# The Brouwer Lecture 2005: Statistical estimation with model selection

@inproceedings{Birge2006TheBL, title={The Brouwer Lecture 2005: Statistical estimation with model selection}, author={Lucien Birg'e}, year={2006} }

The purpose of this paper is to explain the interest and importance of (approximate) models and model selection in Statistics. Starting from the very elementary example of histograms we present a general notion of finite dimensional model for statistical estimation and we explain what type of risk bounds can be expected from the use of one such model. We then give the performance of suitable model selection procedures from a family of such models. We illustrate our point of view by two main… CONTINUE READING

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SHOWING 1-10 OF 62 REFERENCES

## PIECEWISE-POLYNOMIAL APPROXIMATIONS OF FUNCTIONS OF THE CLASSES $ W_{p}^{\alpha}$

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## On some asymptotic properties of maximum likelihood estimates and related Bayes' estimates

VIEW 8 EXCERPTS

HIGHLY INFLUENTIAL

## How many bins should be put in a regular histogram

VIEW 7 EXCERPTS

HIGHLY INFLUENTIAL

## Information Bounds and Nonparametric Maximum Likelihood Estimation

VIEW 8 EXCERPTS

HIGHLY INFLUENTIAL

## Minimum complexity density estimation

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## Deux remarques sur l'estimation

VIEW 10 EXCERPTS

HIGHLY INFLUENTIAL

## On the Mathematical Foundations of Theoretical Statistics

VIEW 10 EXCERPTS

HIGHLY INFLUENTIAL

## The statistical work of Lucien Le Cam

VIEW 1 EXCERPT

HIGHLY INFLUENTIAL

## Degree of nonlinear approximation

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## Local asymptotic minimax and admissibility in estimation

VIEW 2 EXCERPTS

HIGHLY INFLUENTIAL