This paper discusses the use of robust geostatistical methods on a data set of rainfall measurements for Switzerland. The variables are detrended via nonparametric estimation penalized with a smoothing parameter. The optimal trend is computed with a smoothing parameter based on cross-validation. The variogram is then estimated by a highly robust estimator of scale. The parametric variogram mode...

One major problem in cluster analysis is the determination of the number of clusters. In this paper, we describe both theoretical and experimental results in determining the cluster number for a small set of samples using the Bayesian-Kullback Ying-Yang (BYY) model selection criterion. Under the second-order approximation, we derive a new equation for estimating the smoothing parameter in the c...

We introduce the homotopic alternating sequential filter as a new method for smoothing 2D and 3D objects in binary images. Unlike existing methods, our method offers a strict guarantee of topology preservation. This property is ensured by the exclusive use of homotopic transformations defined in the framework of digital topology. Smoothness is obtained by the use of morphological openings and c...

Region of interest (ROI) quantitation is an important task in emission tomography (e.g., positron emission tomography and single photon emission computed tomography). It is essential for exploring clinical factors such as tumor activity, growth rate, and the efficacy of therapeutic interventions. Bayesian methods based on the maximum a posteriori principle (or called penalized maximum likelihoo...

Smoothing parameter selection is among the most intensively studied subjects in nonpara-metric function estimation. A closely related issue, that of identifying a proper index for the smoothing parameter, is however largely neglected in the existing literature. Through heuris-tic arguments and simple simulations, we shall illustrate that most current working indices are conceptually \incorrect"...

Quantum parameter estimation has many applications, from gravitational wave detection to quantum key distribution. The most commonly used technique for this type of estimation is quantum filtering, using only past observations. We present the first experimental demonstration of quantum smoothing, a time-symmetric technique that uses past and future observations, for quantum parameter estimation...

Nonparametric regression makes it possible to visualize and describe spatial trends without requiring the specification of a parametric model, but appropriate choice of smoothing parameters is important to avoid misinterpreting the nonparametric fits. Because spatial data are often correlated, currently available data-driven smoothing parameter selection methods often fail to provide useful res...

Recently Chen and Mangasarian proposed a class of smoothing functions for linear/nonlinear programs and complementarity problems that uniies many previous proposals. Here we study a non-interior continuation method based on these functions in which, like interior path-following methods, the iterates are maintained to lie in a neighborhood of some path and, at each iteration, one or two Newton-t...

Adaptive choice of smoothing parameters for nonparametric Poisson regression (O’Sullivan et. al., 1986) is considered in this paper. A computable approximation of the unbiased risk estimate (AUBR) for Poisson regression is introduced. This approximation can be used to automatically tune the smoothing parameter for the penalized likelihood estimator. An alternative choice is the generalized appr...

In this paper we propose a new derivative-free algorithm for linearly constrained finite minimax problems. Due to the nonsmoothness of this class of problems, standard derivative-free algorithms can only locate points which satisfy weak necessary optimality conditions. In this work we define a new derivative-free algorithm which is globally convergent toward standard stationary points of the fi...