When to Re-Draw a Sample, and Why

One way to estimate a statistic over a large data set is to draw a sample consisting of some records from the data set, and compute the statistic over the sample as an estimate of the statistic over the data set. This procedure may fail to produce an accurate estimate. Using one sample for multiple statistics reduces computation and latency, but it can increase the probability of multiple failures to produce accurate estimates, because estimates based on the same sample may not have independent failure probabilities. We show how to bound the probability of multiple failures for sequences of estimates over one or more samples.