Partially adaptive estimation via quantile functions

The conceptual model ``observation=deterministic component+stochastic component'' underlies most uses of regression analysis. In this paper the deterministic part of the model is linear and we propose a new procedure of partially adaptive estimation of its parameters that responds to a broad class of problems occurring in regression analysis. Quantile functions offer simple and flexible models for the stochastic component and enables us to obtain estimates for which the mean square error is not much lower than the estimates based on normal distribution when the true distribution is normal and, at the same time, yields a smaller mean square error over a range of nonnormalities. Since partially adaptive estimation relies on stringent distributional assumptions, it can be particularly useful in dealing with small samples.