We show lower bounds on the number of sample points and on the number of coin tosses used by general sampling algorithms for estimating the average value of functions over a large domain. The bounds depend on the desired precision and on the error probability of the estimate. Our lower bounds match upper bounds established by known algorithms, up to a multiplicative constant. Furthermore, we give a non-constructive proof of existence of an algorithm that improves the known upper bounds by a constant factor.
- Lower bounds
- Theory of computation