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.