Fast inference for semi-varying coefficient models via local averaging

The semi-varying coefficient models are widely used in the application of finance, economics, medical science and many other areas. In general, the functional coefficients are estimated by local smoothing methods, e.g. local linear estimator. So the computation cost is severe because one should point-wisely estimate the value of a coefficient function. In this paper, we give an insight into the trade-off between statistical efficiency and computation simplicity and proposes a fast inference procedure, local average estimator. The proposed method is easy to implement and avoid repeat estimation since it approximates the coefficient functions with piecewise constants. Though the local average estimator is not asymptotically optimal, it is still efficient enough for further inference. Thus, three tests are derived to check whether a coefficient is constant. The experimental evidence shows that when there is limited room for improving the asymptotic efficiency, a proper trade-off between statistical efficiency and computation simplicity may improve the finite-sample performance.