# No Free Lunch in statistics

I was wondering if the No Free Lunch (NFL) theorem applies to even the estimation problem. Suppose there are $$N$$ points in the input. We are trying to estimate the mean value say weights associated with the $$N$$ points. By randomly selecting $$n$$ of the $$N$$ points, we obtain an unbiased estimate of the population mean weight.

However, the NFL states that the knowledge of the $$n$$ doesn't imply the goodness of the estimate of the remaining $$N-n$$ points. Does this mean there is no best estimator of the population mean in statistics?

I will also be very grateful if someone could share some papers on NFL in sampling and statistics since I haven't been able to find them yet.