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On statistical transform methods and their efficiency. (English) Zbl 0566.62021

In this paper, new inference procedures based on empirical transform functions are developed. The empirical characteristic and moment generating functions are particular cases of these general procedures, obtained by choosing appropriate transform kernels.
For a finite number k of points of these empirical processes, the authors study the asymptotic efficiency of the procedures for parametric estimation and hypothesis testing. In particular, they show that the k-L- method (estimating by maximising the asymptotic Gaussian form of the likelihood) admits arbitrarily high asymptotic efficiency under some regularity condition on \(\partial Log f_{\theta}(x)/\partial \theta_ 0.\)
They discuss also the continuous case and conclude their work with some remarks and applications proving the generality of the transform method.
Reviewer: Ph.Nobelis

MSC:

62F12 Asymptotic properties of parametric estimators
62F05 Asymptotic properties of parametric tests
62F99 Parametric inference
62G30 Order statistics; empirical distribution functions
62M99 Inference from stochastic processes
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