Many statistical methods for continuous distributions assume a linear conditional expectation. Components of multivariate distributions are often measured on a discrete ordinal scale based on a discretization of an underlying continuous latent variable. The results in this paper show that common...

The slope is usually the parameter of primary importance in a simple linear regression. If the straight line model gives a poor fit to the data, one can consider the average slope of the non-linear response. In this paper, we show that if the response is quadratic, then the average slope can be...

The term 'principal points' originated in a problem of determining 'typical' heads for the design of protection masks, as described by Flury. Two principal points in the mask example correspond to a small and a large size. Principal points are cluster means for theoretical distributions, and...