The multivariate normal distribution

Abstract

While partial and multiple regressions and correlations (chapters 23 and 25) belong to multivariate statistical methods in a broad sense, they are often treated separately because they are more widely known and have been used for a longer time. In fact, multiple regression goes back to Karl Friedrich Gauss (1777–1855). Moreover, multiple regression may be used even when the predictor variables are systematic and only the predicted variate is random. On the contrary, multivariate methods in a strict sense, discussed in chapters 29 to 34, have been developed mostly since 1930 and deal typically with the simultaneous analysis of several variates (random variables). For several decades, multivariate methods properly speaking were treated only at a highly technical level and were the object of very few monographs (Anderson, 1958; Kendall, 1957; Rao, 1952; Roy, 1957). However, many books have been published later about them (Anderson, 1984; Dagnelie, 1975; Dempster, 1969; Gnanadesikan, 1977; Kshirsagar, 1972; Lebart, Morineau and Piron, 1995; Morrison, 1967, 1990; Pontier, Dufour and Normand, 1990; Rao, 1965; Seal, 1964; Seber, 1984; Tomassone, Dervin and Masson, 1993). Moreover, some specialized discussions (Blackith and Reyment, 1971) and some reprint collections (Atchley and Bryant, 1975; Bryant and Atchley, 1975) have appeared in the literature.