A Decision-Theoretic Approach to the Problem of Testing a Null Hypothesis.

摘要

The author considers the testing of the 'null hypothesis'theta = 0against the one-dimensional alternative theta not equal to 0. In most problems,the investigator knows that theta = 0is unreasonable,and would prefer to 'accept'theta = 0if absolute value of theta is sufficiently small. The assumption is made that the problem is sufficiently regular,that is,that the likelihood function is sufficiently close to that of a sample from a normal distribution with mean theta and variance 1,after normalization if necessary. A mathematical formulation of this problem is given and the solution is investigated. It is shown that a crude procedure based on a 'small sample'treatment and a 'very large sample'treatment can be very bad in the transition region;also,there is not enough information in those treatments to get robust results. (Author)