Sufficiency with order statistics

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What if we need to look for a sufficient statistic. We do the maths and we end up with a specific formule (with help of the factorization criterion) and we have the random variables X,i bounded; 0 < X,i < THETA.



Which can be written with order statistics as follows: 0 < X(1) =< X(n) < 0.



So why do we choose X(n) to be sufficient? Can all the other order statistic also be efficient? My book just picks X(n) as sufficient statistic without telling me about the others, which I think could also be sufficient.




order-statistics




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  • You need to tell us about the distribution, otherwise there's not much to say. I'm guessing that you intend these variables to be independently uniformly distributed over $[0,theta]$? Where it says "efficient", you probably also mean "sufficient". And please take a look at this tutorial and reference on how to typeset math on this site.
    – joriki
    Jul 18 at 4:32










  • Yes it is uniformly distributed. We did not discuss anything about efficiency.at college.
    – Salim
    Jul 18 at 17:24














up vote
1
down vote

favorite












What if we need to look for a sufficient statistic. We do the maths and we end up with a specific formule (with help of the factorization criterion) and we have the random variables X,i bounded; 0 < X,i < THETA.



Which can be written with order statistics as follows: 0 < X(1) =< X(n) < 0.



So why do we choose X(n) to be sufficient? Can all the other order statistic also be efficient? My book just picks X(n) as sufficient statistic without telling me about the others, which I think could also be sufficient.




order-statistics




share|cite|improve this question



















  • You need to tell us about the distribution, otherwise there's not much to say. I'm guessing that you intend these variables to be independently uniformly distributed over $[0,theta]$? Where it says "efficient", you probably also mean "sufficient". And please take a look at this tutorial and reference on how to typeset math on this site.
    – joriki
    Jul 18 at 4:32










  • Yes it is uniformly distributed. We did not discuss anything about efficiency.at college.
    – Salim
    Jul 18 at 17:24












up vote
1
down vote

favorite









up vote
1
down vote

favorite











What if we need to look for a sufficient statistic. We do the maths and we end up with a specific formule (with help of the factorization criterion) and we have the random variables X,i bounded; 0 < X,i < THETA.



Which can be written with order statistics as follows: 0 < X(1) =< X(n) < 0.



So why do we choose X(n) to be sufficient? Can all the other order statistic also be efficient? My book just picks X(n) as sufficient statistic without telling me about the others, which I think could also be sufficient.




order-statistics




share|cite|improve this question











What if we need to look for a sufficient statistic. We do the maths and we end up with a specific formule (with help of the factorization criterion) and we have the random variables X,i bounded; 0 < X,i < THETA.



Which can be written with order statistics as follows: 0 < X(1) =< X(n) < 0.



So why do we choose X(n) to be sufficient? Can all the other order statistic also be efficient? My book just picks X(n) as sufficient statistic without telling me about the others, which I think could also be sufficient.





order-statistics





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 18 at 3:10









Salim

161




161











  • You need to tell us about the distribution, otherwise there's not much to say. I'm guessing that you intend these variables to be independently uniformly distributed over $[0,theta]$? Where it says "efficient", you probably also mean "sufficient". And please take a look at this tutorial and reference on how to typeset math on this site.
    – joriki
    Jul 18 at 4:32










  • Yes it is uniformly distributed. We did not discuss anything about efficiency.at college.
    – Salim
    Jul 18 at 17:24
















  • You need to tell us about the distribution, otherwise there's not much to say. I'm guessing that you intend these variables to be independently uniformly distributed over $[0,theta]$? Where it says "efficient", you probably also mean "sufficient". And please take a look at this tutorial and reference on how to typeset math on this site.
    – joriki
    Jul 18 at 4:32










  • Yes it is uniformly distributed. We did not discuss anything about efficiency.at college.
    – Salim
    Jul 18 at 17:24















You need to tell us about the distribution, otherwise there's not much to say. I'm guessing that you intend these variables to be independently uniformly distributed over $[0,theta]$? Where it says "efficient", you probably also mean "sufficient". And please take a look at this tutorial and reference on how to typeset math on this site.
– joriki
Jul 18 at 4:32




You need to tell us about the distribution, otherwise there's not much to say. I'm guessing that you intend these variables to be independently uniformly distributed over $[0,theta]$? Where it says "efficient", you probably also mean "sufficient". And please take a look at this tutorial and reference on how to typeset math on this site.
– joriki
Jul 18 at 4:32












Yes it is uniformly distributed. We did not discuss anything about efficiency.at college.
– Salim
Jul 18 at 17:24




Yes it is uniformly distributed. We did not discuss anything about efficiency.at college.
– Salim
Jul 18 at 17:24















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