Götze, and van Zwet (1997), Beran (1997), and Politis, Romano, and Wolf (1999) for discussion and references.”