Prediction in random coefficient regression

Abstract

Random coefficient regression and autoregressive models are important in diverse applications such as the classical statistical analysis of random and mixed effects models, the modelling of certain econometric and biological time series, and as a means for image compression. This paper develops nonparametric prediction intervals for a random coefficient regression model. The construction of these intervals requires a consistent estimate for the joint distribution of the model's random coefficients. Two such consistent estimates — a new one using minimum distance ideas and an earlier one based on estimated moments (Beran and Hall, 1992) — are discussed.