Examples illustrate that splitting a symmetric, unimodal distribution into two groups so as to minimize the sum of the within-group variances does not always occur at the mean. Strong unimodality is shown to be a sufficient condition for the optimal cutpoint to occur at the mean.

Parallel principal axes are introduced and used to investigate the structure of multivariate distributions. In the class of elliptical distributions, it is shown that self-consistency of parallel principal axes characterizes normality. Parallel principal axes are used to illustrate the...

Non-specific responses to treatment (commonly known as placebo response) are pervasive when treating mental illness. Subjects treated with an active drug may respond in part due to non-specific aspects of the treatment, i.e, those not related to the chemical effect of the drug. To determine the...

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...