In statistics, Hájek projection of a random variable on a set of independent random vectors is a particular measurable function of that, loosely speaking, captures the variation of in an optimal way. It is named after the Czech statistician Jaroslav Hájek .
Definition Given a random variable and a set of independent random vectors , the Hájek projection of onto is given by
Properties
Hájek projection is an projection of onto a linear subspace of all random variables of the form , where are arbitrary measurable functions such that for all and hence Under some conditions, asymptotic distributions of the sequence of statistics and the sequence of its Hájek projections coincide, namely, if , then converges to zero in probability.
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