0院究研清银南受王季大門厦餐 WI8目 /图YsmE Hypothesis Testing Professor Yongmiao Hong Cornell University Juy7,2020
Hypothesis Testing Professor Yongmiao Hong Cornell University July 7, 2020
CONTENTS 9.1 Introduction to Hypothesis Testing 9.2 Neyman-Pearson Lemma 9.3 Wald Test 9.4 Lagrangian Multiplier (LM)Test 9.5 Likelihood Ratio Test 9.6 lllustrative Examples 9.7 Conclusion Hypothesis Testing Introduction to Statistics and Econometrics July7,2020 2/110
Hypothesis Testing Introduction to Statistics and Econometrics July 7, 2020 2/110 9.1 Introduction to Hypothesis Testing 9.2 Neyman-Pearson Lemma 9.3 Wald Test 9.4 Lagrangian Multiplier (LM) Test 9.5 Likelihood Ratio Test 9.6 Illustrative Examples 9.7 Conclusion CONTENTS
Parameter Estimation and Evaluation Introduction to Hypothesis Testing Introduction to Hypothesis Testing Question:Given a realization x"of a random sample X" from the population distribution f(x,0),we would also like to know whether the true parameter value 0o belongs to some specific subsetΘof the parameter spaceΘ. Hypothesis Testing Introduction to Statistics and Econometrics Juy7,2020 3/110
Parameter Estimation and Evaluation Hypothesis Testing Introduction to Statistics and Econometrics July 7, 2020 3/110 Introduction to Hypothesis Testing Introduction to Hypothesis Testing
Parameter Estimation and Evaluation Introduction to Hypothesis Testing Introduction to Hypothesis Testing Example 1(9.1)[Return to Education] Let 0 measure the change in hourly wage given another year of education,holding all other factors fixed.Labor economists are interested in testing whether the return to education,con- trolling other factors,is zero.That is,whether or not 0 equal to zero. Hypothesis Testing Introduction to Statistics and Econometrics July7,2020 4/110
Parameter Estimation and Evaluation Hypothesis Testing Introduction to Statistics and Econometrics July 7, 2020 4/110 Introduction to Hypothesis Testing Introduction to Hypothesis Testing Example 1 (9.1) [Return to Education]
Parameter Estimation and Evaluation Introduction to Hypothesis Testing Introduction to Hypothesis Testing Definition 1(9.1)[Hypothesis] A hypothesis is a statement about the population or some attributes of the population distribution.The two comple- mentary hypotheses in a hypothesis testing problem are called the null hypothesis and the alternative hypothesis,denoted by Ho and HA respectively Hypothesis Testing Introduction to Statistics and Econometrics July7,2020 5/110
Parameter Estimation and Evaluation Hypothesis Testing Introduction to Statistics and Econometrics July 7, 2020 5/110 Introduction to Hypothesis Testing Introduction to Hypothesis Testing Definition 1 (9.1) [Hypothesis]