Impossibility Results for Nondifferentiable Functionals

By Keisuke Hirano, J. Porter. 2012

140 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/4d81a982911f1e0b31dbded3ee4e7631834b412b

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In Statistics and Probability

Citations in the corpus

Inference on Directionally Differentiable Functions (2014, methodology): “Hirano and Porter (2012), Song (2014), and Fang (2015), for example, explicitly employ the φ Other work studying these models, though not explicitly relying on the directional differentiability of φ , include Chernozhukov et al .”
STATISTICAL INFERENCE FOR THE MEAN OUTCOME UNDER A POSSIBLY NON-UNIQUE OPTIMAL TREATMENT STRATEGY (2016, result): “The left- and right-hand sides above are referred to as one-sided directional derivatives by Hirano and Porter (2012). This condition for the mean outcome differs slightly from that implied for unrestricted rules in Robins and Rotnitzky (2014) in that we still have pathwise differentiability when th”
Regression Kink With an Unknown Threshold (2017, methodology): “While the general theory of Hong and Li (2015) requires √ nεn → ∞ , in the context of this model they reommended εn = cn−1/2, though they provide no guidance for selection of c.”
Partial Identification of Local Average Treatment Effects With an Invalid Instrument (2013, methodology): “Moreover, Hirano and Porter (2012) showed that there exist no locally asymptotically unbiased estimators and no regular estimators for parameters that are nonsmooth functionals of the underlying data distribution, such as those involving min or max operators.”
Statistical Inference in Dynamic Treatment Regimes (2010, background): “…several reasons: first, it is known that in settings in which there is no unbiased estimator, attempts to eliminate the bias at some parameter values must lead to large mean square error at other parameter values (Doss and Sethuraman, 1989; Liu and Brown 1993; Chen 2004; Hirano and Porter 2009).”
Minimax Estimation of Functionals of Discrete Distributions (2014, unknown): “totically efﬁcient for estimating ’() [48, Lemma 8.14]. Furthermore, it is also known that if the functional is non-differentiable, then it is nearly impossible to get an elegant mathematical theory [80]. The question of estimating functionals of ﬁnite dimensional parameters being satisfactorily ans”
Dynamic treatment regimes: technical challenges and applications (2014, background): “Consequently, estimators of these quantities are necessarily nonregular and asymptotically biased (Van der Vaart, 1991; Robins, 2004; Hirano and Porter, 2009); standard asymptotic approximations to the sampling distributions of these estimators cannot be used directly to form reliable confi- dence…”
Identifying the Effects of SNAP (Food Stamps) on Child Health Outcomes When Participation Is Endogenous and Misreported (2012, unknown): “Recent work by Hirano and Porter (2012) raises some concerns about applying bias corrections when estimating intersection bounds, showing that it may be impossible to completely eliminate bias and that reducing bias too much leads to large increases in variance.”