In many stream monitoring situations, the data arrival rate is so high that it is not even possible to observe each element of the stream. The most common solution is to subsample the data stream and use the sample to infer properties and estimate aggregates of the original stream. However, in many cases, the estimation of aggregates on the original stream cannot be accomplished through simply estimating them on the sampled stream, followed by a normalization. We present algorithms for estimating frequency moments, support size, entropy, and heavy hitters of the original stream, through a single pass over the sampled stream.