• This work overviews some developments on the estimation of the Receiver Operating Characteristic (ROC) curve. Estimation methods in this area are constantly being developed, adjusted and extended, and it is thus impossible to cover all topics and areas of application in a single paper. Here, we focus on some frequentist and Bayesian methods which have been mostly employed in the medical setti...

Since quantile regression curves are estimated individually, the quantile curves can cross, leading to an invalid distribution for the response. A simple constrained version of quantile regression is proposed to avoid the crossing problem for both linear and nonparametric quantile curves. A simulation study and a reanalysis of tropical cyclone intensity data shows the usefulness of the procedur...

The recently developed theory of wavelets has a remarkable property to \zoom in" on very short lived frequency phenomena, such as transients in signals and singularities in functions, and hence provides an ideal tool to study localized changes. This paper proposes a wavelet method to estimate jump and sharp cusp curves of a function in the plane. The method is rst to compute wavelet transformat...

The L-curve criterion is often applied to determine a suitable value of the regularization parameter when solving ill-conditioned linear systems of equations with a right-hand side contaminated by errors of unknown norm. However, the computation of the L-curve is quite costly for large problems; the determination of a point on the L-curve requires that both the norm of the regularized approxima...

Principal curves and manifolds provide a framework to formulate manifold learning within a statistical context. Principal curves define the notion of a curve passing through the middle of a distribution. While the intuition is clear, the formal definition leads to some technical and practical difficulties. In particular, principal curves are saddle points of the mean-squared projection distance...

correct estimation of suspended sediment transported by a river is an important practice in water structure design, environmental problems and water quality issues. conventionally, sediment rating curve used for suspended sediment estimation in rivers. in this method discharge and sediment discharge or concentration related using regression relation that generally is exponential model. respect ...