We consider the problem of regression with selectively observed covariates in a nonparametric framework. Our approach relies on instrumental variables that explain variation latent but have no direct effect selection. The function interest is shown to be weighted version conditional expectation where weighting fraction selection probabilities. Nonparametric identification fractional probability...

Nonparametric estimation of a structural cointegrating regression model is studied. As in the standard linear cointegrating regression model, the regressor and the dependent variable are jointly dependent and contemporaneously correlated. In nonparametric estimation problems, joint dependence is known to be a major complication that affects identification, induces bias in conventional kernel es...

Capturing predictor-dependent correlations amongst the elements of a multivariate response vector is fundamental to numerous applied domains, including neuroscience, epidemiology, and finance. Although there is a rich literature on methods for allowing the variance in a univariate regression model to vary with predictors, relatively little has been done in the multivariate case. As a motivating...

In ordinary least squares regression, dimensionality is a sensitive issue. As the number of independent variables approaches the sample size, the least squares algorithm could easily fail, i.e., estimates are not unique or very unstable, (Draper and Smith, 1981). There are several problems usually encountered in modeling high dimensional data, including the difficulty of visualizing the data, s...

In recent years, learning theory has been increasingly influenced by the fact that many learning algorithms have at least in part a comprehensive interpretation in terms of well established statistical theories. Furthermore, with little modification, several statistical methods can be directly cast into learning algorithms. One family of such methods stems from nonparametric regression. This pa...