Comparison Of Hyperbolic And Constant Width Simultaneous Confidence Bands in Multiple Linear Regression Under MVCS Criterion

‎A simultaneous confidence band gives useful information on the reasonable range of the unknown regression model‎. ‎In this note‎, ‎when the predictor variables are constrained to a special ellipsoidal region‎, ‎hyperbolic and constant width confidence bonds for a multiple linear regression model are compared under the minimum volome confidence set (MVCS) criterion‎. ‎The size of one speical angle that determines the size of the predictor variable region is used to find out which band is better than the other‎. ‎When the angle and consquently the size of the predictor variable region is small‎, ‎the constant width band is better than the hyperbolic band‎.

‎When the angle hence the size of the predictor variable regoin is large‎, ‎the hyperbolic band is considerably better than the constant width band‎.