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Design‐based inference on Bernstein type estimators for continuous populations
Author(s) -
Franceschi Sara,
Marcheselli Marzia,
Naddeo Stefania,
Pisani Caterina
Publication year - 2019
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.201800106
Subject(s) - jackknife resampling , estimator , mathematics , statistics , polygon (computer graphics) , bernstein polynomial , mean squared error , type (biology) , inference , variable (mathematics) , sampling (signal processing) , point (geometry) , computer science , mathematical analysis , artificial intelligence , geometry , telecommunications , ecology , filter (signal processing) , frame (networking) , computer vision , biology
Abstract The estimation of the values of a variable at any point of a study area is performed using Bernstein polynomials when the sampling scheme is implemented by selecting a point in each polygon of a regular grid overimposed onto the area. The evaluation of the precision of the resulting estimates is investigated under a completely design‐based framework. Moreover, as the main contribution to the mean squared error of the Bernstein‐type estimator is due to the bias, also a pseudo‐jackknife estimator is proposed. The performance of both estimators is investigated theoretically and by means of a simulation study. An application to a soil survey performed in Berkshire Downs in Oxfordshire (UK) is considered.