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Circular local likelihood

Author

Listed:
  • Marco Marzio

    (Università di Chieti-Pescara)

  • Stefania Fensore

    (Università di Chieti-Pescara)

  • Agnese Panzera

    (Università di Firenze)

  • Charles C. Taylor

    (University of Leeds)

Abstract

We introduce a class of local likelihood circular density estimators, which includes the kernel density estimator as a special case. The idea lies in optimizing a spatially weighted version of the log-likelihood function, where the logarithm of the density is locally approximated by a periodic polynomial. The use of von Mises density functions as weights reduces the computational burden. Also, we propose closed-form estimators which could form the basis of counterparts in the multidimensional Euclidean setting. Simulation results and a real data case study are used to evaluate the performance and illustrate the results.

Suggested Citation

  • Marco Marzio & Stefania Fensore & Agnese Panzera & Charles C. Taylor, 2018. "Circular local likelihood," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(4), pages 921-945, December.
    • Handle: RePEc:spr:testjl:v:27:y:2018:i:4:d:10.1007_s11749-017-0576-9
    DOI: 10.1007/s11749-017-0576-9
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    References listed on IDEAS

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    1. Pedro Delicado, 2006. "Local likelihood density estimation based on smooth truncation," Biometrika, Biometrika Trust, vol. 93(2), pages 472-480, June.
    2. Marco Di Marzio & Agnese Panzera & Charles C. Taylor, 2013. "Non-parametric Regression for Circular Responses," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(2), pages 238-255, June.
    3. Gill, Jeff & Hangartner, Dominik, 2010. "Circular Data in Political Science and How to Handle It," Political Analysis, Cambridge University Press, vol. 18(3), pages 316-336, July.
    4. Harshinder Singh, 2002. "Probabilistic model for two dependent circular variables," Biometrika, Biometrika Trust, vol. 89(3), pages 719-723, August.
    5. Ingrid K. Glad & Nils Lid Hjort & Nikolai G. Ushakov, 2003. "Correction of Density Estimators that are not Densities," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(2), pages 415-427, June.
    6. Charles C. Taylor & Kanti V. Mardia & Marco Di Marzio & Agnese Panzera, 2012. "Validating protein structure using kernel density estimates," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2379-2388, July.
    7. Kanti V. Mardia & Charles C. Taylor & Ganesh K. Subramaniam, 2007. "Protein Bioinformatics and Mixtures of Bivariate von Mises Distributions for Angular Data," Biometrics, The International Biometric Society, vol. 63(2), pages 505-512, June.
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    Cited by:

    1. Yasuhito Tsuruta & Masahiko Sagae, 2020. "Theoretical properties of bandwidth selectors for kernel density estimation on the circle," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(2), pages 511-530, April.
    2. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    3. Di Marzio, Marco & Fensore, Stefania & Panzera, Agnese & Taylor, Charles C., 2019. "Local binary regression with spherical predictors," Statistics & Probability Letters, Elsevier, vol. 144(C), pages 30-36.

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