Stam’s Bounds Sample Clauses

Stam’s Bounds. Stam’s 1978 bound [47] is more general than suggested in Sect. 1.1. Intuitively (a formal treatment of Stam’s bounds is given in Sect. 3), it covers the idea of 2n possible outcomes being grouped into 2m colors (the number of occurrences per color not necessarily equal) and measures the distance between sampling with or without replacement, where the observer learns the color of every sample. In a later publication in 1986, Stam [48] generalized this result to the case where the number of colors and the grouping of the outcomes into the colors differs per sample. The analysis of Stam is based on the Kullback-Leibler divergence KL(X; Y ) [36] (see Sect. 2.1 for the details), and Xxxxxxx’x inequality [21, 34, 35] stating that Δ(X, Y ) ≤ 1 KL(X; Y ) 1/2 , (2)
Sample 1
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