Nonparametric estimation for linear SPDEs from local measurements

Near-Linear Time Local Polynomial Nonparametric Estimation

Local polynomial regression (Fan & Gijbels, 1996) is an important class of methods for nonparametric density estimation and regression problems. However, straightforward implementation of local polynomial regression has quadratic time complexity which hinders its applicability in large-scale data analysis. In this paper, we significantly accelerate the computation of local polynomial estimates ...

Rapid estimation of sunflower leaf area from linear measurements

Nonparametric Estimation of Nonlinear Dynamics by Local Linear Approximation

This chapter discusses nonparametric estimation of nonlinear dynamical system models by a method of metric-based local linear approximation. By specifying a metric such as the standard metric or the square metric on the Euclidean space and a weighting function based on such as the exponential function or the cut-off function, it is possible to estimate values of an unknown vector field from exp...

Nonparametric conditional hazard rate estimation: A local linear approach

Parametric and semiparametric methods often fail to capture the right shape of the conditional hazard rate in survival analysis. In this paper we propose a new and intuitive nonparametric estimator for the conditional hazard rate, based on local linear estimation techniques. This estimator can deal with both censored and uncensored data. We show that the local linear hazard rate estimator is co...

On Local Linear Estimation in Nonparametric Errors-in-variables Models

Local linear methods are applied to a nonparametric regression model with normal errors in the variables and uniform distribution of the variables. The local neighborhood is determined with help of deconvolution kernels. Two different linear estimation method are used: the naive estimator and the total least squares estimator. Both local linear estimators are consistent. But only the local naiv...