A weighted least squares method is given for the numerical solution of elliptic partial differential equations of Agmon-Douglis-Nirenberg type and an error analysis is provided. Some examples are given.

Accurately evaluating statistical independence among random variables is a key element of independent component analysis (ICA). In this letter, we employ a squared-loss variant of mutual information as an independence measure and give its estimation method. Our basic idea is to estimate the ratio of probability densities directly without going through density estimation, thereby avoiding the di...

This paper studies a weighted local linear regression smoother for longitudinal/clustered data, which takes a form similar to the classical weighted least squares estimate. As a hybrid of the methods of Chen and Jin (2005) and Wang (2003), the proposed local linear smoother maintains the advantages of both methods in computational and theoretical simplicity, variance minimization and bias reduc...

We shall study the general regression model Y = g 0 (X) + ", where X and " are independent. The available information about g 0 can be expressed by g 0 2 G for some class G. As an estimator of g 0 we choose the least squares estimator. We shall give necessary and suucient conditions for consistency of this estimator in terms of (basically) geometric properties of G. Our main tool will be the th...

We consider nonparametric estimation of the state price density encapsulated in option prices. Unlike usual density estimation problems, we only observe option prices and their corresponding strike prices rather than samples from the state price density. We propose to model the state price density directly with a nonparametric mixture and estimate it using least squares. We show that although t...