Publication at Faculty of Mathematics and Physics |
2017
Abstract
A class of nonparametric regression estimators based on penalized least squares over the sets of sufficiently smooth functions is elaborated. We impose additional shape constraint-isotonia-on the estimated regression curve and its derivatives.
The problem of searching for the best fitting function in an infinite dimensional space is transformed into a finite dimensional optimization problem making this approach computationally feasible. The form and properties of the regression estimator in the Sobolev space are investigated.
An application to option pricing is presented. The behavior of the estimator is improved by implementing an approximation of a covariance structure for the observed intraday option prices.