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Measuring Precision of Statistical Inference on Partially Identified Parameters

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  • Aleksey Tetenov

Abstract

Planners of surveys and experiments that partially identify parameters of interest face trade offs between using limited resources to reduce sampling error and using them to reduce the extent of partial identification. I evaluate these trade offs in a simple statistical problem with normally distributed sample data and interval partial identification using different frequentist measures of inference precision (length of confidence intervals, minimax mean sqaured error and mean absolute deviation, minimax regret for treatment choice) and analogous Bayes measures with a flat prior. The relative value of collecting data with better identification properties (e.g., increasing response rates in surveys) depends crucially on the choice of the measure of precision. When the extent of partial identification is significant in comparison to sampling error, the length of confidence intervals, which has been used most often, assigns the lowest value to improving identification among the measures considered.

Suggested Citation

  • Aleksey Tetenov, 2008. "Measuring Precision of Statistical Inference on Partially Identified Parameters," Carlo Alberto Notebooks 98, Collegio Carlo Alberto, revised 2012.
  • Handle: RePEc:cca:wpaper:98
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    Cited by:

    1. Stoye, Jörg, 2012. "Minimax regret treatment choice with covariates or with limited validity of experiments," Journal of Econometrics, Elsevier, vol. 166(1), pages 138-156.
    2. McFadden, Daniel, 2012. "Economic juries and public project provision," Journal of Econometrics, Elsevier, vol. 166(1), pages 116-126.

    More about this item

    Keywords

    statistical treatment choice; survey planning; nonresponse; mean squared error; mean absolute deviation; minimax regret;

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C83 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Survey Methods; Sampling Methods

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