单总体方差检验中一致最大势检验(UMPUT)临界值的研究

Critical values of unbiased test on significance tests in variance of one sample normal distribution

方差检验问题在实际生活中应用广泛,对于同一假设可能有不同的检验方法,这就涉及到检验方法的优劣性问题,本文就正态总体对单总体方差检验作了一些研究.对单总体问题,考虑H0∶σ2=σ02vsH1∶σ2≠σ02,通常采用的χ2检验并不是无偏的,给出了无偏检验的临界值.将该无偏检验与常用的χ2检验就势函数进行比较,指出当样本量n不大时二者是有差别的.

Due to its wide application in different fields, considerable attention has been given to the problem about hypothesis tests on variance of the normal distribution. There are different test methods under the same null and alternative hypothesis. But which is better？ Some analysis on this aspect is made. Significance tests in variance of one sample normal distribution is considered. For testing H0： σ^2 =σ0^2 vs H1 ： σ^2 ≠σ0^2 ,χ^2-test is usually used. But it＇s not unbiased. It is proved that among the given-formed tests, the unbiased test is unique and its critical values were calculated. Monte Carlo simulation studies were carried out to calculate power function of χ^2-test and unbiased test. An empirical power function comparison of the above tests suggested that there are differences between the two tests when the sample n is not large.