[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
IDEAS home Printed from https://ideas.repec.org/p/umc/wpaper/1801.html
   My bibliography  Save this paper

Comparing distributions by multiple testing across quantiles or CDF values

Author

Abstract
When comparing two distributions, it is often helpful to learn at which quantiles or values there is a statistically significant difference. This provides more information than the binary "reject" or "do not reject" decision of a global goodness-of-fit test. Framing our question as multiple testing across the continuum of quantiles tau in (0,1) or values r, we show that the Kolmogorov–Smirnov test (interpreted as a multiple testing procedure) achieves strong control of the familywise error rate. However, its well-known flaw of low sensitivity in the tails remains. We provide an alternative method that retains such strong control of familywise error rate while also having even sensitivity, i.e., equal pointwise type I error rates at each of n (going to infinity) order statistics across the distribution. Our one-sample method computes instantly, using our new formula that also instantly computes goodness-of-fit p-values and uniform confidence bands. To improve power, we also propose stepdown and pre-test procedures that maintain control of the asymptotic familywise error rate. One-sample and two-sample cases are considered, as well as extensions to regression discontinuity designs and conditional distributions. Simulations, empirical examples, and code are provided.

Suggested Citation

  • David M. Kaplan & Matt Goldman, 2018. "Comparing distributions by multiple testing across quantiles or CDF values," Working Papers 1801, Department of Economics, University of Missouri.
  • Handle: RePEc:umc:wpaper:1801
    Note: Title change on 2018-02-22
    as

    Download full text from publisher

    File URL: https://drive.google.com/file/d/1UkkqiyQz8ZD4gX9Aosg1vw2p1C5aYmt-/view?usp=sharing
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Marianne P. Bitler & Jonah B. Gelbach & Hilary W. Hoynes, 2006. "What Mean Impacts Miss: Distributional Effects of Welfare Reform Experiments," American Economic Review, American Economic Association, vol. 96(4), pages 988-1012, September.
    2. Russell Davidson & Jean-Yves Duclos, 2013. "Testing for Restricted Stochastic Dominance," Econometric Reviews, Taylor & Francis Journals, vol. 32(1), pages 84-125, January.
    3. Ivan A Canay & Vishal Kamat, 2018. "Approximate Permutation Tests and Induced Order Statistics in the Regression Discontinuity Design," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(3), pages 1577-1608.
    4. Linton, Oliver & Song, Kyungchul & Whang, Yoon-Jae, 2010. "An improved bootstrap test of stochastic dominance," Journal of Econometrics, Elsevier, vol. 154(2), pages 186-202, February.
    5. Goldman, Matt & Kaplan, David M., 2017. "Fractional order statistic approximation for nonparametric conditional quantile inference," Journal of Econometrics, Elsevier, vol. 196(2), pages 331-346.
    6. David M. Kaplan & Matt Goldman, 2015. "Nonparametric inference on conditional quantile differences and linear combinations, using L-statistics," Working Papers 1503, Department of Economics, University of Missouri.
    7. Ferreira, Francisco H. G. & Firpo, Sergio & Galvao, Antonio F., 2017. "Estimation and Inference for Actual and Counterfactual Growth Incidence Curves," IZA Discussion Papers 10473, Institute of Labor Economics (IZA).
    8. Matt Goldman & David M. Kaplan, 2018. "Non‐parametric inference on (conditional) quantile differences and interquantile ranges, using L‐statistics," Econometrics Journal, Royal Economic Society, vol. 21(2), pages 136-169, June.
    9. Thomas MaCurdy & Xiaohong Chen & Han Hong, 2011. "Flexible Estimation of Treatment Effect Parameters," American Economic Review, American Economic Association, vol. 101(3), pages 544-551, May.
    10. David M. Kaplan, 2015. "Bayesian and frequentist tests of sign equality and other nonlinear inequalities," Working Papers 1516, Department of Economics, University of Missouri.
    11. Shu Shen & Xiaohan Zhang, 2016. "Distributional Tests for Regression Discontinuity: Theory and Empirical Examples," The Review of Economics and Statistics, MIT Press, vol. 98(4), pages 685-700, October.
    12. A. Colin Cameron & Jonah B. Gelbach & Douglas L. Miller, 2008. "Bootstrap-Based Improvements for Inference with Clustered Errors," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 414-427, August.
    13. Moscovich, Amit & Nadler, Boaz, 2017. "Fast calculation of boundary crossing probabilities for Poisson processes," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 177-182.
    14. Qu, Zhongjun & Yoon, Jungmo, 2015. "Nonparametric estimation and inference on conditional quantile processes," Journal of Econometrics, Elsevier, vol. 185(1), pages 1-19.
    15. Joseph P. Romano & Azeem M. Shaikh & Michael Wolf, 2010. "multiple testing," The New Palgrave Dictionary of Economics,, Palgrave Macmillan.
    16. Susan Athey & Guido W. Imbens, 2006. "Identification and Inference in Nonlinear Difference-in-Differences Models," Econometrica, Econometric Society, vol. 74(2), pages 431-497, March.
    17. Stephen G. Donald & Yu-Chin Hsu, 2016. "Improving the Power of Tests of Stochastic Dominance," Econometric Reviews, Taylor & Francis Journals, vol. 35(4), pages 553-585, April.
    18. Bitler, Marianne P. & Gelbach, Jonah B. & Hoynes, Hilary W., 2008. "Distributional impacts of the Self-Sufficiency Project," Journal of Public Economics, Elsevier, vol. 92(3-4), pages 748-765, April.
    19. Uri Gneezy & John A List, 2006. "Putting Behavioral Economics to Work: Testing for Gift Exchange in Labor Markets Using Field Experiments," Econometrica, Econometric Society, vol. 74(5), pages 1365-1384, September.
    20. Jackson, Erika & Page, Marianne E., 2013. "Estimating the distributional effects of education reforms: A look at Project STAR," Economics of Education Review, Elsevier, vol. 32(C), pages 92-103.
    21. R'emy Chicheportiche & Jean-Philippe Bouchaud, 2012. "Weighted Kolmogorov-Smirnov test: Accounting for the tails," Papers 1207.7308, arXiv.org, revised Oct 2012.
    22. Kaplan, David M. & Zhuo, Longhao, 2021. "Frequentist properties of Bayesian inequality tests," Journal of Econometrics, Elsevier, vol. 221(1), pages 312-336.
    23. Djebbari, Habiba & Smith, Jeffrey, 2008. "Heterogeneous impacts in PROGRESA," Journal of Econometrics, Elsevier, vol. 145(1-2), pages 64-80, July.
    24. Sivan Aldor-Noiman & Lawrence D. Brown & Andreas Buja & Wolfgang Rolke & Robert A. Stine, 2013. "The Power to See: A New Graphical Test of Normality," The American Statistician, Taylor & Francis Journals, vol. 67(4), pages 249-260, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Goldman, Matt & Kaplan, David M., 2018. "Comparing distributions by multiple testing across quantiles or CDF values," Journal of Econometrics, Elsevier, vol. 206(1), pages 143-166.
    2. Kaplan, David M., 2015. "Improved quantile inference via fixed-smoothing asymptotics and Edgeworth expansion," Journal of Econometrics, Elsevier, vol. 185(1), pages 20-32.
    3. David M. Kaplan & Matt Goldman, 2015. "Nonparametric inference on conditional quantile differences and linear combinations, using L-statistics," Working Papers 1503, Department of Economics, University of Missouri.
    4. David M. Kaplan, 2014. "Nonparametric Inference on Quantile Marginal Effects," Working Papers 1413, Department of Economics, University of Missouri.
    5. Matt Goldman & David M. Kaplan, 2018. "Non‐parametric inference on (conditional) quantile differences and interquantile ranges, using L‐statistics," Econometrics Journal, Royal Economic Society, vol. 21(2), pages 136-169, June.
    6. Hsu, Yu-Chin & Shen, Shu, 2019. "Testing treatment effect heterogeneity in regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 208(2), pages 468-486.
    7. David M. Kaplan, 2013. "IDEAL Inference on Conditional Quantiles via Interpolated Duals of Exact Analytic L-statistics," Working Papers 1316, Department of Economics, University of Missouri.
    8. Callaway, Brantly & Li, Tong & Oka, Tatsushi, 2018. "Quantile treatment effects in difference in differences models under dependence restrictions and with only two time periods," Journal of Econometrics, Elsevier, vol. 206(2), pages 395-413.
    9. David Lander & David Gunawan & William Griffiths & Duangkamon Chotikapanich, 2020. "Bayesian assessment of Lorenz and stochastic dominance," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 53(2), pages 767-799, May.
    10. Michael J. Kottelenberg & Steven F. Lehrer, 2017. "Targeted or Universal Coverage? Assessing Heterogeneity in the Effects of Universal Child Care," Journal of Labor Economics, University of Chicago Press, vol. 35(3), pages 609-653.
    11. Goldman, Matt & Kaplan, David M., 2017. "Fractional order statistic approximation for nonparametric conditional quantile inference," Journal of Econometrics, Elsevier, vol. 196(2), pages 331-346.
    12. David Lander & David Gunawan & William E. Griffiths & Duangkamon Chotikapanich, 2016. "Bayesian Assessment of Lorenz and Stochastic Dominance Using a Mixture of Gamma Densities," Department of Economics - Working Papers Series 2023, The University of Melbourne.
    13. David M. Kaplan & Lonnie Hofmann, 2019. "High-order coverage of smoothed Bayesian bootstrap intervals for population quantiles," Working Papers 1914, Department of Economics, University of Missouri, revised 19 Sep 2020.
    14. Tinh Thanh Doan & Gibson John & Tuyen Quang Tran, 2016. "Heterogeneous Credit Impacts on Health Care Spending of the Poor in Peri-Urban Areas, Vietnam," SAGE Open, , vol. 6(4), pages 21582440166, November.
    15. Antecol, Heather & Eren, Ozkan & Ozbeklik, Serkan, 2013. "The effect of Teach for America on the distribution of student achievement in primary school: Evidence from a randomized experiment," Economics of Education Review, Elsevier, vol. 37(C), pages 113-125.
    16. Yoichi Arai & Yu‐Chin Hsu & Toru Kitagawa & Ismael Mourifié & Yuanyuan Wan, 2022. "Testing identifying assumptions in fuzzy regression discontinuity designs," Quantitative Economics, Econometric Society, vol. 13(1), pages 1-28, January.
    17. Callaway, Brantly, 2021. "Bounds on distributional treatment effect parameters using panel data with an application on job displacement," Journal of Econometrics, Elsevier, vol. 222(2), pages 861-881.
    18. Sørensen, Kenneth Lykke, 2016. "Heterogeneous impacts on earnings from an early effort in labor market programs," Labour Economics, Elsevier, vol. 41(C), pages 266-279.
    19. Sokbae Lee & Yoon-Jae Whang, 2009. "Nonparametric Tests of Conditional Treatment Effects," Cowles Foundation Discussion Papers 1740, Cowles Foundation for Research in Economics, Yale University.
    20. David M Kaplan & Wei Zhao, 2023. "Comparing latent inequality with ordinal data," The Econometrics Journal, Royal Economic Society, vol. 26(2), pages 189-214.

    More about this item

    Keywords

    Dirichlet; familywise error rate; Kolmogorov–Smirnov; probability integral transform; stepdown;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:umc:wpaper:1801. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chao Gu (email available below). General contact details of provider: https://edirc.repec.org/data/edumous.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.