摘要
The stability of testing hypotheses is discussed.Differing from the usual tests measured by Neyman-Pearson lemma,the regret and correction of the tests are considered.After the decision is made based on the observations X1,X2,...,Xn,one more piece of datum Xn+1 is picked and the test is done again in the same way but based on X1,X2,...,Xn,Xn+1.There are three situations;(i) The previous decision is right but the new decision is wrong; (ii) the previous decision is wrong but the new decision is right; (iii) both of them are right or both of them are wrong.Of course,it is desired that the probability of the occurrence of (i) is as small as possible and the probability of the occurrence of (ii) is as large as possible.Since the sample size is sometimes not chosen very precisely after the type Ⅰ error and the type Ⅱ error are determined in practice,it seems more urgent to consider the above problem.Some optimal plans are also given.
The stability of testing hypotheses is discussed.Differing from the usual tests measured by Neyman-Pearson lemma,the regret and correction of the tests are considered.After the decision is made based on the observations X1,X2,...,Xn,one more piece of datum Xn+1 is picked and the test is done again in the same way but based on X1,X2,...,Xn,Xn+1.There are three situations;(i) The previous decision is right but the new decision is wrong; (ii) the previous decision is wrong but the new decision is right; (iii) both of them are right or both of them are wrong.Of course,it is desired that the probability of the occurrence of (i) is as small as possible and the probability of the occurrence of (ii) is as large as possible.Since the sample size is sometimes not chosen very precisely after the type Ⅰ error and the type Ⅱ error are determined in practice,it seems more urgent to consider the above problem.Some optimal plans are also given.
基金
Project supported by the National Natural Science Foundation of China and the Doctoral Programme Foundation.
