A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations
Citations
32 citations
Cites methods from "A Measure of Asymptotic Efficiency ..."
...[1]), we have p((l+e)a(d¡))<e-x/dl for any 0 < / < (cx -c2)/(nc2), and hence, we can take a ô > 0 such that (2....
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...Applying the well-known Ottaviani maximum inequality, the Chernoff theorem in [1], and (2....
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32 citations
Additional excerpts
...Finally, in symmetric hypothesis testing between two classical (commuting) probability distributions ρ1, ρ2, the optimal error decay rate is given by the Chernoff information ξ(ρ1, ρ2) = − log min0≤s≤1[ρs 1ρ 2 ] [10], [11], which has the property that there exists a distribution σ (from the Hellinger arc between ρ1 and ρ2) satisfying ξ(ρ1, ρ2) = D(σ‖ρ1) = D(σ‖ρ2)....
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32 citations
Additional excerpts
...Then by Chernoff's bound [3], [4], [17],...
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32 citations
Cites background or methods from "A Measure of Asymptotic Efficiency ..."
...Unfortunately, the computational effort involved in the resulting clearance assessment increases exponentially with the number of uncertain parameters that are to be considered (gridding of extreme points) (Fielding et al., 2002), or with the desired statistical confidence levels for the clearance results (Monte Carlo simulation) ( Chernoff, 1952; Vidyasagar, 1998), and this constraint can severely limit the reliability of the analysis in ......
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...The numbers of Monte Carlo trials required to achieve various levels of estimation uncertainty with known probability were calculated using the Chebyshev inequality and central limit theorem in Williams (2001) and are reproduced here in Table 7. Alternatively, using the well-known Chernoff (1952) bound (Vidyasagar, 1998) to estimate the number of simulations required, the numbers are as shown in Table 8 .I n both cases, the exponential ......
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32 citations
Additional excerpts
...Applying the Chernoff bound [17], it can be shown that when r = Ω (√ log n n ) , the number of nodes in the shadowed area is upper bounded by 2rn w....
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