Spline Smoothing in a Partly Linear Model
研究了部分线性模型中参数β和非参数函数f的估计方法，通过最小化残差平方和与粗糙度惩罚得到估计量，证明了在扩散先验下估计量的贝叶斯性质以及β估计的一致性和渐近正态性。
SUMMARY Suppose that Yi = X'iβ + f(ti) + εi, 1 ≤ i ≤ n, where β, f, and εi are unknown, but the m-th derivative of f is square integrable. Estimates of β and f are given which minimize the sum of the residual sum of squares and a roughness penalty. It is shown that these estimates are Bayes under a diffuse prior on β and f, and that, under mild conditions on Xi, ti, εi, and the roughness penalty, the estimate of β is consistent and asymptotically normal.