Classical regression analysis uses partial coefficients to measure the influences of some variables (regressors) on another variable (regressand). However, a descriptive point of view shows that these coefficients are very bad measures of influence. Their interpretation as an average change of...

Explained variance (R^2) is a familiar summary of the fit of a linear regression and has been generalized in various ways to multilevel (hierarchical) models. The multilevel models we consider in this paper are characterized by hierarchical data structures in which individuals are grouped into...

The least-absolute-deviations (LAD) estimator for a median- regression model does not satisfy the standard conditions for obtaining asymptotic refinements through use of the bootstrap because the LAD objective function is not smooth. This paper overcomes this problem by smoothing the objective...

In this supplemental article, we introduce some useful results in spectral theory and perturbation theory. Some of the results are well-established. We briefly review them for the purpose of easy reference. We derive a novel bound for the perturbation of eigenprojections, which plays a key role...

This paper studies a class of exponential family models whose canonical parameters are specified as linear functionals of an unknown infinite-dimensional slope function. The optimal minimax rates of convergence for slope function estimation are established. The estimators that achieve the...

We introduce tests for finite-sample linear regressions with heteroskedastic errors. The tests are exact, i.e., they have guaranteed type I error probabilities when bounds are known on the range of the dependent variable, without any assumptions about the noise structure. We provide upper bounds...

For a broad class of linear biased estimators, we establish conditions under which the F statistic based on biased estimators is identical to the F statistic based on least-squares estimator. Several biased estimators in the literature are shown to satisfy these conditions

We consider inference for predictive regressions with multiple predictors. Extant tests for predictability may perform unsatisfactorily and tend to discover spurious predictability as the number of predictors increases. We propose a battery of new instrumental-variables based tests which involve...

We consider fully modified least squares estimation for systems of cointegrating polynomial regressions, i. e., systems of regressions that include deterministic variables, integrated processes and their powers as regressors. The errors are allowed to be correlated across equations, over time...