# Accession Number:

## AD0725532

# Title:

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

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## PURDUE UNIV LAFAYETTE IND DEPT OF STATISTICS

# Personal Author(s):

# Report Date:

## 1971-06-01

# Pagination or Media Count:

## 10.0

# Abstract:

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

# Subject Categories:

- Statistics and Probability