Abstract
Object oriented data analysis (OODA) has seen many developments over the past decade since Wang and Marron (2007) introduced the topic, and a broad overview of the field has been given by Marron an...
Highlights
Object Oriented Data Analysis (OODA) has seen many developments over the past decade since Wang and Marron (2007) introduced the topic, and a broad overview of the field has been given by Marron and Alonso (2014)
The main methodological contribution is the introduction of the d-covariance, which is the symmetric positive semi-definite matrix Ω that minimizes the expected squared distance of Ω to the random quantity (X − μ)(X − μ)T, where E[X] = μ
The motivation for the new methods in Tavakoli et al (2019) is quite similar, where the population quantity of interest has been substituted from the usual covariance matrix to the the more suitable d-covariance, which can be estimated consistently
Summary
Object Oriented Data Analysis (OODA) has seen many developments over the past decade since Wang and Marron (2007) introduced the topic, and a broad overview of the field has been given by Marron and Alonso (2014). The main methodological contribution is the introduction of the d-covariance, which is the symmetric positive semi-definite matrix Ω that minimizes the expected squared distance of Ω to the random quantity (X − μ)(X − μ)T , where E[X] = μ. The need for the development of d-covariance is reminiscent of issues that have arisen previously in statistical shape analysis, where procedures such as Procrustes estimation produced inconsistent estimates in general for population mean shapes from Gaussian landmark models (Lele, 1993).
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