Estimation And Test For Parameters Of Normal Populations Under Order Restrictions

In this paper, problems of estimation and test for parameters of k normal populations with unknown means and variances under simple semi-order, tree order, ring order and umbrella order restrictions are studied mainly by the statistical inference methods when sample numbers of k normal populations are different. The origins of order restricted statistical inference are usually dated back to the early 1950s. At about the same time, a number of researchers started working independently on similar problems. The field developed rapidly during the 1960s and early 1970s and formed the more perfect theory of estimation and testing. It is still a considerable direction in statistical studies now and its applied background is extensive, especially, a lot of problems, in practice, are explained easily by the structure of ordering and inequalities. So, it has important value to study them. Research on isotonic regression is a key part of statistical inference under order restriction. It mainly considers how to obtain the maximum likelihood estimation of parameters under order restrictions. And the basic methods include pool adjacent violators algorithm, max-min formulas and minimum lower sets etc. The theory of duality in nonlinear program is also applied to the generalized...