A Note on the Assessment of Local Influence in Statistical Models with Equality Constraints

Relationship has been discussed by Tanaka and Zhang(1999) between the sensitivity analyses based on influence functions and on Cook's local influence, and it has been shown that equivalent results are obtained under general conditions by these analyses in statistical modeling without/with equality constraints. However, a condition implicitly assumed in the proof in Tanaka and Zhang(1999) in the case with equality constraints does not necessarily hold. The present paper gives a complete proof without assuming the condition. Also a formula for the normal curvature is derived for the convenience of practical computation.