List of unsolved problems in statistics

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There are many longstanding unsolved problems in mathematics for which a solution has still not yet been found. The unsolved problems in statistics are generally of a different flavor; according to John Tukey,[1] "difficulties in identifying problems have delayed statistics far more than difficulties in solving problems." A list of "one or two open problems" (in fact 22 of them) was given by David Cox.[2]

Inference and testing[edit]

Experimental design[edit]

Problems of a more philosophical nature[edit]


  1. ^ Tukey, John W. (1954). "Unsolved Problems of Experimental Statistics". Journal of the American Statistical Association. Journal of the American Statistical Association, Vol. 49, No. 268. 49 (268): 706–731. doi:10.2307/2281535. JSTOR 2281535. 
  2. ^ Cox, D.R. (1984) "Present position and potential developments: Some personal views — Design of experiments and regression", Journal of the Royal Statistical Society, Series A, 147 (2), 306–315
  3. ^ Nabendu Pal, Wooi K. Lim (1997) "A note on second-order admissibility of the Graybill–Deal estimator of a common mean of several normal populations", Journal of Statistical Planning and Inference, 63 (1), 71–78. doi:10.1016/S0378-3758(96)00202-9
  4. ^ Fraser, D.A.S.; Rousseau, J. (2008) "Studentization and deriving accurate p-values". Biometrika, 95 (1), 1—16. doi:10.1093/biomet/asm093
  5. ^ Jordan, M. I. (2011). "What are the open problems in Bayesian statistics?" The ISBA Bulletin, 18(1).
  6. ^ Zabell, S. L. (1992). "Predicting the unpredictable". Synthese. 90: 205. doi:10.1007/bf00485351. 


  • Linnik, Jurii (1968). Statistical Problems with Nuisance Parameters. American Mathematical Society. ISBN 0-8218-1570-9. 
  • Sawilowsky, Shlomo S. (2002). "Fermat, Schubert, Einstein, and Behrens–Fisher: The Probable Difference Between Two Means When σ1 ≠ σ2", Journal of Modern Applied Statistical Methods, 1(2).