The linearity condition and adaptive estimation in single-index regressions

Details The linearity condition and adaptive estimation in single-index regressions The linearity condition and adaptive estimation in single-index regressions

2010-01-26

arxiv.org/abs/1001.4802v1

Mathematics

Statistics Theory

10 pages

Scientific paper

We show that under a linearity condition on the distribution of the
predictors, the coefficient in single-index regression can be estimated with
the same efficiency as in the case when the link function is known. Thus, the
linearity condition seems to substitute for knowing the exact conditional
distribution of the response given the linear combinations of the predictors.

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