The nonexistence of certain statistical procedures in nonparametric problems

By R. R. Bahadur, L. J. Savage. 1956

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Citations in the corpus

The hardness of conditional independence testing and the generalised covariance measure (2018, background): “Our hardness result for conditional independence contributes to an important literature on impossibility results in statistics and econometrics starting with the work of Bahadur and Savage [2], which shows that there is no nontrivial test for whether a distribution has mean zero.”
On the Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions (2001, background): “Indeed, when one imposes only (6) and (7) on P, it follows from Bahadur and Savage (1956) that there is no “reasonable” test in this setting in the sense that no test can have power against any alternative greater than size.”
Reliable Inference for the Gini Index (2009, background): “This is not quite enough, as the class of admissible CDFs F must be further restricted so as to avoid the Bahadur-Savage problem; see Bahadur and Savage (1956).”
Empirically relevant critical values for hypothesis tests: A bootstrap approach (2000, background): “Bahadur and Savage (1956) demonstrate the second for the case of testing a hypothesis about a population mean. Both problems are consequences of having a null-hypothesis set H 0 that is too large. Dufour (1997) has shown that this happens in a wide variety of settings that are important in applied e”
Estimating the number of classes (2007, unknown): “21 53 v1 [ m at h. ST ] 1 6 A ug 2 00 7 The Annals of Statistics 2007, Vol. 35, No. 2, 917–930 DOI: 10.1214/009053606000001280 c© Institute of Mathematical Statistics, 2007”
Time-uniform central limit theory and asymptotic confidence sequences (2021, background): “For example, as a consequence of Bahadur and Savage [1], it is impossible to derive nonasymptotic CSs (or CIs) for the mean of random variables without prior bounds on their moments.”
Improved Nonparametric Inference for the Mean of a Bounded Random Variable with Application to Poverty Measures (2005, methodology): “For this purpose, we prove that the impossibility theorem of Bahadur and Savage (1956) does not apply in this case.”
The bootstrap and hypothesis tests in econometrics (2001, background): “Even if the size-corrected critical value is finite, the power of the test may be the same as its size (Bahadur and Savage 1956).”
Hypothesis Testing in Econometrics (2010, methodology): “A classical instance of the nonexistence of any useful level α test was provided by Bahadur and Savage (1956). The result is stated in terms of testing the mean of a population in a nonparametric setting.”
Inference with Few Heterogeneous Clusters (2016, background): “At the same time, some assumption seems necessary: The results of Bahadur and Savage (1956) show that without any constraint on the distribution, it is impossible to conduct inference about the population mean, and thus a fortiori, also about differences between population means.”
On Non‐parametric Testing, the Uniform Behaviour of the t‐test, and Related Problems (2004, methodology): “Our criterion, like that of Bahadur & Savage (1956) and the Neyman–Pearson paradigm, is more demanding and requires tests to have level control for a given n. Note that the above argument follows by the Bahadur–Savage result if we assume P consists of all distributions on the real line with finite…”
On the uniform asymptotic validity of subsampling and the bootstrap (2012, background): “Of course, as pointed out by Bahadur and Savage (1956), there may be no nontrivial confidence region or test satisfying (2) or (3) when P is sufficiently rich. For this reason, we will have to restrict P appropriately in our examples. In the case of confidence regions for or tests about the mean, fo”
Covariate-adjusted Fisher randomization tests for the average treatment effect (2020, background): “Without these conditions, the inference becomes challenging (Bahadur and Savage 1956), and frt may not control type one error rates even asymptotically with heavy-tailed outcomes. An alternative class of frts use rank statistics to gain robustness with respect to outliers (Lehmann 1975; Rosenbaum 20”
The limits of distribution-free conditional predictive inference (2019, background): “, Bahadur and Savage [1956], Donoho [1988] for background. More specifically, for the current problem of distribution-free conditional prediction intervals, Vovk [2012], Lei and Wasserman [2014] prove that the (1−α)-CC property (2) is impossible for any algorithm Ĉn, unless Ĉn has the property that ”
Modern robust data analysis methods: measures of central tendency. (2003, background): “When working with means, problems with power were noted nearly a half a century ago by Bahadur and Savage (1956), and results published by Laplace (see Hald, 1998, p. 449) foreshadowed the difficulties we know today.”
Asymptotically Honest Confidence Regions for High Dimensional Parameters by the Desparsified Conservative Lasso (2014, background): “Results (38) and (39) are also remarkable in light of the classical result of Bahadur and Savage (1956) stating that even in the problem of constructing confidence intervals for the mean of a gaussian random variable honest confidence bands are not possible in general if one insists on the diameter ”