Efficient generic integration algorithm to determine confidence intervals and p-values for hypothesis testing
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An algorithm is proposed to calculate confidence intervals and p-values for hypothesis testing that converge to exact values in the limit of investing a large amount of computation time. The frequentist hypothesis test procedure is generic, exact, efficient, conceptually simple, and fairly easy to implement. The procedure is generic in that no assumptions were made on the probability model or the test procedure. The procedure is exact in that independent of the model and the test, the procedure determines exact p-values in the limit of sufficiently large computational resources. The procedure is conceptually simple in that it uses only basic definitions of statistical concepts. With respect to computational efficiency, the proposed algorithm with the likelihood-ratio test is comparable to bootstrap with maximum likelihood estimation of parameters.
Generic and consistent confidence and credible regions. Christian Bartels (2015) figshare.