Monotone regression and density function estimation at a point of discontinuity

Dragi Anevski and Ola Hössjer

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,

ISSN 1403-9338
Pointwise limit distribution results are given for the isotonic regression estimator at a point of discontinuity. The cases treated are independent data, $\phi-$ and $\alpha-$mixing data and suboordinated gaussian long range dependent data. Pointwise limit results for the nonparametric maximum likelihood estimator of a monotone density are given at a point af discontinuity, for independent data. The limit distributions are non-standard and differ from the ones obtained for differentiable regression and density functions.