Can you estimate a player's Elo rating using tests? So I wonder if there are specific positional/tactical tests for every rating range, so that in the end the general rating of a player can be decided prior to competition.
Obviously the best test is playing in an actual competition, and most trainers will advise their players to play in as many as possible.

Other than that, there are books that try to do this. I don't know how accurate they can be, but it's likely that they need to be taken with a grain of salt: there is probably too much variance in the concentration level and time taken to solve the problems between different readers that they can't all get good answers. Also, chess skill isn't only related to skill in solving chess positions: confidence, controlling nerves, concentrating deeply for hours, judging when to play for a win and when to be content with a draw, most of those are competition skills that will only be reliably judged by actually playing in a competition.

There are many many books of exercises, and some of those try to do Elo estimation based on how many of them you got correct.

Books that I think that do that (there must be more):


The classic "The Best Move", by Vlastimil Hort and Vlastimil Jansa was probably the first of this type.
Barden's "How Good is Your Chess"
Keene's "Discover Your Chess Strength"
Alburt's "Test &amp; Improve Your Chess" (I think)
Bosch's "The Chess Combat Simulator"
King's "How Good Is Your Chess?" (yep, same title as Barden)
Evans' "How Good Is Your Chess?" (seriously, I'm finding these on Amazon and they have different covers)


There's also this site: The Automated Chess Rating Utility website 

Sites like Chesstempo have only tactics puzzles, but they also ask users to enter their FIDE rating and use this to calculate a correlation between Chesstempo and FIDE ratings; inaccurate, but better than nothing.

But again: a rating is an estimate of how well you did in competitions. Estimating ratings some other way seems a bit besides the point -- why not just play in competitions?