Research On The Calibration Approach Of Hypothesis Testing P-values

In statistical hypothesis testing, a p-value is expected to be distributed as the uniform distribution on the interval (0,1) under the null hypothesis. However, some p-values, such as the generalized p-value and the posterior predictive p-value, cannot be assured of this property. In this paper, we hope to calibrate them and make cali-brated p-values close to the uniform distribution on the interval (0,1) under the null hypothesis.(i) we propose an adaptive p-value calibration approach, and show that the cali-brated p-value is asymptotically distributed as the uniform distribution. For Behrens-Fisher problem and goodness-of-fit test under a normal model, the calibrated p-values are constructed and their behavior is evaluated numerically. Simulations show that the calibrated p-values are superior than original ones.(ii) This paper proposes a posterior predictive calibration approach of p-values ap-plicable for this class of problems and investigates its properties in theory and simula-tions. The calibrated p-value is shown to enjoy correct asymptotic frequentist behavior. Also, the behavior of the advised approach is numerically compared with that of the generalized p-value for Fieller’s problem. Simulation results show that the calibrated p-value is superior to the uncalibrated one in the frequentist performance,(iii) We study the calibration of p-values for one-sided hypothesis testing in linear calibration. The posterior predictive calibration approach is used to calibrate the generalized p-value of the univariate linear calibration model. It can be seen from simulations that the calibrated p-value is applicable for this problem.