Tilted Nonparametric Estimation of Volatility Functions With Empirical Applications
提出一种新的正条件方差非参数估计量，无需对数变换，基于经验似然修正局部水平回归，保证有限样本非负，并应用于职业声望与收入关系及国债利率波动率拟合。
This article proposes a novel positive nonparametric estimator of the conditional variance function without reliance on logarithmic or other transformations. The estimator is based on an empirical likelihood modification of conventional local-level nonparametric regression applied to squared residuals of the mean regression. The estimator is shown to be asymptotically equivalent to the local linear estimator in the case of unbounded support but, unlike that estimator, is restricted to be nonnegative in finite samples. It is fully adaptive to the unknown conditional mean function. Simulations are conducted to evaluate the finite-sample performance of the estimator. Two empirical applications are reported. One uses cross-sectional data and studies the relationship between occupational prestige and income, and the other uses time series data on Treasury bill rates to fit the total volatility function in a continuous-time jump diffusion model.