Year: 2005
Type: preprint
Abstract: :\nStandard approaches to sample surveys take as the point of departure the estimation of one or\nseveral population totals (or means), or a few predefined sub-totals (or sub-means). While the\nmodel-based prediction approach provides an attractive framework for estimation and inference, a\nmodel-based theory for the variety of randomization sampling designs has been lacking. In this paper\nwe extend the model-based approach to the prediction of individuals in addition to totals and means.\nSince, given the sample, the conditional prediction error is zero for the selected units but positive for\nthe units outside of the sample, it is possible to use the sampling design to control the unconditional\nindividual prediction mean square errors. This immediately raises the need for probability sampling. It\nturns out that balancing between optimal prediction of the population total and control over individual\npredictions provides a fruitful model-based approach to sampling design. Apart from raising the need\nfor probability sampling in general, it leads naturally to a number of important design features that are\nfirmly established in the sampling practice, including the use of simple random sampling for\nhomogeneous populations and unequal probability sampling otherwise, the division of a business\npopulation into the take-all, take-some and take-none units, the most common two-stage sampling\ndesigns, the use of stratification with proportional allocation, etc.. Most of them have not received\nadequate model-based treatment previously. Our approach enables us to give an appraisal of these\nmethods from a prediction point of view.\nKeywords: Individual prediction, business survey, unequal probability sampling, two-stage sampling,\nlinear regression population, common parameter model
Authors: Li‐Chun Zhang, Ib Thomsen
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2166127828