Distribution Estimation and Applications II
summary
Estimators for combined probabilities (s0, s1, …) use Poissonization and show Good–Turing is unbiased: its expected g_mu equals E[s_mu], fixing empirical frequency’s failure which gives zero mass to unseen symbols and thus requires Ω(k) samples. Combining Good–Turing with empirical frequency at cutoff n^0.4 yields l1 error ≍ n^(-1/6); a refined estimator achieves the optimal l1 ≍ n^(-1/4). For unlabeled probability multisets, pattern maximum likelihood cuts sample needs to about k / log k in experiments (e.g., k=500, n=350).
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