LJKProbability & Statistics Seminar

On Thursday January 22 2015 at 14h00 in Salle 1  Tour IRMA

Seminary of Mr Markus REISS (HumboltUniversität zu Berlin (Allemagne))

Estimating nonparametric functionals efficiently under onesided errors

Summary

For nonparametric regression with onesided errors and a related
continuoustime model for Poisson point processes we consider the problem
of efficient estimation for linear functionals of the regression function.
The optimal rate is obtained by an unbiased estimation method which
nevertheless depends on a H"older condition or monotonicity assumption
for the underlying regression function.
We first construct a simple blockwise estimator and then build up a
nonparametric maximumlikelihood approach for exponential noise variables
and the point process model. In that approach also nonasymptotic
efficiency is obtained (UMVU: uniformly minimum variance among all
unbiased estimators). In addition, under monotonicity the estimator is
automatically rateoptimal and adaptive over H"older classes. The proofs
rely essentially on martingale stopping arguments for counting processes
and the point process geometry. The estimators are easily computable and a
small simulation study confirms their applicability.
(joint with L. Selk)
