Limit theorems for negatively dependent random variables

Patterson, Ronald F.; Smith, Wendy D.; Taylor, Robert L.; Bozorgnia, Abolghasem

doi:10.1016/s0362-546x(01)00265-6

Cited by 12 publications

(10 citation statements)

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“…Recently, the asymptotic normality has also been studied for more general classes of processes (that include the determinantal ones): processes with negative or positive associations (Patterson et al (2001), Yuan et al (2003)), and processes that satisfy the strong Rayleigh property Brändén and Jonasson (2012). We adapt here Theorem 2.4 of Patterson et al (2001) in the case of the Horvitz-Thompson estimator of the total based on determinantal sampling designs. The variance of the Horvitz-Thompson estimator decomposes as For processes satisfying the strong Rayleigh property, Pemantle and Peres (2014) recently proved concentration and deviation inequalities that extend those of Lyons (2003) for the number of points of determinantal processes in a subdomain.…”

Section: Statistical Properties Of the Estimatormentioning

confidence: 99%

Determinantal sampling designs

Loonis¹,

Mary

2019

Journal of Statistical Planning and Inference

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In this article, recent results about point processes are used in sampling theory. Precisely, we define and study a new class of sampling designs: determinantal sampling designs. The law of such designs is known, and there exists a simple selection algorithm. We compute exactly the variance of linear estimators constructed upon these designs by using the first and second order inclusion probabilities. Moreover, we obtain asymptotic and finite sample theorems. We construct explicitly fixed size determinantal sampling designs with given first order inclusion probabilities. We also address the search of optimal determinantal sampling designs.

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Section: Statistical Properties Of the Estimatormentioning

confidence: 99%

Determinantal sampling designs

Loonis¹,

Mary

2019

Journal of Statistical Planning and Inference

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“…whereas Patterson, Smith, Taylor, and Bozorgnia [15] established the conditional asymptotic normality of the dependent bootstrap mean. Hu, Ordóñez Cabrera, and Volodin [10] found an upper bound for the exact convergence rate (i.e., a law of the iterated logarithm type result) for dependent bootstrap means.…”

Section: The Dependent Bootstrapmentioning

confidence: 99%