In this paper using a non-negative regular summability matrix A and a non trivial admissible ideal I of subsets of N we have introduced the notion of AI-statistical limit point as a generalization of A-statistical limit point of sequences of real numbers. We have also studied some basic properties of the sets of all AI-statistical limit points and AI-statistical cluster points of real sequences including their interrelationship. Also introducing additive property of AI-density zero sets we have established AI-statistical analogue of some completeness theorems of R.