146
Views
1
CrossRef citations to date
0
Altmetric
Articles

Permutation inference distribution for linear regression and related models

&
Pages 722-742 | Received 24 Jun 2016, Accepted 10 Jun 2019, Published online: 20 Jun 2019

References

  • Anderson, M.J., and Robinson, J. (2001), ‘Permutation Tests for Linear Models’, Australian and New Zealand Journal of Statistics, 43, 75–88. doi: 10.1111/1467-842X.00156
  • Basso, D., and Salmaso, L. (2006), ‘A Discussion of Permutation Tests Conditional to Observed Responses in Unreplicated 2M Full Factorial Design’, Communications in Statistics – Theory and Methods, 35, 83–97. doi: 10.1080/03610920500437277
  • Basso, D., Pesarin, F., Salmaso, L., and Solari, A. (2009), Permutation Tests for Stochastic Ordering and ANOVA, New York, NY: Springer.
  • Bonnini, S., Piccolo, D., Salmaso, L., and Solmi, F. (2012), ‘Permutation Inference for a Class of Mixture Models’, Communications in Statistics – Theory and Methods, 41, 2879–2895. doi: 10.1080/03610926.2011.590915
  • Cox, D.R. (1958), ‘Some Problems Connected with Statistical Inference’, The Annals of Mathematical Statistics, 29, 357–372. doi: 10.1214/aoms/1177706618
  • Cox, D.R. (2006), Principles of Statistical Inference, London: Cambridge University Press.
  • Cox, D.R., and Hinkley, D.V. (1974), Theoretical Statistics, London: Chapman & Hall, Section 7.2(iii).
  • Dempster, A.P. (1969), Elements of Continuous Multivariate Analysis (Vol. 388), Massachusetts: Addison-Wesley Reading.
  • Edgington, E.S. (1995), Randomization Tests (3rd ed.), New York, NY: Marcel Dekker.
  • Efron, B. (1993), ‘Bayes and Likelihood Calculations from Confidence Intervals’, Biometrika, 80, 3–26. doi: 10.1093/biomet/80.1.3
  • Efron, B. (1998), ‘R.A. Fisher in the 21st Century’, Statistical Science, 13, 95–122. doi: 10.1214/ss/1028905930
  • Efron, B., and Tibshirani, R.J. (1993), An Introduction to the Bootstrap, New York: Chapman & Hall/CRC.
  • Ernst, M.D. (2004), ‘Permutation Methods: A Basis for Exact Inference’, Statistical Science, 19, 676–685. doi: 10.1214/088342304000000396
  • Fay, M.P. (2010), ‘Two-sided Exact Tests and Matching Confidence Intervals for Discrete Data’, The R Journal, 2, 53–58. doi: 10.32614/RJ-2010-008
  • Finos, L., Brombin, C., and Salmaso, L. (2010), ‘Adjusting Stepwise p-Values in Generalized Linear Models’, Communications in Statistics – Theory and Methods, 39, 1832–1846. doi: 10.1080/03610920902912968
  • Fisher, R.A. (1925-1952), Statistical Methods for Research Workers, New York, NY: Hafner.
  • Fisher, R.A. (1935), The Design of Experiments, New York, NY: Hafner.
  • Fraser, D.A.S. (1957), Nonparametric Methods in Statistics, New York, NY: John Wiley & Sons.
  • Freedman, D., and Lane, D. (1983), ‘A Nonstochastic Interpretation of Reported Significance Levels’, Journal of Business and Economic Statistics, 1, 292–298.
  • Greenland, S., Senn, S.J., Rothman, K.J., Carlin, J.B., Poole, C., Goodman, S.N., and Altman, D.G. (2016), ‘Statistical Tests, P Values, Confidence Intervals, and Power: A Guide to Misinterpretations’, European Journal of Epidemiology, 31, 337–350. doi: 10.1007/s10654-016-0149-3
  • Grenander, U., and Rosenblatt, M. (1957), Statistical Analysis of Stationary Time Series, New York: Wiley.
  • Kennedy, P.E. (1995), ‘Randomization Tests in Econometrics’, Journal of Business and Economic Statistics, 13, 85–94.
  • Kennedy, P.E., and Cade, B.S. (1996), ‘Randomization Tests for Multiple Regression’, Communications in Statistics – Simulation and Computation, 25, 923–936. doi: 10.1080/03610919608813350
  • Lehmann, L.E. (1999), Elements of Large-Sample Theory, New York, NY: Springer.
  • Manley, B.F.J. (1997), Randomization, Bootstrap, and Monte Carlo Methods in Biology (2nd ed.), London: Chapman & Hall.
  • Mazer, M.A., Alligood, C.M., and Wu, Q. (2011), ‘The Infusion of Opioids During Terminal Withdrawal of Mechanical Ventilation in the Medical Intensive Care Unit’, Journal of Pain and Symptom Management, 42, 44–51. doi: 10.1016/j.jpainsymman.2010.10.256
  • Pagano, M., and Tritchler, D. (1983), ‘On Obtaining Permutation Distributions in Polynomial Time’, Journal of the American Statistical Association, 78, 435–440. doi: 10.1080/01621459.1983.10477990
  • Pesarin, F., and Salmaso, L. (2010), Permutation Tests for Complex Data: Theory, Applications, and Software, West Sussex, UK: John Wiley & Sons.
  • Pesarin, F., Salmaso, L., Carrozzo, E., and Arboretti, R. (2016), ‘Union–intersection Permutation Solution for Two-sample Equivalence Testing’, Statistics and Computing, 26, 693–701. doi: 10.1007/s11222-015-9552-y
  • Rao, C.R., Toutenburg, H., Shalabh, and Heumann, C. (2008), Linear Models and Generalizations (3rd ed.), Berlin: Springer.
  • Samuh, M.H., Grilli, L., Rampichini, C., Salmaso, L., and Lunardon, N. (2012), ‘The Use of Permutation Tests for Variance Components in Linear Mixed Models’, Communications in Statistics – Theory and Methods, 41, 3020–3029. doi: 10.1080/03610926.2011.587933
  • Scheffé, H. (1959), The Analysis of Variance, New York, NY: Wiley.
  • Schweder, T., and Hjort, N.L. (2002), ‘Confidence and Likelihood’, Scandinavian Journal of Statistics, 29, 309–332. doi: 10.1111/1467-9469.00285
  • Singh, K., Xie, M., and Strawderman, W.E. (2005), ‘Combining Information from Independent Sources through Confidence Distributions’, Annals of Statistics, 33, 159–183. doi: 10.1214/009053604000001084
  • Singh, K., Xie, M., and Strawderman, W.E. (2007), ‘Confidence Distribution (CD)-distribution Estimator of a Parameter’, in Complex Datasets and Inverse Problems, IMS Lecture Notes-Monograph Series, Vol. 54, pp. 132–150.
  • Tableman, M., Nguyen, M., and Ernst, M.D. (2014), ‘On Confidence Intervals from Permutation Tests’, in Sustainability in Statistics Education, eds. K. Makar, B. de Sousa, and R. Gould, the Ninth International Conference on Teaching Statistics.
  • ter Braak, C.J.F. (1992), ‘Permutation versus Bootstrap Significance Tests in Multiple Regression and ANOVA’, in Bootstrapping and Related Techniques, eds. K.H. Jöckel, G. Rothe, and W. Sendler, Berlin: Springer, pp. 79–86.
  • Tritchler, D. (1984), ‘On Inverting Permutation Tests’, Journal of the American Statistical Association, 79, 200–207. doi: 10.1080/01621459.1984.10477085
  • Vos, P.W., and Hudson, S. (2005), ‘Evaluation Criteria for Discrete Confidence Intervals: Beyond Coverage and Length’, The American Statistician, 59, 137–142. doi: 10.1198/000313005X42453

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.