Deleting o(n) terms (for the laws of large numbers) or o(√n) terms (for the central limit theorem) from an i.i.d. sample leaves the classical limit theorems valid, provided the deleted indices are chosen without using the data.
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Extension of Limit Theory with Deleting Items Partial Sum of Random Variable Sequence
Deleting o(n) terms (for the laws of large numbers) or o(√n) terms (for the central limit theorem) from an i.i.d. sample leaves the classical limit theorems valid, provided the deleted indices are chosen without using the data.