The Generalized Maximum Likelihood Estimation Of Proportion Of False Null Hypothesis

This paper mainly uses the generalized maximum likelihood estimation(GMLE)to study the problem of estimating the proportion of false null hypothesis and improves three different methods of estimating the proportion of false null hypothesis. GMLE is used to estimate prior distribution in the empirical bayesian problem[10,14]. For computing GMLE, we use the EM algorithm to get the weight iteration expression.Because the EM algorithm converges slowly, weight iteration needs to choose a good initial estimation. In theory, any reasonable estimation can be used for estimating the initial weight. the initial estimation of zero weight can be converted into estimating the proportion of false null hypothesis, so the fourth chapter reviews three methods of estimating the proportion of false null hypothesis and simply describes the structure of the estimators. The first one bases on frequency change[8] and the second one bases on p-value distribution of null hypothesis[13] and the last one bases on the Bernoulli distribution[17]. GMLE estimation method is proposed to improve them in the end.To explain estimated effect of GMLE method, we do data simulation and compare the effect of estimation before improvement with that after improvement. We finally conclude that estimated values from the improved GMLE method are more close to the real value. So improvement has significant effect.