| Research Abstract |
In this research project, we have mainly studied the following three subjects.
1.Theory of statistical inference on several multivariate normal mean vectors under order restrictions.
2.Theory of testing hypotheses on parameters of non-normal distributions under order restrictions.
3.Study of statistical inference and distribution theory under order restrictions or inequality restrictions other than those in 1.or2., related statistical problems and their applications.
First, as for 1., since the distribution of the likelihood ratio test statistic cannot be derived easily, we considered modified methods to circumvent this difficulty, conducted numerical experiments by Monte Carlo simulation, examined the properties of the likelihood ratio test and the modified methods, and then obtained many interesting findings. As for 2., when several binomial parameters are restricted by an ordering, we studied the problem of testing their homogeneity, examined the properties of several test statistics by using computer simulation, analyzed the results, and then obtained many interesting findings. We also have started more mathematical and theoretical study of the same problem, which will be continued next year. Also as for 3., many results have been obtained. Some of important results are as follows. (1) We made a unified review of statistical inference under general inequality restrictions including order restrictions. (2) About a growth curve model with two types of design matrices, assuming the covariance matrices are unknown positive definite matrices, we derived the maximum likelihood estimator and examined its basic properties. (3) We found a new monotone transformation which enables us to improve chi-squared approximation of statistics whose chi-squared approximation cannot be improved by Bartlett transformation.
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