On the Asymptotic Accuracy of Efron's Bootstrap

By Kesar Singh. 1981

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Citations in the corpus

Trend analysis of climate time series: A review of methods (2019, background): “Singh (1981) soon pointed out that the ordinary bootstrap fails for autocorrelated noise components because it does not preserve the autocorrelation.”
A test for the two-sample problem based on empirical characteristic functions (2008, methodology): “These two methods yield consistent estimators for the distribution of sample means (see for example Bickel and Freedman (1981), Singh (1981), Hall (1986, 1988a,b), Shorack (1996), Janssen and Pauls (2003)), Therefore, since e.c.f. are particular averages, it is expected they work for approximating…”
Generalized Method of Moments, Efficient Bootstrapping, and Improved Inference (2002, unknown): “The bootstrap improvement can be explained in terms of Edgeworth expansions, as done by Singh (1981), Hall (1986), and Beran (1988).”
BLOCK BOOTSTRAP HAC ROBUST TESTS: THE SOPHISTICATION OF THE NAIVE BOOTSTRAP (2011, background): “Ex ante, it is not intuitively obvious that the i.i.d. bootstrap could be more accurate than the standard normal approximation (see Singh, 1981).”
RESAMPLING FEWER THAN n OBSERVATIONS: GAINS, LOSSES, AND REMEDIES FOR LOSSES (2012, methodology): “Proof: We make a standard application of Singh (1981). If ̂(2) 1 n P (Xi X)(2), K̂3 1 n P (Xi X)(3) we get, after some algebra.”
ON THE CHOICE OF m IN THE m OUT OF n BOOTSTRAP AND CONFIDENCE BOUNDS FOR EXTREMA (2008, methodology): “Case 2: An upper bound for µ, when σ is unknown, is ¯ X n − t n−1,α s n / √ n; the n-bootstrap works (Singh (1981), Bickel and Freedman (1981)), and the tquantile is replaced by the quantile of the bootstrap distribution of √ m( ¯ X * m − ¯ X n )/s * m .”
The Impact of Bootstrap Methods on Time Series Analysis (2003, background): “…an arbitrary resample size was noted as early on as in Bickel and Freedman (1981); nevertheless, the research community focused for some time on the case of resample size n since that choice leads to improved performance, i.e., higher-order accuracy, in the sample mean case—cf. Singh (1981).”
Asymptotics and the theory of inference (2003, background): “…tool, the bootstrap is indispensable, but in terms of understanding when and how it is useful, its asymptotic properties are paramount and in this connection the result that the bootstrap provides second order correct confidence limits was key [Bickel and Freedman (1981), Singh (1981)].”
On m out of n Bootstrapping for Nonstandard M-Estimation With Nuisance Parameters (2006, methodology): “, n out of n) bootstrap in this context can be proved along the same lines as done for proving bootstrap consistency for sums of independent and identically distributed observations (see, e.g., Bickel and Freedman 1981; Singh 1981; Lahiri 1992).”