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(4 citation statements)

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“…It is noteworthy, in fact surprising, that though previous research regarding information diagrams have worked with the probability of error in place of index of coincidence, exactly the same constants α k and β k have appeared in related inequalities (due to the form of inequalities considered it is in fact α k + β k and β k that appears in previous research). To be precise, we refer to equations (12) in Kovalevskij [18], ( 6) in Tebbe and Dwyer [26], (29) in Ben-Bassat [1] and, finally, to equation ( 14) in Feder and Merhav [7]. An explanation for this phenomenon is given in the discussion.…”

confidence: 99%

“…It is noteworthy, in fact surprising, that though previous research regarding information diagrams have worked with the probability of error in place of index of coincidence, exactly the same constants α k and β k have appeared in related inequalities (due to the form of inequalities considered it is in fact α k + β k and β k that appears in previous research). To be precise, we refer to equations (12) in Kovalevskij [18], ( 6) in Tebbe and Dwyer [26], (29) in Ben-Bassat [1] and, finally, to equation ( 14) in Feder and Merhav [7]. An explanation for this phenomenon is given in the discussion.…”

confidence: 99%

“…As indicated in the announcement [29], the inequality ( 19) can be proved in a straightforward way by induction (over n with P ∈ M 1 + (n)) in case k = 1. Simple direct proofs of ( 19) for other values of k are not known to the authors.…”

confidence: 99%

“…It seems that first the method was considered in [12]; then the problem of optimal estimation was considered in [13] and an asymptotically optimal method was suggested. Recently, new results about exact prediction were found in [14]. The results that follow are nonasymptotic (as opposed to [13]) and remain true if the samples are not i.i.d.…”

confidence: 97%

“…The author, jointly with Peter Harremoës, has pointed to exact results for Bernoulli sources, cf. [3]. In [2] numerical methods are indicated, but based on the same theoretical reasoning as here (and with some associated exact results, not stated there).…”

mentioning

confidence: 99%