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LOCAL SEMIPARAMETRIC EFFICIENCY BOUNDS UNDER SHAPE RESTRICTIONS

Published online by Cambridge University Press:  05 October 2000

Gautam Tripathi
Gautam Tripathi
Affiliation:
University of Wisconsin
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Abstract

Consider the model y = x′β0 + f*(z) + ε, where ε [d over =] N(0, σ02). We calculate the smallest asymptotic variance that n1/2 consistent regular (n1/2CR) estimators of β0 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 n1/2CR estimators of β0, homogeneity of f* may lead to substantial asymptotic efficiency gains in estimating β0. In contrast, at least asymptotically, concavity and monotonicity of f* do not help in estimating β0 more efficiently, at least for n1/2CR estimators of β0.

Type
Research Article
Information
Econometric Theory , Volume 16 , Issue 5 , October 2000 , pp. 729 - 739
Copyright
© 2000 Cambridge University Press

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