Linear Conditional Expectation for Discretized Distributions
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 examples of discretized bivariate and trivariate distributions will have a linear conditional expectation. Examples and simulations are provided to illustrate the results.
& Sanders, R. D.
(2004). Linear Conditional Expectation for Discretized Distributions. Journal of Applied Statistics, 31 (3), 361-372.