EFFECTS OF DESIGN AND ERROR ON NORMAL CONVERGENCE-RATES IN REGRESSION PROBLEMS

We describe the way in which design and experimental error interact to determine convergence rates in central limit theorems for regression estimators. For example, we show that if the convergence rate in a central limit theorem for experimental errors alone is n-α, where n is sample size and 0<α<1/2, then this rate is maintain in a central limit theorem for intercept and slope parameters if and only if the distribution generating design has finite (2+2α)'th moment. We prove that in other circumstances a careful choice of design can substantially improve convergence rates by introducing a degree of symmetry not present in the error distribution. Other results on the relationship between design and error are also derived. © 1990 Springer-Verlag.