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2017 | OriginalPaper | Buchkapitel

Testing of Coarsening Mechanisms: Coarsening at Random Versus Subgroup Independence

verfasst von : Julia Plass, Marco E. G. V. Cattaneo, Georg Schollmeyer, Thomas Augustin

Erschienen in: Soft Methods for Data Science

Verlag: Springer International Publishing

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Abstract

Since coarse(ned) data naturally induce set-valued estimators, analysts often assume coarsening at random (CAR) to force them to be single-valued. Using the PASS data as an example, we re-illustrate the impossibility to test CAR and contrast it to another type of uninformative coarsening called subgroup independence (SI). It turns out that SI is testable here.

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Vorheriges Kapitel Square of Opposition Under Coherence

Nächstes Kapitel Two-Sample Similarity Test for the Expected Value of Random Intervals

When dealing with coarse data, it is important to distinguish between epistemic data imprecision, considered here, and ontic data imprecision (cf. [2]).

This error-freeness implies that Y is an almost sure selector of \(\mathcal {Y}\) (in the sense of e.g. [10]).

The PASS data provide income in different levels of coarseness induced by follow-up questions for non-respondents. For sake of simplicity, we consider only the income question explained in the box, but the study provides also coarse ordinal data in the general sense.

Identifiability may not only be obtained by assumptions on the coarsening: e.g. for discrete graphical models with one hidden node, conditions based on the associated concentration graph are used in [13].

While the denominator of \(\varLambda \) can be obtained using any values in (2) compatible with each other, the numerator must in general be calculated by numerical optimization. Alternatives to this statistic include a test decision based on uncertainty regions [15].

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Titel: Testing of Coarsening Mechanisms: Coarsening at Random Versus Subgroup Independence
verfasst von: Julia Plass
Marco E. G. V. Cattaneo
Georg Schollmeyer
Thomas Augustin
Verlag: Springer International Publishing
Buch: Soft Methods for Data Science
Print ISBN: 978-3-319-42971-7

Electronic ISBN: 978-3-319-42972-4

Copyright-Jahr: 2017
DOI: https://doi.org/10.1007/978-3-319-42972-4_51

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