LOCAL SEMIPARAMETRIC EFFICIENCY BOUNDS UNDER SHAPE RESTRICTIONS
研究了在部分线性模型中，当未知函数具有同质性、凹性或单调性等形状约束时，参数β0的n^(1/2)一致正则估计量的最小渐近方差，发现同质性可显著提高效率，而凹性和单调性无帮助。
Consider the model y = x ′ β 0 + f * ( z ) + ε, where ε [d over =] N(0, σ 0 2 ). We calculate the smallest asymptotic variance that n 1/2 consistent regular ( n 1/2 CR) estimators of β 0 can have when the only information we possess about f * is that it has a certain shape. We focus on three particular cases: (i) when f * is homogeneous of degree r , (ii) when f * is concave, (iii) when f * is decreasing. Our results show that in the class of all n 1/2 CR estimators of β 0 , homogeneity of f * may lead to substantial asymptotic efficiency gains in estimating β 0 . In contrast, at least asymptotically, concavity and monotonicity of f * do not help in estimating β 0 more efficiently, at least for n 1/2 CR estimators of β 0 .