Diminished Confidence Levels in the Interval Estimation of an Unknown Regressor in Model I of Linear Regression

✍ Scribed by Dr. M. Horn; Dr. W. Rausch

• Publisher: John Wiley and Sons
• Year: 1984
• Tongue: English
• Weight: 404 KB
• Volume: 26
• Category: Article
• ISSN: 0323-3847
• DOI: 10.1002/bimj.4710260306

✦ Synopsis

For the model ~=/3,,+/?~ z + e (model 1 of linear regression) in the literature confidence estimators of an unknown position z , are given at which either the expectation of y is given (see FIELLER, 1944; FINNEP, 1952), or realizations of y are given (see GRAYBILL, 1981). These confidence regions with level 1 -a need not be intervals. The occurrence of interval shape is a random event. Its probability is equal to the power of the l-test for the examination of the hypothesis H : B i = O .

The papers mentioned above claim to provide confidence intervals with level 1 -a . But because of the restriction of (1 -a)-confidence regions to intervals the true confidence probability is the conditional probability U',:

W , = P (the confidence region covers zol the region has interval shape). Here this conditional probability is shown to be less than 1 -a. Evidence on the posRible deviations from 1 -a has been obtained by simulations.