Robby, thanks for your exceptional and insightful comments! I'm lucky to stumble on a real expert in this field! However let me point to you that this last comment doesn't deliver what's promised in one of the comments above (ie. explain WHY Niels' estimator is good). Rather it provides rigorous definition of it + simulation results. For the real explanations (proof of the Theorem) the reader is referred to you thesis :) Of course it is incorrect for me to expect the full answer in a page or 2. If i'll need to address more similar questions i'll surely take a read of all the links.

Niels, thanks a lot! I didn't know the RMS concept. If i did it might ring a bell. It's indeed THE best answer in the sense i asked for.

The summation works in the case the direction is "signed" i.e. not symmetrical around 0. In my case this wont work: e.g. if there're 100 points at $p$ and 100 points at $-p$ their sum will be 0... Thanks for useful link, though.