A Decision-Theoretic Approach to the Problem of Testing a Null Hypothesis.
PURDUE UNIV LAFAYETTE IND DEPT OF STATISTICS
Pagination or Media Count:
The author considers the testing of the null hypothesis theta 0 against the one-dimensional alternative theta not equal to 0. In most problems, the investigator knows that theta 0 is unreasonable, and would prefer to accept theta 0 if 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
- Statistics and Probability