Robust model-based stratification sampling designs

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  • Author: Zhichun Zhai and Douglas P. Wiens
  • Date: 27 October 2015

Researchers from Canada have addressed the resistance, somewhat pervasive within the sampling community, to model-based methods. They do this by introducing notions of ‘approximate models’ and then deriving sampling methods which are robust to model misspecification within neighbourhoods of the sampler's approximate, working model. Specifically, they study robust sampling designs for model-based stratification, when the assumed distribution of an auxiliary variable, the mean function and the variance function in the associated regression model, are only approximately specified. They introduce neighbourhoods of the ‘working’ distribution function, and working regression model. Then, they adopt an approach of ‘minimax robustness’ to maximize the prediction mean squared error for the empirical best predictor, of a population total, over these neighbourhoods.

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To do this, they define the loss function as an upper bound on the maximum of the prediction mean squared error for the empirical best predictor over these neighbourhoods. Finally, they implement a modified genetic algorithm suitable for stratified sampling to find the robust designs which minimize this loss function. They add an ‘artificial’ implantation process into this algorithm to accelerate the speed in searching for the robust design. All these methods are illustrated in a case study of Australian sugar farms. They found that the robust designs did give substantial protecting against possible misspecifications of the model and the distribution functions.

Robust model-based stratification sampling designs

Zhichun Zhai and Douglas P. Wiens

Canadian Journal of Statistics

Early View (Online Version of Record published before inclusion in an issue)

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