A Seemingly Unrelated Nonparametric Additive Model with Autoregressive Errors
研究了一个具有自回归误差的非参数可加似不相关回归模型，提出了结合多项式样条和SCAD惩罚的估计方法，并证明其渐近有效性优于忽略误差相关性的估计量。
This article considers a nonparametric additive seemingly unrelated regression model with autoregressive errors, and develops estimation and inference procedures for this model. Our proposed method first estimates the unknown functions by combining polynomial spline series approximations with least squares, and then uses the fitted residuals together with the smoothly clipped absolute deviation (SCAD) penalty to identify the error structure and estimate the unknown autoregressive coefficients. Based on the polynomial spline series estimator and the fitted error structure, a two-stage local polynomial improved estimator for the unknown functions of the mean is further developed. Our procedure applies a prewhitening transformation of the dependent variable, and also takes into account the contemporaneous correlations across equations. We show that the resulting estimator possesses an oracle property, and is asymptotically more efficient than estimators that neglect the autocorrelation and/or contemporaneous correlations of errors. We investigate the small sample properties of the proposed procedure in a simulation study.