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Review Article

On approximations via convolution-defined mixture models

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Pages 3945-3955 | Received 03 Mar 2018, Accepted 04 Jun 2018, Published online: 30 Oct 2018

References

  • Barron, A. R. 1993. Universal approximation bound for superpositions of a sigmoidal function. IEEE Transactions on Information Theory 39:930–45.
  • Buhmann, M. D. 2003. Radial basis functions: Theory and implementation. New York: Cambridge University Press.
  • Cheney, W., and W. Light. 2000. A course in approximation theory. Pacific Grove: Brooks/Cole.
  • DasGupta, A. 2008. Asymptotic theory of statistics and probability. New York: Springer.
  • Ferguson, T. S. 1983. Bayesian density estimation by mixtures of normal distributions. In Recent advances in statistics: Papers in honour of Herman Chernoff on his sixtieth birthday, 287–302. New York: Springer.
  • Hoskins, R. F. 2009. Delta functions: Introduction to generalized functions. Oxford: Woodhead.
  • Kosorok, M. R. 2008. Introduction to empirical processes and semiparametric inference. New York: Springer.
  • Kullback, S., and R. A. Leibler. 1951. On information and sufficiency. Annals of Mathematical Statistics 22:79–86.
  • Li, J. Q., and A. R. Barron. 1999. Mixture density estimation. In Advances in neural information processing systems, ed. S. A. Solla, T. K. Leen, and K. R. Mueller, vol. 12. Cambridge: MIT Press.
  • Light, W. A. 1993. Techniques for generating approximations via convolution kernels. Numerical Algorithms 5:247–61.
  • Lindsay, B. G. 1995. Mixture models: Theory, geometry and applications. NSF-CBMS Regional Conference Series in Probability and Statistics. vol. 5, pp. i-iii+v-ix+1-163.
  • Lo, J. T.-H. 1972. Finite-dimensional sensor orbits and optimal nonlinear filtering. IEEE Transactions on Information Theory 18:583–88.
  • Makarov, B., and A. Podkorytov. 2013. Real analysis: Measures, integrals and applications. New York: Springer.
  • McLachlan, G. J., and D. Peel. 2000. Finite mixture models. New York: Wiley.
  • McLachlan, G. J., S. X. Lee, and S. I. Rathnayake. 2019. Finite mixture models. Annual Review of Statistics and Its Application 6. To appear.
  • Melnykov, V., and R. Maitra. 2010. Finite mixture models and model-based clustering. Statistical Surveys 4:80–116.
  • Podlaski, R., and F. A. Roesch. 2014. Modelling diameter distributions of two-cohort forest stands with various proportions of dominant species: A two-component mixture model approach. Mathematical Biosciences 249:60–74.
  • Rakhlin, A., D. Panchenko, and S. Mukherjee. 2005. Risk bounds for mixture density estimation. ESAIM: Probability and Statistics 9:220–9.
  • Rossi, P. E. 2014. Bayesian non- and semiparametric methods and applications. Princeton: Princeton University Press.
  • Schlattmann, P. 2009. Medical applications of finite mixture models. Berlin: Springer.
  • Titterington, D. M., A. F. M. Smith, and U. E. Makov. 1985. Statistical analysis of finite mixture distributions. New York: Wiley.
  • Walker, J. L., and M. Ben-Akiva. 2011. A handbook of transport economics Elgar, 160–87. Edward. Advances in discrete choice: Mixture models.
  • White, H. 1982. Maximum likelihood estimation of misspecified models. Econometrica 50:1–25.
  • Willink, R. 2005. Normal moments and Hermite polynomials. Statistics and Probability Letters 73:271–75.
  • Xu, L., T. Hanson, E. J. Bedrick, and C. Restrepo. 2010. Hypothesis tests on mixture model components with applications in ecology and agriculture. Journal of Agricultural, Biological, and Environmental Statistics 15:308–26.
  • Yona, G. 2011. Introduction to computational proteomics. Boca Raton: CRC Press.
  • Zeevi, A. J., and R. Meir. 1997. Density estimation through convex combinations of densities: Approximation and estimation bounds. Neural Computation 10:99–109.

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