Discussion About The Estimation Of Up-and-Down Method

The up-and-down method is one of the most important method of the sensitive tests.This method was first advanced at the Explosive Research Labo-ratory,Bruceton,Pennsylvania,in the early 1940s,and then widely used in many domains,such as military affairs,medicine and so on.As the key point of the up-and-down data analysis,the estimation of the up-and-down method is very important.In this paper, the Monte Carlo Method is used to improve the research of the others.Firstly,the traditional estimation of the up-and-down data is simply introduced. It shows how how the experimental factors effect the parameter estimations by the orthogonal test.Then the experimental factors are cheese by those results.The ML equations are solved by the Newton Method,and the estimation compare with the estimation of the traditional estimation. The approximate effect of the traditional estimation can be kown.The parameter Bootstrap method is advanced to estimate the intervals and then compare with the intervals estimated by other methods.Secondly,it simply introduces the estimations of the small sample.It can be proved that all the small sample estimations are asymptotically equivalent with traditional estimation.Meanwhile, the scope of the up-and-down method for small samples also can be found.Finally,a new method is advanced to ascertain the distribution of the up-and-down data,because of its particularity.After that,the Newton method can be used to solve the ML equations.