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Nonparametric estimation of normal ranges given one-way ANOVA random effects assumptions

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  • Hutson, Alan D.

Abstract

In this note, we compare three strategies that are commonly used in practice for estimating quantiles and quantile functions when data are assumed generated from a standard balanced one-way ANOVA random effects model, e.g. data from repeated assays, where the goal is to nonparametrically estimate/define a normal range. Strategy 1 consists of averaging the within subject values and then estimating quantiles based upon the averaged values in a standard fashion. Strategy 2 consists of estimating quantiles within each replication and then averaging the marginal quantiles over the replications. Strategy 3 consists of estimating quantiles and ignoring the repeated measures mechanism all together. We show that Strategy 1 is generally a poor choice when the goal is to refine the quantile estimation from a single replication through the application of repeated repetitions of an experiment. Strategy 2 and 3 are shown to be asymptotically equivalent.

Suggested Citation

  • Hutson, Alan D., 2003. "Nonparametric estimation of normal ranges given one-way ANOVA random effects assumptions," Statistics & Probability Letters, Elsevier, vol. 64(4), pages 415-424, October.
    • Handle: RePEc:eee:stapro:v:64:y:2003:i:4:p:415-424
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    References listed on IDEAS

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    1. Abdous, B. & Theodorescu, R., 1992. "Note on the spatial quantile of a random vector," Statistics & Probability Letters, Elsevier, vol. 13(4), pages 333-336, March.
    2. Babu, G. Jogesh & Rao, C. Radhakrishna, 1988. "Joint asymptotic distribution of marginal quantiles and quantile functions in samples from a multivariate population," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 15-23, October.
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