Geometrical foundations of the sampling design with fixed sample size
We study the sampling design with fixed sample size from a geometric point of view. The first-order and second-order inclusion probabilities are chosen by the statistician. They are subjective probabilities. It is possible to study them inside of linear spaces provided with a quadratic and linear me...
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| Format: | Article |
| Language: | English |
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Accademia Piceno Aprutina dei Velati
2020-06-01
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| Series: | Ratio Mathematica |
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| Online Access: | http://eiris.it/ojs/index.php/ratiomathematica/article/view/511 |
| Summary: | We study the sampling design with fixed sample size from a geometric point of view. The first-order and second-order inclusion probabilities are chosen by the statistician. They are subjective probabilities. It is possible to study them inside of linear spaces provided with a quadratic and linear metric. We define particular random quantities whose logically possible values are all logically possible samples of a given size. In particular, we define random quantities which are complementary to the Horvitz-Thompson estimator. We identify a quadratic and linear metric with regard to two univariate random quantities representing deviations. We use the α-criterion of concordance introduced by Gini in order to identify it. We innovatively apply to probability this statistical criterion. |
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| ISSN: | 1592-7415 2282-8214 |