We propose a completely kernel based method of estimating the call price function or the state price density of options. The new estimator of the call price function fulfills the constraints like monotonicity and convexity given in Breeden and Litzenberger (1978) without necessarily estimating...

A central limit theorem for the weighted integrated squared error of kernel-type estimators of the first two derivatives of a nonparametric regression function is proved by using results for martingale differences and U-statistics. The results focus on the setting of the Nadaraya-Watson...

We consider inverse regression models with convolution-type operators which mediate convolution on (d=1) and prove a pointwise central limit theorem for spectral regularisation estimators which can be applied to construct pointwise confidence regions. Here, we cope with the unknown bias of such...

We consider the problem of testing hypotheses regarding the covariance matrix of multivariate normal data, if the sample size s and dimension n satisfy . Recently, several tests have been proposed in the case, where the sample size and dimension are of the same order, that is y[set membership,...

We propose a test for shape constraints which can be expressed by transformations of the coordinates of multivariate regression functions. The method is motivated by the constraint of symmetry with respect to some unknown hyperplane but can easily be generalized to other shape constraints of...