Efficient and Adaptive Estimation for Semiparametric Models

@inproceedings{Bickel1993EfficientAA,
  title={Efficient and Adaptive Estimation for Semiparametric Models},
  author={Peter J. Bickel},
  year={1993}
}
  • P. Bickel
  • Published 1 September 1993
  • Mathematics
Introduction.- Asymptotic Inference for (Finite-Dimensional) Parametric Models.- Information Bounds for Euclidean Parameters in Infinite-Dimensional Models.- Euclidean Parameters: Further Examples.- Information Bounds for Infinite-Dimensional Parameters.- Infinite-Dimensional Parameters: Further Examples: Construction of Examples. 
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References

SHOWING 1-6 OF 6 REFERENCES
Information and Asymptotic Efficiency in Parametric-Nonparametric Models
Asymptotic lower bounds for estimation of the parameters of models with both parametric and nonparametric components are given in the form of representation theorems (for regular estimates) and
New Ways to Prove Central Limit Theorems
This paper describes some techniques for proving asymptotic normality of statistics defined by maximization of random criterion function. The techniques are based on a combination of recent results
CONTRIBUTIONS TO A GENERAL ASYMPTOTIC STATISTICAL THEORY
0. Introduction.- 0.1. Why asymptotic theory?.- 0.2. The object of a unified asymptotic theory,.- 0.3. Models,.- 0.4. Functionals,.- 0.5. What are the purposes of this book?.- 0.6. A guide to the
ON CONVERGENCE OF STOCHASTIC PROCESSES
It is clear that for given I,un } and t, the better theorem of this kind would be the one in which (2) is proved for the larger class of functions f. In this paper we shall show that certain known
van der Vaart There seem to be fake copies of Sankhy¯ a in circulation, supplied by unscrupulous distributors. To learn more about this, please visit the Sankhy¯ a web site http
  • van der Vaart There seem to be fake copies of Sankhy¯ a in circulation, supplied by unscrupulous distributors. To learn more about this, please visit the Sankhy¯ a web site http