Journal Article10.1111/ECTJ.12095
Non-parametric inference on (conditional) quantile differences and interquantile ranges, using L-statistics
Matt Goldman,David M. Kaplan +1 more
10
TL;DR: In this article, the authors use the probability integral transform and a Dirichlet reference distribution to pick appropriate L-statistics as confidence interval endpoints, achieving high-order accuracy.
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Abstract: Summary
We provide novel, high-order accurate methods for nonparametric inference on quantile differences between two populations in both unconditional and conditional settings. These quantile differences corresponds to (conditional) quantile treatment effects under (conditional) independence of a binary treatment and potential outcomes. Our methods use the probability integral transform and a Dirichlet (rather than Gaussian) reference distribution to pick appropriate L-statistics as confidence interval endpoints, achieving high-order accuracy. Using a similar approach, we also propose confidence intervals/sets for 1) vectors of quantiles, 2) interquantile ranges, and 3) differences of linear combinations of quantiles. In the conditional setting, when smoothing over continuous covariates, optimal bandwidth and coverage probability rates are derived for all methods. Simulations show the new confidence intervals to have a favourable combination of robust accuracy and short length compared with existing approaches. Detailed steps for confidence interval construction are provided in Supplemental Appendix E, and code for all methods, simulations, and empirical examples is provided.
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References
•Journal Article
R: A language and environment for statistical computing.
TL;DR: Copyright (©) 1999–2012 R Foundation for Statistical Computing; permission is granted to make and distribute verbatim copies of this manual provided the copyright notice and permission notice are preserved on all copies.
410.8K
Density estimation for statistics and data analysis
Bernard W. Silverman
- 01 Jan 1986
TL;DR: The Kernel Method for Multivariate Data: Three Important Methods and Density Estimation in Action.
A Bayesian Analysis of Some Nonparametric Problems
TL;DR: In this article, a class of prior distributions, called Dirichlet process priors, is proposed for nonparametric problems, for which treatment of many non-parametric statistical problems may be carried out, yielding results that are comparable to the classical theory.
•Book
Nonparametrics: Statistical Methods Based on Ranks
Erich L. Lehmann,H. J. M. D'Abrera +1 more
- 01 Jan 1975
TL;DR: Rank Tests for Comparing Two Treatments and Blocked Comparisons for two Treatments in a Population Model and the One-Sample Problem as discussed by the authors were used to compare more than two treatments.
3.4K