Abstract 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.

中文翻译：

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通过局部平均快速推断半变系数模型

摘要 半变异系数模型广泛应用于金融、经济、医学等诸多领域。通常，函数系数是通过局部平滑方法估计的，例如局部线性估计器。因此计算成本是严重的，因为人们应该逐点估计系数函数的值。在本文中，我们深入了解了统计效率和计算简单性之间的权衡，并提出了一种快速推理过程，即局部平均估计器。所提出的方法易于实现并且避免重复估计，因为它用分段常数近似系数函数。尽管局部平均估计量不是渐近最优的，但它仍然足够有效以进行进一步的推理。因此，推导出三个测试来检查系数是否为常数。实验证据表明，当提高渐进效率的空间有限时，统计效率和计算简单性之间的适当权衡可能会提高有限样本性能。