# Qualitative robustness of statistical functionals under strong mixing

@inproceedings{Zahle2012QualitativeRO, title={Qualitative robustness of statistical functionals under strong mixing}, author={Henryk Zahle}, year={2012} }

A new concept of (asymptotic) qualitative robustness for plug-in estimators based on identically distributed possibly dependent observations is introduced, and it is shown that Hampel’s theorem for general metrics d still holds. Since Hampel’s theorem assumes the UGC property w.r.t. d, i.e. convergence in probability of the empirical probability measure to the true marginal distribution w.r.t. d uniformly in the class of all admissible laws on the sample path space, this property is shown for a… CONTINUE READING

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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 37 REFERENCES

## Some mixing properties of time series models

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## A General Qualitative Definition of Robustness

VIEW 20 EXCERPTS

HIGHLY INFLUENTIAL

## Contributions to the theory of robust estimation

VIEW 18 EXCERPTS

HIGHLY INFLUENTIAL

## Qualitative and infinitesimal robustness of tail-dependent statistical functionals

VIEW 6 EXCERPTS

HIGHLY INFLUENTIAL

## Robust statistics. Wiley, New York

VIEW 11 EXCERPTS

HIGHLY INFLUENTIAL

## Marcinkiewicz–Zygmund strong laws for statistical functionals and empirical distribution functions

VIEW 1 EXCERPT

## On the stability of bootstrap estimators

VIEW 1 EXCERPT