Abstract
Chapter 12 centers around the modified likelihood test for high-order null hypotheses within the finite mixture model. While the fundamental concept of testing for high-order null hypotheses remains akin to the modified likelihood ratio test for homogeneity, the endeavor of deriving the limiting distribution is significantly more intricate. This chapter offers a comprehensive exposition of various technical tools and intricate details involved in this challenging task.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Billingsley, P. 2008. Probability and Measure. Hoboken: Wiley.
Chen, J., and P. Cheng. 1997. On testing the number of components in finite mixture models with known relevant component distributions. The Canadian Journal of Statistics/La Revue Canadienne de Statistique 25 (3): 389–400.
Chen, J., and J. D. Kalbfleisch. 1996. Penalized minimum-distance estimates in finite mixture models. Canadian Journal of Statistics 24 (2): 167–175.
Chen, H., J. Chen, and J. D. Kalbfleisch. 2004. Testing for a finite mixture model with two components. Journal of the Royal Statistical Society: Series B 66: 95–115.
Dacunha-Castelle, D., and E. Gassiat. 1999. Testing the order of a model using locally conic parametrization: Population mixtures and stationary ARMA processes. The Annals of Statistics 27 (4): 1178–1209.
Henna, J. 1985. On estimating of the number of constituents of a finite mixture of continuous distributions. Annals of the Institute of Statistical Mathematics 37: 235–240.
Lindsay, B., and K. Roeder. 1997. Moment-based oscillation properties of mixture models. The Annals of Statistics 25 (1): 378–386.
Lindsay, B. G. 1989. Moment matrices: applications in mixtures. The Annals of Statistics 17 (2): 722–740.
Roeder, K. 1994. A graphical technique for determining the number of components in a mixture of normals. Journal of the American Statistical Association 89 (426): 487–495.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2023 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Chen, J. (2023). Modified Likelihood Ratio Test for Higher Order. In: Statistical Inference Under Mixture Models. ICSA Book Series in Statistics. Springer, Singapore. https://doi.org/10.1007/978-981-99-6141-2_12
Download citation
DOI: https://doi.org/10.1007/978-981-99-6141-2_12
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-99-6139-9
Online ISBN: 978-981-99-6141-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)