L Bounds in Normal Approximation
نویسنده
چکیده
The zero bias distribution W ∗ of W , defined though the characterizing equation EWf(W ) = σ2Ef ′(W ∗) for all smooth functions f , exists for all W with mean zero and finite variance σ2. For W and W ∗ defined on the same probability space, the L1 distance between F , the distribution function of W with EW = 0 and Var(W ) = 1, and the cumulative standard normal Φ has the simple upper bound ||F − Φ||1 ≤ 2E|W ∗ −W |. This inequality is used to provide explicit L1 bounds with moderate-sized constants for independent sums, projections of cone measure on the sphere S(`n), simple random sampling and combinatorial central limit theorems.
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