A Unified Theory of Estimation 1 Rev Extended Feb 1960
A Unified Theory of Estimation 1 Rev Extended Feb 1960
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©=1 u=l On the other hand, for any multidecislon problem specified as above, let Q, = Q, (u, ©) > be an arbitrary weight-function; then it. For any multidecislon function © the corresponding Bayes risk is: 61^ .. K k . , • R«(Q, Q*"") =EZEZq(^*®) b(u, e, 9") . Q=l u=l For any given Q" and q(u, Q), vje have R(q, ®'") =IZ Q ' u>a q(u, ©) b(j, o, a'"') + q{u, ©) b(j, o, © J>u u3 u>a ju>« ^(J^-S) = ^ q(u, Q), for j > e, , for j = «, EZ q(u, o), for j Q, and non- increasing in j for j ^ ©; that is,... :(J, '5) has a single relative minimum which it assumes on one or more consecutive values of j including J = ©. Thus each welght-fixnction q(u, o) for the esti- mation problem determines \miquely a weight-function Q{ jj'S) for the multidecision problem^ which has, for each 9, a single relative minim\am» Conversely a weight-function Q. ( j, 0) for the multidecision problem having, for each ©^ a single relative minimum (in the pre- ceding sense) determines ■uniquely (through the last equation) a unique weight-function q(u, o) for the estimation problem.
What to read after A Unified Theory of Estimation 1 Rev Extended Feb 1960?
You can find similar books in the "Read Also" column, or choose other free books by Allan Birnbaum to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
©=1 u=l On the other hand, for any multidecislon problem specified as above, let Q, = Q, (u, ©) > be an arbitrary weight-function; then it. For any multidecislon function © the corresponding Bayes risk is: 61^ .. K k . , • R«(Q, Q*"") =EZEZq(^*®) b(u, e, 9") . Q=l u=l For any given Q" and q(u, Q), vje have R(q, ®'") =IZ Q ' u>a q(u, ©) b(j, o, a'"') + q{u, ©) b(j, o, © J>u u3 u>a ju>« ^(J^-S) = ^ q(u, Q), for j > e, , for j = «, EZ q(u, o), for j Q, and non- increasing in j for j ^ ©; that is,... :(J, '5) has a single relative minimum which it assumes on one or more consecutive values of j including J = ©. Thus each welght-fixnction q(u, o) for the esti- mation problem determines \miquely a weight-function Q{ jj'S) for the multidecision problem^ which has, for each 9, a single relative minim\am» Conversely a weight-function Q. ( j, 0) for the multidecision problem having, for each ©^ a single relative minimum (in the pre- ceding sense) determines ■uniquely (through the last equation) a unique weight-function q(u, o) for the estimation problem.
What to read after A Unified Theory of Estimation 1 Rev Extended Feb 1960?
You can find similar books in the "Read Also" column, or choose other free books by Allan Birnbaum to read onlineMoreLess
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