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Equivalence theory for density estimation, Poisson processes and Gaussian white noise with drift. (English) Zbl 1062.62083
Summary: This paper establishes the global asymptotic equivalence between a Poisson process with variable intensity and white noise with drift under sharp smoothness conditions on the unknown function. This equivalence is also extended to density estimation models by Poissonization. The asymptotic equivalences are established by constructing explicit equivalence mappings. The impact of such asymptotic equivalence results is that an investigation in one of these nonparametric models automatically yields asymptotically analogous results in the other models.

MSC:
62G20 Asymptotic properties of nonparametric inference
62B15 Theory of statistical experiments
62G07 Density estimation
62M05 Markov processes: estimation; hidden Markov models
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