  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.
