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Linguistic pitch analysis using functional principal component mixed effect models

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  • John A. D. Aston
  • Jeng‐Min Chiou
  • Jonathan P. Evans

Abstract

Summary. Fundamental frequency (F0, broadly ‘pitch’) is an integral part of spoken human language; however, a comprehensive quantitative model for F0 can be a challenge to formulate owing to the large number of effects and interactions between effects that lie behind the human voice's production of F0, and the very nature of the data being a contour rather than a point. The paper presents a semiparametric functional response model for F0 by incorporating linear mixed effects models through the functional principal component scores. This model is applied to the problem of modelling F0 in the tone language Qiang, a language in which relative pitch information is part of each word's dictionary entry.

Suggested Citation

  • John A. D. Aston & Jeng‐Min Chiou & Jonathan P. Evans, 2010. "Linguistic pitch analysis using functional principal component mixed effect models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(2), pages 297-317, March.
    • Handle: RePEc:bla:jorssc:v:59:y:2010:i:2:p:297-317
    DOI: 10.1111/j.1467-9876.2009.00689.x
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    References listed on IDEAS

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    1. Jeng‐Min Chiou & Hans‐Georg Müller & Jane‐Ling Wang, 2003. "Functional quasi‐likelihood regression models with smooth random effects," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 405-423, May.
    2. Wensheng Guo, 2002. "Functional Mixed Effects Models," Biometrics, The International Biometric Society, vol. 58(1), pages 121-128, March.
    3. Jeffrey S. Morris & Raymond J. Carroll, 2006. "Wavelet‐based functional mixed models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 179-199, April.
    4. Matthew J. Gurka & Lloyd J. Edwards & Keith E. Muller & Lawrence L. Kupper, 2006. "Extending the Box–Cox transformation to the linear mixed model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(2), pages 273-288, March.
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    Cited by:

    1. Victor GINSBURGH & Shlomo WEBER, 2016. "Linguistic distances and ethnolinguistic fractionalization and disenfranchisement indices," LIDAM Reprints CORE 2855, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Dabo-Niang, S. & Guillas, S. & Ternynck, C., 2016. "Efficiency in multivariate functional nonparametric models with autoregressive errors," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 168-182.
    3. Victor Ginsburgh & Shlomo Weber, 2020. "The Economics of Language," Journal of Economic Literature, American Economic Association, vol. 58(2), pages 348-404, June.
    4. Chau, Van Vinh & von Sachs, Rainer, 2016. "Functional mixed effects wavelet estimation for spectra of replicated time series," LIDAM Discussion Papers ISBA 2016013, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Shiers, Nathaniel & Aston, John A.D. & Smith, Jim Q. & Coleman, John S., 2017. "Gaussian tree constraints applied to acoustic linguistic functional data," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 199-215.
    6. Shang, Han Lin, 2013. "Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 185-198.
    7. Lin Zhang & Veerabhadran Baladandayuthapani & Hongxiao Zhu & Keith A. Baggerly & Tadeusz Majewski & Bogdan A. Czerniak & Jeffrey S. Morris, 2016. "Functional CAR Models for Large Spatially Correlated Functional Datasets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 772-786, April.
    8. Han Shang, 2014. "A survey of functional principal component analysis," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(2), pages 121-142, April.

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