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On the absolute bias ratio of ratio estimators

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  • Meng, Xiao-Li

Abstract

The elegant Hartley--Ross inequality on the absolute bias ratio (ABR [reverse not equivalent] Bias /S.E.) of a ordinary ratio estimator is here generalized to that of a separate ratio estimator with stratified sampling. It is shown that, as long as the numerators and denominators used to form strata ratios are unbiased estimators, the absolute bias ratio of a separate ratio estimator will never exceed the square root of the sum of squares of the coefficient of variation of the denominators across strata. This provides, at design stages, a simple bound in practice to assess the limit and magnitude of the bias ratio of any separate ratio estimator that shares the same denominators. Exact expressions for biases of separate ratio estimators are also given.

Suggested Citation

  • Meng, Xiao-Li, 1993. "On the absolute bias ratio of ratio estimators," Statistics & Probability Letters, Elsevier, vol. 18(5), pages 345-348, December.
    • Handle: RePEc:eee:stapro:v:18:y:1993:i:5:p:345-348
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    Cited by:

    1. Martínez-Ovando Juan Carlos & Olivares-Guzmán Sergio I. & Roldán-Rodríguez Adriana, 2014. "Predictive Inference on Finite Populations Segmented in Planned and Unplanned Domains," Working Papers 2014-04, Banco de México.
    2. Weissman-Miller Deborah, 2013. "Novel Point Estimation from a Semiparametric Ratio Estimator (SPRE): Long-Term Health Outcomes from Short-Term Linear Data, with Application to Weight Loss in Obesity," The International Journal of Biostatistics, De Gruyter, vol. 9(2), pages 175-184, November.
    3. Celik, Nurcin & Son, Young-Jun, 2011. "State estimation of a shop floor using improved resampling rules for particle filtering," International Journal of Production Economics, Elsevier, vol. 134(1), pages 224-237, November.

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