Large knowledge bases typically contain data adhering to various schemas with incomplete and/or noisy type information. This seriously complicates further integration and post-processing efforts, as type information is crucial in correctly handling the data. In this paper, we introduce a novel statistical type inference method, called StaTIX, to effectively infer instance types in Linked Data sets in a fully unsupervised manner. Our inference technique leverages a new hierarchical clustering algorithm that is robust, highly effective, and scalable. We introduce a novel approach to reduce the processing complexity of the similarity matrix specifying the relations between various instances in the knowledge base. This approach speeds up the inference process while also improving the correctness of the inferred types due to the noise attenuation in the input data. We further optimize the clustering process by introducing a dedicated hash function that speeds up the inference process by orders of magnitude without negatively affecting its accuracy. Finally, we describe a new technique to identify representative clusters from the multi-scale output of our clustering algorithm to further improve the accuracy of the inferred types. We empirically evaluate our approach on several real-world datasets and compare it to the state of the art. Our results show that StaTIX is more efficient than existing methods (both in terms of speed and memory consumption) as well as more effective. StaTIX reduces the F1-score error of the predicted types by about 40% on average compared to the state of the art and improves the execution time by orders of magnitude.