On the Bahadur slope of the Lilliefors and the Cramér–von Mises tests of normality

@inproceedings{Arcones2006OnTB,
  title={On the Bahadur slope of the Lilliefors and the Cram{\'e}r–von Mises tests of normality},
  author={Miguel A. Arcones},
  year={2006}
}
where ψ is a (nonnegative) weight function. The asymptotic distribution of the statistics in (1.1)–(1.3) can be found in [20]. A natural definition of efficiency of tests was given by Bahadur [5, 6]. Let {f(·, θ) : θ ∈ Θ} be a family of p.d.f.’s on a measurable space (S,S) with respect to a measure μ, where Θ is a Borel subset of R. Let X1, . . . , Xn be i.i.d.r.v.’s with values in (S,S) and p.d.f. f(·, θ), for some unknown value of θ ∈ Θ. Let Θ0 ⊂ Θ and let Θ1 := Θ −Θ0. Consider the hypothesis… CONTINUE READING

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