Abstract
This note concentrates on the notion of the informative composite density, that is the composite density function which stands closer, in a sense, to the true but unknown model which describes the data. It aims to provide a preliminary discussion on how the composite density is affected by the components of the random vector that constitute the basis for the definition of this special type of density. It is expected that the composite maximum likelihood estimator is similarly affected by the components of the composite density.
This work is dedicated to the 65th birthday of Prof. Leandro Pardo, honoring his outstanding work and contribution in the fields of statistics and statistical information theory. In this occasion, I cordially thank Leandro for the long standing collaboration and friendship and I express my deep appreciation to him who is one of my most valuable collaborators and friends.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Besag, J.: Spatial interaction and the statistical analysis of lattice systems. J. R. Stat. Soc. Ser. B 36, 192–236 (1974)
Blumentritt, T., Schmid, F.: Mutual information as a measure of multivariate association: analytical properties and statistical estimation. J. Stat. Comput. Simul. 82, 1257–1274 (2012)
Castilla, E., Martín, N., Pardo, L., Zografos, K.: Composite likelihood methods based on minimum density power divergence estimator. Entropy 20, e20010018 (2018)
Castilla, E., Martín, N., Pardo, L., Zografos, K.: Model Selection in a composite likelihood framework based on density power divergence. Entropy 22(3), e22030270 (2020)
Castilla, E., Martín, N., Pardo, L., Zografos, K.: Composite likelihood methods: Rao-type tests based on composite minimum density power divergence estimator. Statist. Pap. 62, 1003–1041 (2021)
Cover, T.M., Thomas, J.A.: Elements of Information Theory, 2nd edn. Wiley, New York (2006)
Cox, D.R.: Partial likelihood. Biometrika 62, 269–276 (1975)
Joe, H., Reid, N., Somg, P.-X., Firth, D., Varin, C.: Composite Likelihood Methods. Report on the Workshop on Composite Likelihood (2012). http://www.birs.ca/events/2012/5-day-workshops/12w5046
Lindsay, G.: Composite likelihood methods. Contemp. Math. 80, 221–239 (1988)
Martín, N., Pardo, L., Zografos, K.: On divergence tests for composite hypotheses under composite likelihood. Statist. Papers 60, 1883–1919 (2019)
Mazo, G., Karlis, D., Rau, A.: A randomized pairwise likelihood method for complex statistical inferences (2021). ffhal-03126621f. https://hal.archives-ouvertes.fr/hal-03126621/document
Micheas, A., Zografos, K.: Measuring stochastic dependence using \(\phi \)-divergence. J. Multivar. Anal. 97, 765–784 (2006)
Pardo, L.: Statistical Inference Based on Divergence Measures. Chapman & Hall/CRC, Boca Raton (2006)
Reid, N.: Aspects of likelihood inference. Bernoulli 19, 1404–1418 (2013)
Reid, N., Lindsay, B., Liang, K.-Y.: Introduction to special issue. Statist. Sinica 21, 1–3 (2011)
Varin, C.: On composite marginal likelihoods. Adv. Stat. Anal. 92, 1–28 (2008)
Varin, C., Reid, N., Firth, D.: An overview of composite likelihood methods. Statist. Sinica 21, 5–42 (2011)
Wang, X., Wu, Y.: Theoretical properties of composite likelihoods. Open J. Statist. 4, 188–197 (2014)
Xu, X., Reid, N.: On the robustness of maximum composite estimate. J. Statist. Plann. Infer. 141, 3047–3054 (2011)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Zografos, K. (2023). A Note on the Notion of Informative Composite Density. In: Balakrishnan, N., Gil, M.Á., Martín, N., Morales, D., Pardo, M.d.C. (eds) Trends in Mathematical, Information and Data Sciences. Studies in Systems, Decision and Control, vol 445. Springer, Cham. https://doi.org/10.1007/978-3-031-04137-2_11
Download citation
DOI: https://doi.org/10.1007/978-3-031-04137-2_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-04136-5
Online ISBN: 978-3-031-04137-2
eBook Packages: EngineeringEngineering (R0)