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I'm helping my father to translate a text from my own native Latvian language to English. Even though I'm a fair English speaker and have a bit of mathematics in my past, I never did have a firm grasp of statistics. :(

The term I'm looking for has something to do with error calculation. A GPS device is measuring coordinates and then trying to estimate the error. In wikipedia I've come across two different likely terms - Mean squared error and Root mean square error. From what I can understand, they are not one and the same thing, but what each of them means is beyond me.

A direct translation from Latvian language would be "average (mean?) squared error estimate". No idea what that means either, I'm afraid.

Perhaps someone here has a better idea?

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There are a lot of terms which could be what you are after, but without more details or at least more context (how is the estimate calculated?) I don't see how anybody could help you. – Glen Wheeler Apr 1 '11 at 9:05
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@Vilx-, can you provide the latvian term in the comments? I am Lithuanian, so I might guess better. Also in what context that term is used? Maybe there is some data on which it is calculated? It would be easier to guess precisely what it is. – mpiktas Apr 1 '11 at 9:08
Give a few examples, without seeing some numbers and the process we can't help – Arjang Apr 1 '11 at 9:08
The Latvian term is "vidējo kvadrātisko kļūdu novērtējums". I'll try to get some formulas, though I doubt my father will know them. It's just something that the device does. :P – Vilx- Apr 1 '11 at 9:14
@Vilx-, I suspect this is root mean square error, if we assume that latvian statistical terminology is based on russian, as lithuanian is. Unfortunately without formulas or data examples it will be impossible to tell for non-Latvian. There is a strong possibility that this term was translated from English by non-statistician with liberal interpretation, so exact meaning might be lost. – mpiktas Apr 1 '11 at 9:34
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migrated from math.stackexchange.com Apr 1 '11 at 13:10

2 Answers

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Google translate gives "rms error of assessment" which (as root mean square error) seems to be the intended meaning.

The difference between mean square error and root mean square error is similar to the differrence between variance and standard deviation: if you want the average error to be reported in the same units as the measurement (metres or degrees or whatever) then you need to take the square root.

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I played with lithuanian language and it seems that google translator has a rule to translate mean square to rms no matter what comes afterwards. I suspect strongly that this holds for latvian also. – mpiktas Apr 1 '11 at 10:22
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@mpiktas: It probably means that most of the times that Google has come across the Latvian phrase, it has also come across rms in parallel English texts. The obvious environment is European Union documentation. – Henry Apr 1 '11 at 10:45
Turns out this was it. – Vilx- Apr 1 '11 at 13:13
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I would guess, it is a Least Mean Squared Error (LMSE) estimator. publication1 publication2 wikipedia

the GPS is trying to estimate coordinates, it does so by minimizing a square error function, so reporting the coordinate that is best in terms of MSE.

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