基于泊松过程尖点模型的修正假设检验

Modified Hypothesis Testing Based on Cusp Model of Poisson Process

文章以减小检验犯第一类和第二类错误的概率为主要目标,在泊松过程强度函数存在尖点时修正并、平均和分类运算建立投票、p值平均及判别修正检验。各检验均给出在局部备择假设成立时势函数的极限表达式,对数值拟合进行比较的结果表明,修正极大似然检验和判别修正检验分别在有限样本场合和极限场合整体拥有较好的势。

In order to reduce the probability of Type-one and Type-two error,this paper modifies the asymptotic significance test when the intensity function of Poisson process has a cusp.The modified maximum likelihood test and modified Wald test are established through modified likelihood function,and the voting,p-value averaging and discriminant modified tests are established by crossing,union,averaging and classification operations for the above test results.Each test gives the limit expression of the potential function when the local alternative hypothesis holds.The results of numerical fitting comparison show that the modified maximum likelihood test and the discriminant modified test have better potential on the whole in the finite sample case and the limit case respectively.