J. Japan Statist. Soc., Vol. 31 (No. 2), pp. 187-191, 2001
Abstract. We give a transformation such that, for a k-dimensional finite normal mixture, the number of components and the mixing ratios are preserved on each marginal density through the transformation. Furthermore, under the only assumption of a k-dimensional finite normal mixture, we construct a one-dimensional random variable with a finite normal mixture of the true number of components and the true mixing ratios.
Key words and phrases: Finite mixture, k-dimensional distribution, One-dimensional distribution, Orthogonal matrix.