From: ted.dunning@gmail.com   
      
   vinaykadiyam@gmail.com wrote:   
   > Hi all,   
   >   
   > I want to know which one has highest priority in comparison.I want to   
   > analyse my results so for that   
   > one to which measure i hav to give more priority.   
   >   
   > can you please suggest me .   
   >   
      
   You should provide just a hint of context when asking questions like   
   this.   
      
   That said, I will guess that I know what you are asking about.  Correct   
   me if I am misinterpreting what you asked.   
      
   I am assuming that you are asking about MMRE = Mean Magnitude Relative   
   Error and   
   and NRMSE = normalized root mean square errors.   
      
   In general, you can't really make a case that any particular error   
   measure is categorically superior to all others.  You ahve to look at   
   your problem and what you know about it and decide.  It helps to try   
   several measures to see which is most useful in practice.   
      
   There are several issues that you are asking about.  One is whether   
   absolute or relative error is better, and another is which distance   
   metric is better (absolute magnitude (L_1) or squared error (L_2).  It   
   is easy to concoct pretty realistic examples where either of these   
   choices is enormously better than the other.  These nasty cases happen   
   in practice with distressing regularity.   
      
   Relative error makes sense where you have measurements that are   
   scale-invariant while absolute error makes sense when you have   
   measurements that are translation invariant.  With scale invariant   
   systems, you may have already taken the log of your measurement which   
   would convert the scael invariance into a translation invariance.   
      
   Error magnitude is less sensitive to the effect of outliers.  If you   
   have non-normal error distributions, this can be a very desirable   
   effect.  In fact, I would recommend that you not stop with error   
   magnitude, but go all the way and investigate M-estimaters, all kinds   
   of R statistics and margin methods (such as SRM or SVN).  Mixture   
   distributions and Bayesian methods can also be helpful if you suspect   
   long tails due to multiple error processes.   
      
   In summary, your question has no universal answer.   
      
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