A number of methods have been proposed to estimate the period of a variable star; e.g., a recent approach uses smoothing spline regression to fit tentative periodic functions (light curves) and selects the period minimizing a robust goodness-of-fit criterion. These methods assume that measurement errors vary independently over time. Empirical evidence, however, indicates substantial temporal de...

2 Proofs for the Poisson model 3 2.1 Bounds for general linear estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Negative result for truncated Good-Toulmin estimator . . . . . . . . . . . . . . . . . 5 2.3 Bounds on SGT estimators: arbitrary smoothing . . . . . . . . . . . . . . . . . . . . 5 2.4 Poisson smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Smoothing techniques are of major importance for the generation of surface meshes. For this reason a considerable amount of research has been spent on developing a large variety of sophisticated smoothing approaches. However, these methods either require direct access to the analytic surface description or are restricted to flat meshes in two dimensions. In particular, if no analytic surface da...

A robust local linear regression smoothing estimator for a nonparametric regression model with heavy-tailed dependent errors is considered in this paper. Under certain regularity conditions, the weak consistency and asymptotic distribution of the proposed estimators are obtained. If the errors are short-range dependent, then the limiting distribution of the estimator is normal. If the data are ...

We consider the nonlinear Schrödinger equation in higher dimension with Dirichlet boundary conditions and with a non-local smoothing nonlinearity. We prove the existence of small amplitude periodic solutions. In the fully resonant case we find solutions which at leading order are wave packets, in the sense that they continue linear solutions with an arbitrarily large number of resonant modes. T...

A local linear method for estimating the conditional ROC curve under the presence of continuous and categorical covariates has been introduced in this paper. A data driven smoothing parameter has been proposed via the bootstrap method. The methods have been illustrated with real data coming from a discrimination problem emerging in the context of a computer-aided diagnosis system. The bootstrap...

We consider a family of surfaces of revolution, each with a single periodic geodesic which is degenerately unstable. We prove a local smoothing estimate for solutions to the linear Schrödinger equation with a loss that depends on the degeneracy, and we construct explicit examples to show our estimate is saturated on a weak semiclassical time scale. As a byproduct of our proof, we obtain a cutof...

In this paper, we propose a smoothing inexact Newton method for solving variational inequalities with nonlinear constraints. Based on the smoothed Fischer-Burmeister function, the variational inequality problem is reformulated as a system of parameterized smooth equations. The corresponding linear system of each iteration is solved approximately. Under some mild conditions, we establish the glo...

In this paper a new nonparametric estimate of conditional quantiles is proposed, that avoids the problem of crossing quantile curves [calculated for various p ∈ (0, 1)]. The method uses an initial estimate of the conditional distribution function in a first step and solves the problem of inversion and monotonization with respect to p ∈ (0, 1) simultaneously. It is demonstrated that the new esti...