Sufficient conditions for uniqueness of a locally optimal quantizer for a class of convex error weighting functions

Trushkin, A.

doi:10.1109/tit.1982.1056480

Cited by 121 publications

(83 citation statements)

References 4 publications

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“…Similarly, Figure 7 demonstrates the existence of multiple mixture model solutions for a two dimensional distribution using the population-based EM algorithm. In 1-dimension, there will often be a unique set of k self-consistent points (Trushkin, 1982;Li and Flury, 1995;Tarpey, 1994;Mease and Nair, 2006), for instance if the density is log-concave. It would be interesting to determine if conditions exist that guarantee the existence of a unique set of (non-degenerate) solutions for the population-based EM algorithm.…”

Section: Population-basedmentioning

confidence: 99%

Model misspecification

Tarpey

Yun

Petkova

2008

Statistical Modelling

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A common problem in statistical modelling is to distinguish between finite mixture distribution and a homogeneous non-mixture distribution. Finite mixture models are widely used in practice and often mixtures of normal densities are indistinguishable from homogenous non-normal densities. This paper illustrates what happens when the EM algorithm for normal mixtures is applied to a distribution that is a homogeneous non-mixture distribution. In particular, a population-based EM algorithm for finite mixtures is introduced and applied directly to density functions instead of sample data. The population-based EM algorithm is used to find finite mixture approximations to common homogeneous distributions. An example regarding the nature of a placebo response in drug treated depressed subjects is used to illustrate ideas.

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Section: Population-basedmentioning

confidence: 99%

Model misspecification

Tarpey

Yun

Petkova

2008

Statistical Modelling

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“…For some special cases involving normal distributions see Gray and Karnin (1982) and Baubkus (1985). On the other hand, in the one-dimensional case, uniqueness holds, e.g., if log f (x) is concave (Fleischer 1964, Trushkin 1982, Kieffer 1983. The corresponding solution for the normal distribution may be found in Ogawa (1951Ogawa ( , 1962, Cox (1957), or Bock (1974.f).…”

Section: The Asymptotic Distribution Of the Test Statistics G~ And K~mentioning

confidence: 99%

On some significance tests in cluster analysis

Bock¹

1985

Journal of Classification

132

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“…This assumption has been discussed very often in the k-means literature (see, for instance, [2]). Some results are known in the case that E = IR and α = 0 (see, for instance, [13], [8], [5], [14], and [9]), but, at our best acknowledge, yet there is no satisfactory result even in the case E = IR 2 , k = 2 and α = 0.…”

Section: Remark 36mentioning

confidence: 79%