4208 In this paper we are concerned with shape restricted estimation in inverse regression problems with convolution-type operator. We use increasing rearrangements to compute increasingand convex estimates from an (in principle arbitrary) unconstrained estimate of the unknown regression...

In this paper we study statistical inference for certain inverse problems. We go beyond mere estimation purposes and review and develop the construction of confidence intervals and confidence bands in some inverse problems, including deconvolution and the backward heat equation. Further, we...

We construct uniform confidence bands for the regression function in inverse, homoscedastic regression models with convolution-type operators. Here, the convolution is between two non-periodic functions on the whole real line rather than between two period functions on a compact interval, since...

The computation of robust regression estimates often relies on minimization of a convex functional on a convex set. In this paper we discuss a general technique for a large class of convex functionals to compute the minimizers iteratively which is closely related to majorization-minimization...

In this paper a new method for monotone estimation of discount curves is proposed. The main idea of this approach is a simple modification of the commonly used (unconstrained) McCulloch Spline. We construct an integrated density estimate from the predicted values of the discount curve. It can be...

We propose two test statistics for use in inverse regression problems Y = Kcedil; + , where K is a given matrix or operator which cannot be continuously inverted. Thus, only noisy, indirect observations Y for the function cedil; are available. The tests are designed for hypotheses of the form H0...