A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations

We calculate learning rates when agents are informed through both public and private observation of other agents' actions. We provide an explicit solution for the evolution of the distribution of posterior beliefs. When the private learning channel is present, we show that convergence of the distribution of beliefs to the perfect-information limit is exponential at a rate equal to the sum of the mean arrival rate of public information and the mean rate at which individual agents are randomly matched with other agents. If, however, there is no private information sharing, then convergence is exponential at a rate strictly lower than the mean arrival rate of public information. JEL Classification Numbers: D83, D82.

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“…The lower bound immediately follows. For the upper bound, we will use the Chernoff (1953) bound, stating that…”

Section: Proofs Of Convergence Ratesmentioning

confidence: 99%

The Relative Contributions of Private Information Sharing and Public Information Releases to Information Aggregation

2009

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“…To estimate the total number of samples in the whole database, we will use the Chernoff bound [3], which asserts that with probability (1 − α):…”

Section: Number Of Samples In Databasementioning

confidence: 99%

Is Enough Enough? What Is Sufficiency in Biometric Data?

Veres

Nixon

Carter

2006

Lecture Notes in Computer Science

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Abstract. Gait recognition has become a popular new biometric in the last decade. Good recognition results have been achieved using different gait techniques on several databases. However, not much attention has been paid to get major questions: how good are biometrics data; how many subjects are needed to cover diversity of population (hypothetical or actual) in gait and how many samples per subject will give good representation of similarities and differences in the gait of the same subject. In this paper we try to answer these questions from the point of view of statistical analysis not only for gait recognition but for other biometrics as well. Though we do not think that we have a whole answer, we content this is the start of the answer.

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“…Remember that ψ(i) is the number of successes of a set of independent trials with success probabilities that add up to ξ(i). The standard Chernoff bound theorem [9,16] states that if we have a set of independent trials with the sum of success probabilities µ, the probability that the number of successes is below (1 − δ)µ is below e −δ 2 µ/2 . In our case, µ = ξ(i) and (1 − δ)µ is β(i).…”

Section: Improved Performance Bounds For Osc Kmentioning

confidence: 99%

Approximating the Online Set Multicover Problems via Randomized Winnowing

Berman

DasGupta

2005

Lecture Notes in Computer Science

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In this paper, we consider the weighted online set k-multicover problem. In this problem, we have a universe V of elements, a family S of subsets of V with a positive real cost for every S ∈ S, and a "coverage factor" (positive integer) k. A subset {i 0 , i 1 , . . .} ⊆ V of elements are presented online in an arbitrary order. When each element i p is presented, we are also told the collection of all (at least k) sets S ip ⊆ S and their costs to which i p belongs and we need to select additional sets from S ip if necessary such that our collection of selected sets contains at least k sets that contain the element i p . The goal is to minimize the total cost of the selected sets 1 . In this paper, we describe a new randomized algorithm for the online multicover problem based on a randomized version of the winnowing approach of [15]. This algorithm generalizes and improves some earlier results in [1,2]. We also discuss lower bounds on competitive ratios for deterministic algorithms for general k based on the approaches in [2].

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A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations

Cited by 3,088 publications

References 1 publication

The Relative Contributions of Private Information Sharing and Public Information Releases to Information Aggregation

The Relative Contributions of Private Information Sharing and Public Information Releases to Information Aggregation

Is Enough Enough? What Is Sufficiency in Biometric Data?

Approximating the Online Set Multicover Problems via Randomized Winnowing

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