HYPOTHESIS TESTING
1. Introduction
a. Three types of restrictions
1. Fixed value restriction
2. Linear restriction
3. Nonlinear restriction
b. Three uses for restrictions
1. Impose
2. Test
3. Test and if valid impose
2. Examples of restrictions
a. Fixed-value restrictions
b. Linear restrictions
c. Nonlinear restrictions
3. Imposing restrictions
a. Advantage and disadvantage
b. Unrestricted and restricted models
4. Testing restrictions/hypotheses
a. Maintained and testable hypotheses
b. Steps in testing an hypothesis
1. Specify null and alternative hypotheses
2. Derive appropriate test statistic and sampling distribution under the null
3. Choose the level of significance and find critical value(s)
4. Use sample data to calculate test statistic
5. Compare calculated value to critical value and accept or reject null
5. Statistical tests
a. Small (finite) sample tests
1. Small sample t-test
2. Small sample F-test
b. Large sample (asymptotic) tests
1. Asymptotic t-test
2. Approximate F-test
3. Likelihood ratio test
4. Wald test
5. Lagrange multiplier test
c. Preferred test
6. t-test
a. Small sample t-test
1. What type of restrictions can be tested?
2. t-statistic
3. t-distribution
4. Testing a fixed value restriction
5. Testing a linear restriction
b. Asymptotic t-test
1. What type of restrictions can be tested?
2. t-statistic
3. Approximate t-distribution
4. Testing a nonlinear restriction
7. F-test
a. Small sample F-test
1. What type of restrictions can be tested?
2. Two F-statistic approaches
a. Unrestricted/restricted model approach
b. Unrestricted model approach
3. F-distribution
4. Testing one or more linear restrictions
b. Approximate F-test
1. What type of restrictions can be tested?
2. F-statistic
3. Approximate F-distribution
8. Likelihood ratio test
a. What type of restrictions can be tested?
b. LR statistic
c. Approximate chi-square distribution
d. Logic of test
9. Wald test
a. What type of restrictions can be tested?
b. Wald statistic
1. Matrix of partial derivatives
c. Approximate chi-square distribution
10. Lagrange multiplier test
a. What type of restrictions can be tested?
b. LM statistic
c. Approximate chi-square distribution