Analytical queries are queries with numerical aggregators: computing the average number of objects per property, identifying the most frequent subjects, etc. Such queries are essential to monitor the quality and the content of the Linked Open Data (LOD) cloud. Many analytical queries cannot be executed directly on the SPARQL endpoints, because the fair use policy cuts off expensive queries. In this paper, we show how to rewrite such queries into a set of queries that each satisfy the fair use policy. We then show how to execute these queries in such a way that the result provably converges to the exact query answer. Our algorithm is an anytime algorithm, meaning that it can give intermediate approximate results at any time point. Our experiments show that the approach converges rapidly towards the exact solution, and that it can compute even complex indicators at the scale of the LOD cloud.