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where the fact that (N - 2n*) ~ (N - n*) has been used, with the inequality generally holding as soon as N1 exceeds n* by a small integer. We obtain a recursion for an ever better approximation to n*as a function of N1by rewriting this as |
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where, again, the error rapidly approaches zero as N increases. Finally, where it is desirable to have n* approximated by an explicit function of N, the steps here can be redone in terms of N/n*,noting that N1/n* rapidly approaches N/n* as N increases. Then |
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where, still, the error rapidly approaches zero as N increases. |
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The expected loss per trial L*(N)when n* trials have been allocated to x(2)(t, N)is |
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