Projection indices and multimodality for mixtures of normal distributions
β Scribed by G. Eslava; F.H.C. Marriott
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 179 KB
- Volume
- 43
- Category
- Article
- ISSN
- 0167-7152
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β¦ Synopsis
Projection pursuit indices are intended to give 'interesting' one-or two-dimensional projections of data points in higher-dimensional spaces. This paper compares the performance of seven such indices. They are all minimum for a normal distribution, and are standardized to be zero for that case. They are compared by considering projections of a mixture of four trivariate spherical normal distributions with means at the vertices of a regular tetrahedron.
π SIMILAR VOLUMES
For a scale mixture of normal vector, X=A 1Γ2 G, where X, G # R n and A is a positive variable, independent of the normal vector G, we obtain that the conditional variance covariance, Cov(X 2 | X 1 ), is always finite a.s. for m 2, where X 1 # R n and m<n, and remains a.s. finite even for m=1, if an
This article concerns with the problem of testing whether a mixture of two normal distributions with bounded means and speciΓΏc variance is simply a pure normal. The large sample behavior of the likelihood ratio test for the problem is carefully investigated. In the case of one mean parameter, it is