Stochastic Expansions and Moment Approximations for Three Indirect Estimators

Demos, Antonis and Arvanitis, Stelios (2010): Stochastic Expansions and Moment Approximations for Three Indirect Estimators. Published in:

Abstract

This paper deals with properties of three indirect estimators that are known to be (first order) asymptotically equivalent. Specifically, we examine a) the issue of validity of the formal Edgeworth expansion of an arbitrary order. b) Given a), we are concerned with valid moment approximations and employ them to characterize the second order bias structure of the estimators. Our motivation resides on the fact that one of the three is reported by the relevant literature to be second order unbiased. However, this result was derived without any establishment of validity. We provide this establishment, but we are also able to massively generalize the conditions under which this second order property remains true. In this way, we essentially prove their higher order inequivalence. We generalize indirect estimators by introducing recursive ones, emerging from multistep optimization procedures. We are able to establish higher order unbiaseness for estimators of this sort.

• Item Type: MPRA Paper
• Language: English
• Keywords: symptotic Approximation, Second Order Bias Structure, Binding Function, Local Canonical Representation, Convex Variational Distance, Recursive Indirect Estimators, Higher order Bias
• Subjects: C - Mathematical and Quantitative Methods > C0 - General; Y - Miscellaneous Categories > Y1 - Data: Tables and Charts

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