Title: Shape constrained regression in Sobolev spaces and tests of isotonicity
Authors: Michal Pesta - Charles University, Faculty of Mathematics and Physics (Czech Republic) [presenting]
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. Tests of isotonicity based on U-statistics and bootstrap are provided. 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.