We propose methods for outlier handling and noise reduction using weighted local linear smoothing for a set of noisy points sampled from a nonlinear manifold. The methods can be used by manifold learning methods such as Isomap, LLE and LTSA as a preprocessing step to obtain a more accurate reconstruction of the underlying nonlinear manifolds. Weighted PCA is used as a building block for our met...

Local linear regression is commonly used in practice because of its excellent numerical and theoretical properties. It involves fitting a straight line segment over a small region whose midpoint is the target point x, and the local linear estimate at x is the estimated intercept of that straight line segment. Local linear estimator has an asymptotic bias of order h and variance of order (nh) wi...

Wavelets are explored as a data smoothing (or de-noising) option for solution monitoring data in nuclear safeguards. In wavelet-smoothed data, the Gibbs phenomenon can obscure important data features that may be of interest. This paper compares wavelet smoothing to piecewise linear smoothing and local kernel smoothing, and illustrates that the Haar wavelet basis is effective for reducing the Gi...

‎In this article‎, ‎we develop two nonparametric smoothing estimators for parameter of a time-variant parametric model‎. ‎This parameter can be from any parametric family or from any parametric or semi-parametric regression model‎. ‎Estimation is based on a two-step procedure‎, ‎in which we first get the raw estimate of the parameter at a set of disjoint time...

We propose a new method for local linear smoothing, filtering and prediction of noisy data. Its novelty consists in two of its steps: a sliding window filter that uses Student’s t-statistics to perform smoothing and filtering, and a trend change detection scheme that uses a convex hull construction to determine a change of slope or intercept of the local linear trend. The final linear trend det...

This paper shows how abstract resolvent estimates imply local smoothing for solutions to the Schrödinger equation. If the resolvent estimate has a loss when compared to the optimal, non-trapping estimate, there is a corresponding loss in regularity in the local smoothing estimate. As an application, we apply well-known techniques to obtain well-posedness results for the semi-linear Schrödinger ...

An important problem for tting local linear regression is the choice of the smoothing parameter. As the smoothing parameter becomes large, the estimator tends to a straight line, which is the least squares t in the ordinary linear regression setting. This property may be used to assess the adequacy of a simple linear model. Motivated by Silverman's (1981) work for testing multimodality in kerne...