Robust Data-Driven Inference for Density-Weighted Average Derivatives

Cattaneo, Matias D.; Crump, Richard K.; Jansson, Michael

doi:10.1198/jasa.2010.tm09590

Cited by 35 publications

(30 citation statements)

References 21 publications

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“…6 In a preliminary simulation study, results are similar for different values of M including M = 1,4, and 16. 7 The linear regression is understood to be a special case of the power series estimator of µ(d, x) presented in Footnote 2. In a preliminary simulation study, we consider different series lengths and find that results are similar overall.…”

Section: Simulationmentioning

confidence: 99%

Bootstrap Inference of Matching Estimators for Average Treatment Effects

Otsu

Rai

2017

Journal of the American Statistical Association

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Abstract. Abadie and Imbens (2008) showed that the naive bootstrap is not asymptotically valid for a matching estimator of the average treatment effect with a fixed number of matches. In this article, we propose asymptotically valid inference methods for matching estimators based on the weighted bootstrap. The key is to construct bootstrap counterparts by resampling based on certain linear forms of the estimators.Our weighted bootstrap is applicable for the matching estimators of both the average treatment effect and its counterpart for the treated population. Also, by incorporating a bias correction method in Abadie and Imbens (2011), our method can be asymptotically valid even for matching based on a vector of covariates. A simulation study indicates that the weighted bootstrap method is favorably comparable with the asymptotic normal approximation by Abadie and Imbens (2006). As an empirical illustration, we apply the proposed method to the National Supported Work data.

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Section: Simulationmentioning

confidence: 99%

Bootstrap Inference of Matching Estimators for Average Treatment Effects

Otsu

Rai

2017

Journal of the American Statistical Association

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“…We wish to thank our discussants Xiaohong Chen, Holger Dette, Enno Mammen, and Donglin Zeng for a very stimulating discussion of our article (Cattaneo, Crump, and Jansson, 2013a;CCJ, hereafter). We also acknowledge the fantastic work of Jun Liu, Xuming He, and Jin Sun in shaping this intellectual exchange.…”

Section: Commentmentioning

confidence: 99%

Generalized Jackknife Estimators of Weighted Average Derivatives

Cattaneo

Crump

Jansson

2013

Journal of the American Statistical Association

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With the aim of improving the quality of asymptotic distributional approximations for nonlinear functionals of nonparametric estimators, this article revisits the large-sample properties of an important member of that class, namely a kernel-based weighted average derivative estimator. Asymptotic linearity of the estimator is established under weak conditions. Indeed, we show that the bandwidth conditions employed are necessary in some cases. A bias-corrected version of the estimator is proposed and shown to be asymptotically linear under yet weaker bandwidth conditions. Implementational details of the estimators are discussed, including bandwidth selection procedures. Consistency of an analog estimator of the asymptotic variance is also established. Numerical results from a simulation study and an empirical illustration are reported. To establish the results, a novel result on uniform convergence rates for kernel estimators is obtained. The online supplemental material to this article includes details on the theoretical proofs and other analytic derivations, and further results from the simulation study.

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“…In all cases, these choices of bandwidths appear to be too high for us to recommend them to be used with our procedures. On the other hand, the bandwidth selection procedures developed in Cattaneo, Crump, and Jansson (2010) were found in that paper to perform very well and we would recommend those to be used.…”

Section: Resultsmentioning

confidence: 99%

Small Bandwidth Asymptotics for Density-Weighted Average Derivatives

2013

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This paper proposes (apparently) novel standard error formulas for the densityweighted average derivative estimator of Powell, Stock, and Stoker (Econometrica 57, 1989). Asymptotic validity of the standard errors developed in this paper does not require the use of higher-order kernels, and the standard errors are "robust" in the sense that they accommodate (but do not require) bandwidths that are smaller than those for which conventional standard errors are valid. Moreover, the results of a Monte Carlo experiment suggest that the finite sample coverage rates of confidence intervals constructed using the standard errors developed in this paper coincide (approximately) with the nominal coverage rates across a nontrivial range of bandwidths.

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Robust Data-Driven Inference for Density-Weighted Average Derivatives

Cited by 35 publications

References 21 publications

Bootstrap Inference of Matching Estimators for Average Treatment Effects

Bootstrap Inference of Matching Estimators for Average Treatment Effects

Generalized Jackknife Estimators of Weighted Average Derivatives

Small Bandwidth Asymptotics for Density-Weighted Average Derivatives

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