정규모집단에서 다섯수치요약의 피셔 정보행렬에 관한 연구

Abstract

In the meta-analysis, most individual research provide information in the form of {sample mean, sample standard deviation; sample size}. This is the basis for the estimate of the parameter, its standard error, confidence interval, and hypothesis test. However, in some cases, only ‘five-number summary’ information {minimum, first quartile, median, third quartile, maximum; sample size} is given. In this case, for maximum utilization of meta-information, the work of unifying information must be preceded. In most cases, it is transformed in the form {sample mean, sample standard deviation; sample size}. Several previous studies have already suggested several methods of estimating the population mean and population standard deviation from the five-number summary under the assumption of a normal population. In performance comparison studies of these methods, Lee(2022) recently proposed the maximum likelihood estimation method and showed the superiority of it, but studies on the characteristics of the standard error of the estimates were not presented. Therefore, in this study, in order to estimate the standard error of the maximum likelihood estimate(mle) based on the five-number summary, the log-likelihood function, the score function, and the Fisher information matrix(FIM) are first derived algebraically under the assumption of a normal population, and using these we create a function that computes them easily in R. Through a simulation using these, the characteristics of the standard error of the mle are identified. In addition, after estimating the FIM of the five-number summary, it was compared with the FIM of sufficient statistics and the relative efficiency was examined.