Multiple Correspondence Analysis of Coupled Lancaster Sequences

Meet the abstract. This is the abstract. 1. A SEQUENCE OF STANDARD NORMALS Suppose x and y are two standard normal random variables , with correlation ρ. The bivariate normal density isφρ(•,•) and the univariate normal density isφ(•). The function s(•) is the standardized Hermite-Chebyshev polynomial of order s, with s = 0,1, · · ·. Mehler’s formula tells us that for all s ∫ +∞ −∞ φρ(x, y)hs(y)d y = ρφ(x)Hs(x), (1a) ∫ +∞ −∞ φρ(y, x)hs(x)d y = ρφ(y)hs(y), (1b) or E(hs(y) | x) = ρhs(x), (2a) E(hs(x) | y) = ρhs(y). (2b) Equation (1) says that the hs(•) are the left and right singular functions of the kernel φρ(•,•), normalized by the marginals, which are both equal to φ(•). The successive powers ρs are the singular values. Date: Monday 15th March, 2010 — 12h 1min — Typeset in UTOPIA.