The results from classical asymptotic theory typically require assumptions of pointwise differentiability of a criterion function with respect an unknown parameter. Taylor expansion about some " true " value in the parameter space then gives a quadratic approximation to the criterion function, within error terms that can be bounded using the remainder from the Taylor expansion. With appropriate...

State price densities (SPD) are an important element in applied quantitative finance. In a Black-Scholes model they are lognormal distributions with constant volatility parameter. In practice volatility changes and the distribution deviates from log-normality. We estimate SPDs using EUREX option data on the DAX index via a nonparametric estimator of the second derivative of the (European) call ...

To compensate for lack of robustness in using regression splines via the least squares principle, a robust data smoothing procedure is proposed for obtaining a robust regression spline estimator of an unknown regression function, g 0 , of a one-dimensional measurement variable. This robust regression spline estimator is computed by using the usual M-type iteration procedures proposed for linear...

Densities of functions of two or more independent random variables can be estimated by local U-statistics. Frees (1994) gives conditions under which they converge pointwise at the parametric root-n rate. Uniform convergence at this rate was established by Schick and Wefelmeyer (2004) for sums of random variables. Giné and Mason (2007) give conditions under which this rate also holds in Lp-norms...

We find limiting distributions of the nonparametric maximum likelihood estimator (MLE) of a log-concave density, i.e. a density of the form f(0) = exp varphi(0) where varphi(0) is a concave function on R. Existence, form, characterizations and uniform rates of convergence of the MLE are given by Rufibach (2006) and Dümbgen and Rufibach (2007). The characterization of the log-concave MLE in term...

Stuetzle and Mittal (1979) for ordinary nonparametric kernel regression and Kauermann and Tutz (1996) for nonparametric generalized linear model kernel regression constructed estimators with lower order bias than the usual estimators, without the need for devices such as second derivative estimation and multiple bandwidths of diierent order. We derive a similar estimator in the context of local...

In this article, we consider the state feedback stabilization of ODESchrödinger cascaded systems with the external disturbance. We use the backstepping transformation to handle the unstable part of the ODE, then design a feedback control which is used to cope with the disturbance and stabilize the Schrödinger part. By active disturbance rejection control (ADRC) approach, the disturbance is esti...

We consider the problem of estimating the slope parameter in functional linear regression, where scalar responses Y1, . . . , Yn are modeled in dependence of second order stationary random functions X1, . . . , Xn. An orthogonal series estimator of the functional slope parameter with additional thresholding in the Fourier domain is proposed and its performance is measured with respect to a wide...

This paper presents a method for the on-line identification of the payload carried by a single-link flexible manipulator whose movement is constrained to the vertical plane. The vertical movement of the robot makes the effect of gravity not negligible, and determines therefore, the non-linear behaviour of the analysed system. The proposed estimator is based on the algebraic derivative approach ...

This work proposes a systematic two-degree freedom control scheme to improve the reference input tracking and load disturbance rejection for an unstable magnetic levitation system. The proposed control strategy is a two-step design process. Firstly, a proportional derivative controller is introduced purposely to get the desired set-point response of the magnetic levitation system and then, an i...