Statistical inference for stochastic processes : concepts and developments in asymptotic theory

@inproceedings{Yoshida2004StatisticalIF,
  title={Statistical inference for stochastic processes : concepts and developments in asymptotic theory},
  author={Nakahiro Yoshida},
  year={2004}
}
1 Frame of the first-order asymptotic decision theory Consider a sequence of statistical experiments ET = (X T ,AT , {P T θ }θ∈Θ) (T ∈ R+). Let θ̂T : X T → Θ be a sequence of estimators of the unknown parameter θ. A basic property θ̂T should have is the consistency : θ̂T →P T θ θ (T → ∞) for every θ ∈ Θ. The analyst should not use any estimator without checking this property. For example, if one uses an estimator which is not consistent ∗Graduate School of Mathematical Sciences, University of… CONTINUE READING
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