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Fast Inference Procedures for Semivarying Coefficient Models via Local Averaging

The semivarying coefficient models are widely used in the application of finance, economics, medical science and many other areas. The functional coefficients are commonly estimated by local smoothing methods, e.g. local linear estimator. This implies that one should implement the estimation procedure for hundreds of times to obtain an estimate of one function. So the computation cost is very severe. In this paper, we give an insight to the trade-off between statistical efficiency and computation simplicity, and proposes a fast inference procedure for semivarying coefficient model. In our method, the coefficient functions are approximated by piecewise constants, which is a simple and rough approximation. This makes our estimators easy to implement and avoid repeat estimation. In this work, we shall show that though these estimators are not asymptotically optimal, they are efficient enough for building further inference procedure. Furthermore, three tests are brought out to check whether certain coefficient is constant. Our results clearly show that when the room for improving the asymptotic efficiency is limited, a proper trade-off between statistical efficiency and computation simplicity can be taken into consideration to improve the performance of the inference procedure.