IDEAS home Printed from https://ideas.repec.org/p/upf/upfgen/1109.html
   My bibliography  Save this paper

A new method for constructing exact tests without making any assumptions

Author

Listed:
  • Karl Schlag

Abstract

We present a new method for constructing exact distribution-free tests (and confidence intervals) for variables that can generate more than two possible outcomes. This method separates the search for an exact test from the goal to create a non- randomized test. Randomization is used to extend any exact test relating to means of variables with finitely many outcomes to variables with outcomes belonging to a given bounded set. Tests in terms of variance and covariance are reduced to tests relating to means. Randomness is then eliminated in a separate step. This method is used to create confidence intervals for the difference between two means (or variances) and tests of stochastic inequality and correlation.

Suggested Citation

  • Karl Schlag, 2008. "A new method for constructing exact tests without making any assumptions," Economics Working Papers 1109, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:1109
    as

    Download full text from publisher

    File URL: https://econ-papers.upf.edu/papers/1109.pdf
    File Function: Whole Paper
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fishman, George S., 1991. "Confidence intervals for the mean in the bounded case," Statistics & Probability Letters, Elsevier, vol. 12(3), pages 223-227, September.
    2. Quinn McNemar, 1947. "Note on the sampling error of the difference between correlated proportions or percentages," Psychometrika, Springer;The Psychometric Society, vol. 12(2), pages 153-157, June.
    3. Nancy Buchan & Rachel Croson, 1999. "Gender and Culture: International Experimental Evidence from Trust Games," American Economic Review, American Economic Association, vol. 89(2), pages 386-391, May.
    4. Djankov, Simeon & La Porta, Rafael & Lopez-de-Silanes, Florencio & Shleifer, Andrei, 2008. "The law and economics of self-dealing," Journal of Financial Economics, Elsevier, vol. 88(3), pages 430-465, June.
    5. Romano, Joseph P. & Wolf, Michael, 2001. "Explicit nonparametric confidence intervals for the variance with guaranteed coverage," DES - Working Papers. Statistics and Econometrics. WS ws010302, Universidad Carlos III de Madrid. Departamento de Estadística.
    6. Karl Schlag, 2008. "Bringing game theory to hypothesis testing: Establishing finite sample bounds on inference," Economics Working Papers 1099, Department of Economics and Business, Universitat Pompeu Fabra.
    7. Africa Borges del Rosal & Concepción San Luis & Alfonso Sánchez-Bruno, 2003. "Dominance Statistics: A Simulation Study on the d Statistic," Quality & Quantity: International Journal of Methodology, Springer, vol. 37(3), pages 303-316, August.
    8. Reiczigel, Jeno & Zakarias, Ildiko & Rozsa, Lajos, 2005. "A Bootstrap Test of Stochastic Equality of Two Populations," The American Statistician, American Statistical Association, vol. 59, pages 156-161, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Galbiati, Roberto & Schlag, Karl H. & van der Weele, Joël J., 2013. "Sanctions that signal: An experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 94(C), pages 34-51.
    2. Bernhard Kasberger & Karl H. Schlag, 2024. "Robust Bidding in First-Price Auctions: How to Bid Without Knowing What Others Are Doing," Management Science, INFORMS, vol. 70(7), pages 4219-4235, July.
    3. Bernhard Kasberger & Karl H. Schlag, 2017. "Robust Bidding in First-Price Auctions: How to Bid without Knowing what Otheres are Doing," Vienna Economics Papers 1707, University of Vienna, Department of Economics.
    4. Karl H.Schlag, 2015. "Who gives Direction to Statistical Testing? Best Practice meets Mathematically Correct Tests," Vienna Economics Papers vie1512, University of Vienna, Department of Economics.
    5. Heczko, Alexander & Kittsteiner, Thomas & Ott, Marion, 2023. "The benefits of auctioneer competition: Merging auctions and adding auctioneers," ZEW Discussion Papers 23-038, ZEW - Leibniz Centre for European Economic Research.
    6. Matteo Rizzolli & James Tremewan, 2016. "Hard Labour in the lab: Are monetary and non-monetary sanctions really substitutable?," Vienna Economics Papers vie1606, University of Vienna, Department of Economics.
    7. Lippert, Steffen & Tremewan, James, 2021. "Pledge-and-review in the laboratory," Games and Economic Behavior, Elsevier, vol. 130(C), pages 179-195.
    8. Karl Schlag & James Tremewan, 2021. "Simple belief elicitation: An experimental evaluation," Journal of Risk and Uncertainty, Springer, vol. 62(2), pages 137-155, April.
    9. Heczko, Alexander & Kittsteiner, Thomas & Ott, Marion, 2018. "The Performance of Core-Selecting Auctions: An Experiment," EconStor Preprints 176842, ZBW - Leibniz Information Centre for Economics.
    10. Dugar, Subhasish & Mitra, Arnab & Shahriar, Quazi, 2019. "Deception: The role of uncertain consequences," European Economic Review, Elsevier, vol. 114(C), pages 1-18.
    11. Thomas A. Stephens & Jean-Robert Tyran, 2012. "“At least I didn’t lose money” - Nominal Loss Aversion Shapes Evaluations of Housing Transactions," Discussion Papers 12-14, University of Copenhagen. Department of Economics.
    12. Gossner, Olivier & Schlag, Karl H., 2013. "Finite-sample exact tests for linear regressions with bounded dependent variables," Journal of Econometrics, Elsevier, vol. 177(1), pages 75-84.
    13. Müller, Julia & Schwieren, Christiane & Spitzer, Florian, 2022. "How to prevent destruction – On the malleability of anti-social behavior," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 97(C).
    14. Karl H.Schlag, 2015. "Who gives Direction to Statistical Testing? Best Practice meets Mathematically Correct Tests," Vienna Economics Papers 1512, University of Vienna, Department of Economics.
    15. repec:spo:wpmain:info:hdl:2441/7o52iohb7k6srk09o0ks2e12i is not listed on IDEAS
    16. Galbiati, Roberto & Schlag, Karl H. & van der Weele, Joël J., 2013. "Sanctions that signal: An experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 94(C), pages 34-51.
    17. repec:hal:spmain:info:hdl:2441/7o52iohb7k6srk09o0ks2e12i is not listed on IDEAS
    18. Chakrabarty, Manisha & Hildenbrand, Werner, 2011. "Engel's Law Reconsidered," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 289-299.
    19. Roberto Galbiati & Karl Schlag & Joël van der Weele, 2009. "Can sanctions induce pessimism? An experiment," Economics Working Papers 1150, Department of Economics and Business, Universitat Pompeu Fabra.
    20. Müller, Julia & Schwieren, Christiane & Spitzer, Florian, 2016. "What Drives Destruction? On the Malleability of Anti-Social Behavior," Department of Economics Working Paper Series 238, WU Vienna University of Economics and Business.
    21. Matteo Rizzolli & James Tremewan, 2016. "Hard Labour in the lab: Are monetary and non-monetary sanctions really substitutable?," Vienna Economics Papers 1606, University of Vienna, Department of Economics.
    22. Karl Schlag & Olivier Gossner, 2010. "Finite sample nonparametric tests for linear regressions," Economics Working Papers 1212, Department of Economics and Business, Universitat Pompeu Fabra.

    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. Long,Cheryl Xiaoning & Xu,L. Colin & Yang,Jin, 2020. "Business Environment and Dual-Track Private Sector Development : China's Experience in Two Crucial Decades," Policy Research Working Paper Series 9161, The World Bank.
    2. Shagata Mukherjee, 2020. "What Drives Gender Differences in Trust and Trustworthiness?," Public Finance Review, , vol. 48(6), pages 778-805, November.
    3. Fidrmuc, Jana P. & Jacob, Marcus, 2010. "Culture, agency costs, and dividends," Journal of Comparative Economics, Elsevier, vol. 38(3), pages 321-339, September.
    4. Robert Jiro Netzer & Matthias Sutter, 2009. "Intercultural trust. An experiment in Austria and Japan," Working Papers 2009-05, Faculty of Economics and Statistics, Universität Innsbruck.
    5. Francesco Caselli & Nicola Gennaioli, 2008. "Economics and Politics of Alternative Institutional Reforms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(3), pages 1197-1250.
    6. Becchetti, Leonardo & Degli Antoni, Giacomo & Ottone, Stefania & Solferino, Nazaria, 2013. "Allocation criteria under task performance: The gendered preference for protection," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 45(C), pages 96-111.
    7. Osei-Tutu, Francis & Weill, Laurent, 2023. "Individualism reduces borrower discouragement," Journal of Economic Behavior & Organization, Elsevier, vol. 211(C), pages 370-385.
    8. Nadia Saghi-Zedek & Amine Tarazi, 2015. "Droits de contrôle versus droits pécuniaires, crise financière et vulnérabilité des banques européennes," Revue économique, Presses de Sciences-Po, vol. 66(3), pages 527-535.
    9. Lepetit, Laetitia & Saghi-Zedek, Nadia & Tarazi, Amine, 2015. "Excess control rights, bank capital structure adjustments, and lending," Journal of Financial Economics, Elsevier, vol. 115(3), pages 574-591.
    10. Rouine, Ibtissem, 2018. "Target country's leadership style and bidders' takeover decisions," International Review of Financial Analysis, Elsevier, vol. 60(C), pages 17-29.
    11. Uttam Bandyopadhyay & Atanu Biswas & Shirsendu Mukherjee, 2009. "Adaptive two-treatment two-period crossover design for binary treatment responses incorporating carry-over effects," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(1), pages 13-33, March.
    12. Imen Ghadhab, 2023. "Bonding, signaling theory and dividend policy: Evidence from multinational firms," Journal of Asset Management, Palgrave Macmillan, vol. 24(1), pages 69-83, February.
    13. Mohd Mohid Rahmat & Kamran Ahmed & Gerald J. Lobo, 2020. "Related Party Transactions, Value Relevance and Informativeness of Earnings: Evidence from Four Economies in East Asia," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 23(01), pages 1-42, March.
    14. Enikolopov, Ruben & Petrova, Maria & Stepanov, Sergey, 2014. "Firm value in crisis: Effects of firm-level transparency and country-level institutions," Journal of Banking & Finance, Elsevier, vol. 46(C), pages 72-84.
    15. Knack, Steve & Xu, Lixin Colin, 2017. "Unbundling institutions for external finance: Worldwide firm-level evidence," Journal of Corporate Finance, Elsevier, vol. 44(C), pages 215-232.
    16. Chacón, José E. & Fernández Serrano, Javier, 2024. "Bayesian taut splines for estimating the number of modes," Computational Statistics & Data Analysis, Elsevier, vol. 196(C).
    17. Hatzigeorgiou, Andreas & Lodefalk, Magnus, 2011. "Trade and Migration: Firm-Level Evidence (LONG VERSION)," Working Papers 2011:6, Örebro University, School of Business.
    18. Finocchiaro Castro, Massimo, 2008. "Where are you from? Cultural differences in public good experiments," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 37(6), pages 2319-2329, December.
    19. Cakici, Nusret & Zaremba, Adam, 2022. "Salience theory and the cross-section of stock returns: International and further evidence," Journal of Financial Economics, Elsevier, vol. 146(2), pages 689-725.
    20. Tamilina, Larysa, 2012. "Characteristics of social policies and social trust," MPRA Paper 96517, University Library of Munich, Germany.

    More about this item

    Keywords

    Distribution-free; nonparametric; exact hypothesis testing; unavoidable inaccuracy; nonparametric Behrens-Fisher problem; UMPU test; Kendall's tau; Qn;
    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:upf:upfgen:1109. 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: the person in charge (email available below). General contact details of provider: http://www.econ.upf.edu/ .

    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.