Optimal convergence rates, Bahadur representation, and asymptotic normality of partitioning estimators☆

By M. D. Cattaneo, Max H. Farrell. 2013

65 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/ab57669054482a3b5f0324ab8979cb0215de756c

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In Statistics and Probability

Citations in the corpus

Robust Data-Driven Inference in the Regression-Discontinuity Design (2014, methodology): “These selectors are obtained by approximating the asymptotic integrated variance and bias of certain partitioning-type estimators (see Cattaneo and Farrell [2013] for references) and are implemented nonparametrically using spacings and series estimators.”
Inference in Linear Regression Models with Many Covariates and Heteroscedasticity (2015, methodology): “For further technical details on series-based methods see, for example, Newey (1997), Chen (2007), Cattaneo and Farrell (2013), and Belloni et al. (2015), and references therein.”
Robust Nonparametric Confidence Intervals for Regression‐Discontinuity Designs (2014, methodology): “…e¤ects, Card, Lee, Pei, and Weber (2012), Dong (2012) and Dong and Lewel (2012) study the so-called kink RD designs, Marmer, Feir, and Lemieux (2012) discuss robust to weak-IV inference in fuzzy RD designs, and Cattaneo, Frandsen, and Titiunik (2013) propose randomization-inference methods.”
Cross-fitting and fast remainder rates for semiparametric estimation (2017, methodology): “Cattaneo and Farrell (2013) exploited other special properties of the Haar basis to obtain sharp uniform nonparametric rates. For b-splines of any order we can obtain remainder rates by combining Lemma 1 with Theorem 8 of Ichimura and Newey (2017). Theorem 4: If Assumptions 1-6 are satisfied then √ ”
Conditional quantile processes based on series or many regressors (2011, result): “These findings on optimality of series estimators in the quantile regression setting complement results in the literature on optimality of series estimators in the mean regression setting; see [67, 49, 15, 9, 22].”
Rdrobust: Software for Regression-discontinuity Designs (2017, methodology): “This formula is justified by pre-asymptotic inference, and as a nonparametric inference procedure, up to smoothing bias, following the results in Cattaneo and Farrell (2013) for partitioning regression methods.”
Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions (2014, background): “ﬁnish the paper. The authors did circulate the note among some colleagues and their former students who work in this area. 5Belloni et al. (2014) recast the local polynomial partitioning estimator of Cattaneo and Farrell (2013) as a series LS estimator. 3 for p>d/2 (resp. p>d(2 + γ)/(2γ)). It ”
On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference (2015, methodology): “7 exp{−16(2x− 1)2} Model 4: m(x) = x+ 5φ(10x) Model 5: m(x) = sin(3πx/2) 1 + 18x2[sgn(x) + 1] Model 6: m(x) = sin(πx/2) 1 + 2x2[sgn(x) + 1] Models 1 to 3 were used by Fan and Gijbels (1996) and Cattaneo and Farrell (2013), while Models 4 to 6 are from Hall and Horowitz (2013), with some originally s”
Optimal Data-Driven Regression Discontinuity Plots (2015, methodology): “To describe this construction formally, we employ ideas from the nonparametric literature on partitioning estimators (for further details, see Cattaneo and Farrell 2013, and references therein).”
Some new asymptotic theory for least squares series: Pointwise and uniform results (2012, methodology): “uired kξ2 k/n→ 0. For series satisfying ξk . √ k, the condition ξ2 k logk/n→ 0 amounts to klogk/n→ 0. (4.10) This condition is the same as that imposed in Stone (1994), Huang (2003a), and recently by Cattaneo and Farrell (2013) but the result (4.8) is obtained under the condition (4.10) in Stone (19”
Robust Inference on Average Treatment Effects with Possibly More Covariates than Observations (2013, unknown): “14This is standard fixed-dimension models, and has been used for diverging-dimensions parametric models (He and Shao 2000) and nonparametrics (Newey 1997, Huang 2003, Belloni, Chen, Chernozhukov, and Kato 2012, Cattaneo and Farrell 2013).”
Efficient Estimation of the Dose–Response Function Under Ignorability Using Subclassification on the Covariates (2011, methodology): “Cattaneo and Farrell (2011) give details on the appropriate rotation and demonstrate its existence under the conditions imposed in Theorem 1.”
Optimal sup-norm rates and uniform inference on nonlinear functionals of nonparametric IV regression (2015, unknown): “6Even for the simple nonparametric LS regression of h0 (without endogeneity), the optimal sup-norm rates for series LS estimators of h0 were not obtained until recently in Cattaneo and Farrell (2013) for locally partitioning series LS, Belloni, Chernozhukov, Chetverikov, and Kato (2015) for spline L”