Seminarium i matematisk statistik
fredagen den 10 mars 13.15 i MH:227

Dragi Anevski
Matematisk statistik
Matematikcentrum
Lunds universitet

Titel:
Nonparametric Functional Estimation under Order Restrictions

Abstract:
I will try to give an overview of the results in my thesis.

The thesis consists of three papers on problems in
nonparametric functional estimation, in particular density and
regression function estimation and deconvolution, under order
assumptions. Pointwise limit distribution results are stated for the
obtained estimators, which include isotonic regression estimates,
nonparametric maximum likelihood estimates of monotone densities,
estimates of convex regression and density functions and deconvolution
estimates.

Our methods give a unified approach to regression and density function
estimation with order restrictions, thereby restating many previously
known results as special cases as well as obtaining new results, mainly
for dependent data and/or discontinuous functions.