2 kXk 6mM+iBQM H .2+QKTQbBiBQM In multivariate data analysis, a random sample ( x1; : : :xn) is typically a collection of vectors in Rp

fbeta 2nh (nh 1)2 (dj c) p 2, nh p 1 2 (2) for c < d j < (nh1)2 2nh + c, nh > p + 1, where c = log ^ h + p 2 log(2 ) + 1 2 logjShj, nh is the number of points in cluster h, ^ h = nh=n, Sh = 1 nh 1 nX i=1 zih(xi xh)(xi xh)> is the sample co · 2005