Dataset Information

Ball Covariance: A Generic Measure of Dependence in Banach Space.

ABSTRACT: Technological advances in science and engineering have led to the routine collection of large and complex data objects, where the dependence structure among those objects is often of great interest. Those complex objects (e.g, different brain subcortical structures) often reside in some Banach spaces, and hence their relationship cannot be well characterized by most of the existing measures of dependence such as correlation coefficients developed in Hilbert spaces. To overcome the limitations of the existing measures, we propose Ball Covariance as a generic measure of dependence between two random objects in two possibly different Banach spaces. Our Ball Covariance possesses the following attractive properties: (i) It is nonparametric and model-free, which make the proposed measure robust to model mis-specification; (ii) It is nonnegative and equal to zero if and only if two random objects in two separable Banach spaces are independent; (iii) Empirical Ball Covariance is easy to compute and can be used as a test statistic of independence. We present both theoretical and numerical results to reveal the potential power of the Ball Covariance in detecting dependence. Also importantly, we analyze two real datasets to demonstrate the usefulness of Ball Covariance in the complex dependence detection.

SUBMITTER: Pan W

PROVIDER: S-EPMC7720858 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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Ball Covariance: A Generic Measure of Dependence in Banach Space.

Pan Wenliang W Wang Xueqin X Zhang Heping H Zhu Hongtu H Zhu Jin J

Journal of the American Statistical Association 20190411 529

Technological advances in science and engineering have led to the routine collection of large and complex data objects, where the dependence structure among those objects is often of great interest. Those complex objects (e.g, different brain subcortical structures) often reside in some Banach spaces, and hence their relationship cannot be well characterized by most of the existing measures of dependence such as correlation coefficients developed in Hilbert spaces. To overcome the limitations of ...[more]

PMID: 33299261

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Project description:BackgroundSelf-report resource-use measures (RUMs) are often used to collect healthcare use data from participants in healthcare studies. However, RUMs are typically adapted from existing measures on a study-by-study basis, resulting in a lack of standardisation which limits comparability across studies. Psychometric testing of RUMs is rarely conducted. This paper reports on cognitive interviews with patients to test the content validity and acceptability of a new RUM (ModRUM). ModRUM is a brief, generic RUM with a core module on healthcare use and questions/modules to increase depth and breadth.MethodsA purposeful sampling strategy with maximum variation was used to recruit patients from primary care to participate in "think-aloud" interviews with retrospective probing. Participants verbalised their thought processes as they completed ModRUM, which allowed errors (issues with completion) to be identified. The interviewer asked follow-up and probing questions to investigate errors, clarity and acceptability. Interviews were audio-recorded and transcribed verbatim. Research team members independently scored transcripts to identify errors in comprehension, recall, judgement and response. Members met to agree on final scores. Interview transcripts were analysed qualitatively using techniques of constant comparison, to identify common themes and ideas for improvement. Data collection and analysis were performed concurrently and in rounds.ResultsTwenty participants were interviewed between December 2019 and March 2020. Interviews were conducted in three rounds, with revisions made iteratively and in response to interview findings. Seven participants completed the core module and 13 completed the core module plus depth questions. Of 71 issues, 28 were in comprehension, 14 in retrieval, 10 in judgement, 18 in response and 1 uncategorised. Most issues (21 issues by 2 participants) were due to participants including family healthcare use. Other issues included using incorrect recall periods (5 issues) and overlooking questions leading to missing responses (9 issues). Common participant suggestions included highlighting important details and providing additional definition or examples for some terms. The length, content and layout were acceptable to most participants.ConclusionsA generic RUM is needed to increase study comparability. RUM development requires thorough testing to demonstrate and enhance validity. Cognitive interviewing has demonstrated the acceptability and content validity of ModRUM.

Dataset Information

Ball Covariance: A Generic Measure of Dependence in Banach Space.

Publications

Ball Covariance: A Generic Measure of Dependence in Banach Space.

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