In this paper we extend the concepts of statistical inner and outer limits (as introduced by Talo, Sever and Başar) to $\mathcal I$-inner and $\mathcal I$-outer limits and give some $\mathcal I$-analogue of properties of statistical inner and outer limits for sequences of closed sets in metric spaces, where $\mathcal I$ is an ideal of subsets of the set $\mathbb N$ of positive integers. We extend the concept of Kuratowski statistical convergence to Kuratowski $\mathcal I$-convergence for a sequence of closed sets and get some properties for Kuratowski $\mathcal I$-convergent sequences. Also, we examine the relationship between Kuratowski $\mathcal I$-convergence and Hausdorff $\mathcal I$-convergence.