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Gaussian tree constraints applied to acoustic linguistic functional data

Published version
Peer-reviewed

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Authors

Aston, JAD 
Smith, JQ 
Coleman, JS 

Abstract

Evolutionary models of languages are usually considered to take the form of trees. With the development of so-called tree constraints the plausibility of the tree model assumptions can be addressed by checking whether the moments of observed variables lie within regions consistent with trees. In our linguistic application, the data set comprises acoustic samples (audio recordings) from speakers of five Romance languages or dialects. We wish to assess these functional data for compatibility with a hereditary tree model at the language level. A novel combination of canonical function analysis (CFA) with a separable covariance structure provides a method for generating a representative basis for the data. This resulting basis is formed of components which emphasize language differences whilst maintaining the integrity of the observational language-groupings. A previously unexploited Gaussian tree constraint is then applied to component-by-component projections of the data to investigate adherence to an evolutionary tree. The results indicate that while a tree model is unlikely to be suitable for modeling all aspects of the acoustic linguistic data, certain features of the spoken Romance languages highlighted by the separable-CFA basis may indeed be suitably modeled as a tree.

Description

Keywords

stat.AP, stat.AP, stat.ME

Journal Title

Journal of Multivariate Analysis

Conference Name

Journal ISSN

0047-259X
1095-7243

Volume Title

154

Publisher

Elsevier BV
Sponsorship
Engineering and Physical Sciences Research Council (EP/K021672/2)
NS acknowledges the support of Economics and Social Science Research Council grant ES/I90427/1. JADA acknowledges the support of UK Engineering and Physical Sciences Research Council grant EP/K021672/2. JSC acknowledges the support of UK Arts and Humanities Research Council grant AH/M002993/1.