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Frontiers in Statistics: Dedicated to Peter John Bickel in Honor of his 65th Birthday

Convergence and consistency of Newton’s algorithm for estimating mixing distribution

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Ghosh, JK; Tokdar, ST
January 1, 2006

We provide a new convergence and consistency proof of Newton’s algorithm for estimating a mixing distribution under some rather strong conditions. An auxiliary result used in the proof shows that the Kullback Leibler divergence between the estimate and the true mixing distribution converges as the number of observations tends to infinity. This holds under much weaker conditions. It is pointed out that Newton’s proof of convergence, based on a representation of the algorithm as a nonhomogeneous weakly ergodic Markov chain, is incomplete. Our proof is along quite different lines. We also study various other aspects of the estimate, including its claimed superiority to the Bayes estimate based on a Dirichlet mixture.

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DOI

ISBN

9781860946707

Publication Date

January 1, 2006

Start / End Page

429 / 443
 

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Ghosh, J. K., & Tokdar, S. T. (2006). Convergence and consistency of Newton’s algorithm for estimating mixing distribution. In Frontiers in Statistics: Dedicated to Peter John Bickel in Honor of his 65th Birthday (pp. 429–443). https://doi.org/10.1142/9781860948886_0019
Ghosh, J. K., and S. T. Tokdar. “Convergence and consistency of Newton’s algorithm for estimating mixing distribution.” In Frontiers in Statistics: Dedicated to Peter John Bickel in Honor of His 65th Birthday, 429–43, 2006. https://doi.org/10.1142/9781860948886_0019.
Ghosh JK, Tokdar ST. Convergence and consistency of Newton’s algorithm for estimating mixing distribution. In: Frontiers in Statistics: Dedicated to Peter John Bickel in Honor of his 65th Birthday. 2006. p. 429–43.
Ghosh, J. K., and S. T. Tokdar. “Convergence and consistency of Newton’s algorithm for estimating mixing distribution.” Frontiers in Statistics: Dedicated to Peter John Bickel in Honor of His 65th Birthday, 2006, pp. 429–43. Scopus, doi:10.1142/9781860948886_0019.
Ghosh JK, Tokdar ST. Convergence and consistency of Newton’s algorithm for estimating mixing distribution. Frontiers in Statistics: Dedicated to Peter John Bickel in Honor of his 65th Birthday. 2006. p. 429–443.
Journal cover image

DOI

ISBN

9781860946707

Publication Date

January 1, 2006

Start / End Page

429 / 443