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  • 1. Constructing all determinantal sampling designs
    Articles and reports: 12-001-X202300200008
    Description: In this article, we use a slightly simplified version of the method by Fickus, Mixon and Poteet (2013) to define a flexible parameterization of the kernels of determinantal sampling designs with fixed first-order inclusion probabilities. For specific values of the multidimensional parameter, we get back to a matrix from the family PII from Loonis and Mary (2019). We speculate that, among the determinantal designs with fixed inclusion probabilities, the minimum variance of the Horvitz and Thompson estimator (1952) of a variable of interest is expressed relative to PII. We provide experimental R programs that facilitate the appropriation of various concepts presented in the article, some of which are described as non-trivial by Fickus et al. (2013). A longer version of this article, including proofs and a more detailed presentation of the determinantal designs, is also available.
    Release date: 2024-01-03
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  • 1. Constructing all determinantal sampling designs
    Articles and reports: 12-001-X202300200008
    Description: In this article, we use a slightly simplified version of the method by Fickus, Mixon and Poteet (2013) to define a flexible parameterization of the kernels of determinantal sampling designs with fixed first-order inclusion probabilities. For specific values of the multidimensional parameter, we get back to a matrix from the family PII from Loonis and Mary (2019). We speculate that, among the determinantal designs with fixed inclusion probabilities, the minimum variance of the Horvitz and Thompson estimator (1952) of a variable of interest is expressed relative to PII. We provide experimental R programs that facilitate the appropriation of various concepts presented in the article, some of which are described as non-trivial by Fickus et al. (2013). A longer version of this article, including proofs and a more detailed presentation of the determinantal designs, is also available.
    Release date: 2024-01-03
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