The Quadratic Loss of Isotonic Regression Under Normality

Isotonic Regression under Lipschitz Constraint

The pool adjacent violators (PAV) algorithm is an efficient technique for the class of isotonic regression problems with complete ordering. The algorithm yields a stepwise isotonic estimate which approximates the function and assigns maximum likelihood to the data. However, if one has reasons to believe that the data were generated by a continuous function, a smoother estimate may provide a bet...

Weighted isotonic regression under the L1 norm

Isotonic regression, the problem of finding values that best fit given observations and conform to specific ordering constraints, has found many applications in biomedical research and other fields. When the constraints form a partial ordering, solving the problem under the L1 error measure takes O(n) when there are n observations. The analysis of large-scale microarray data, which is one of th...

Regression with quadratic loss

Regression with quadratic loss is another basic problem studied in statistical learning theory. We have a random couple Z = (X ,Y ), where, as before, X is anRd -valued feature vector (or input vector) and Y is the real-valued response (or output). We assume that the unknown joint distribution P = PZ = PX Y of (X ,Y ) belongs to some class P of probability distributions over Rd ×R. The learning...

On the Preservation of Local Asymptotic Normality Under Information Loss

Bayesian isotonic density regression.

Density regression models allow the conditional distribution of the response given predictors to change flexibly over the predictor space. Such models are much more flexible than nonparametric mean regression models with nonparametric residual distributions, and are well supported in many applications. A rich variety of Bayesian methods have been proposed for density regression, but it is not c...