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Full-Text Articles in Economics
A Simple Adjustment For Bandwidth Snooping, Timothy B. Armstrong, Michal Kolesár
A Simple Adjustment For Bandwidth Snooping, Timothy B. Armstrong, Michal Kolesár
Cowles Foundation Discussion Papers
Kernel-based estimators are often evaluated at multiple bandwidths as a form of sensitivity analysis. However, if in the reported results, a researcher selects the bandwidth based on this analysis, the associated confidence intervals may not have correct coverage, even if the estimator is unbiased. This paper proposes a simple adjustment that gives correct coverage in such situations: replace the Normal quantile with a critical value that depends only on the kernel and ratio of the maximum and minimum bandwidths the researcher has entertained. We tabulate these critical values and quantify the loss in coverage for conventional confidence intervals. For a …
A Simple Adjustment For Bandwidth Snooping, Timothy B. Armstrong, Michal Kolesár
A Simple Adjustment For Bandwidth Snooping, Timothy B. Armstrong, Michal Kolesár
Cowles Foundation Discussion Papers
>Kernel-based estimators are often evaluated at multiple bandwidths as a form of sensitivity analysis. However, if in the reported results, a researcher selects the bandwidth based on this analysis, the associated confidence intervals may not have correct coverage, even if the estimator is unbiased. This paper proposes a simple adjustment that gives correct coverage in such situations: replace the normal quantile with a critical value that depends only on the kernel and ratio of the maximum and minimum bandwidths the researcher has entertained. We tabulate these critical values and quantify the loss in coverage for conventional confidence intervals. For a …
A Simple Adjustment For Bandwidth Snooping, Timothy B. Armstrong, Michal Kolesár
A Simple Adjustment For Bandwidth Snooping, Timothy B. Armstrong, Michal Kolesár
Cowles Foundation Discussion Papers
Kernel-based estimators are often evaluated at multiple bandwidths as a form of sensitivity analysis. However, if in the reported results, a researcher selects the bandwidth based on this analysis, the associated confidence intervals may not have correct coverage, even if the estimator is unbiased. This paper proposes a simple adjustment that gives correct coverage in such situations: replace the Normal quantile with a critical value that depends only on the kernel and ratio of the maximum and minimum bandwidths the researcher has entertained. We tabulate these critical values and quantify the loss in coverage for conventional confidence intervals. For a …
A Simple Adjustment For Bandwidth Snooping, Timothy B. Armstrong, Michal Kolesár
A Simple Adjustment For Bandwidth Snooping, Timothy B. Armstrong, Michal Kolesár
Cowles Foundation Discussion Papers
Kernel-based estimators such as local polynomial estimators in regression discontinuity designs are often evaluated at multiple bandwidths as a form of sensitivity analysis. However, if in the reported results, a researcher selects the bandwidth based on this analysis, the associated confidence intervals may not have correct coverage, even if the estimator is unbiased. This paper proposes a simple adjustment that gives correct coverage in such situations: replace the normal quantile with a critical value that depends only on the kernel and ratio of the maximum and minimum bandwidths the researcher has entertained. We tabulate these critical values and quantify the …
Adaptive Testing On A Regression Function At A Point, Timothy B. Armstrong
Adaptive Testing On A Regression Function At A Point, Timothy B. Armstrong
Cowles Foundation Discussion Papers
We consider the problem of inference on a regression function at a point when the entire function satisfies a sign or shape restriction under the null. We propose a test that achieves the optimal minimax rate adaptively over a range of Hölder classes, up to a log log n term, which we show to be necessary for adaptation. We apply the results to adaptive one-sided tests for the regression discontinuity parameter under a monotonicity restriction, the value of a monotone regression function at the boundary, and the proportion of true null hypotheses in a multiple testing problem.
Adaptive Testing On A Regression Function At A Point, Timothy B. Armstrong
Adaptive Testing On A Regression Function At A Point, Timothy B. Armstrong
Cowles Foundation Discussion Papers
We consider the problem of inference on a regression function at a point when the entire function satisfies a sign or shape restriction under the null. We propose a test that achieves the optimal minimax rate adaptively over a range of Holder classes, up to a log log n term, which we show to be necessary for adaptation. We apply the results to adaptive one-sided tests for the regression discontinuity parameter under a monotonicity restriction, the value of a monotone regression function at the boundary, and the proportion of true null hypotheses in a multiple testing problem.