Essential Statistical Inference by Dennis D Boos & L. A Stefanski

Author:Dennis D Boos & L. A Stefanski
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

where and are the slopes from the least squares regressions ofY onT andW onT, respectively, is a consistent estimator of β under the stated assumptions regardless of σ U 2.

The instrumental variable estimator, is a partial M-estimator as defined in the Introduction, and there are a number of ways to complete the ψ function in this case. Provided interest lies only in estimation of the β, a simple choice is

with associated M-estimator,

The and matrices calculated at the true parameters assuming the instrumental variable model are

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