Residual terms that appear in nonlinear PDEs that are constructed to generate filtered representations of the variables of the fully resolved system are examined by way of a consistency condition. It is shown that certain commonly used empirical gradient models for the residuals fail the test of consistency and therefore cannot be validated as approximations in any reliable sense. An alternate ...

In boundary element analysis, first order function derivatives, e.g., boundary potential gradient or stress tensor, can be accurately computed by evaluating the hypersingular integral equation for these quantities. However, this approach requires a complete integration over the boundary and is therefore computationally quite expensive. Herein it is shown that this method can be significantly si...

It is shown that in the estimation of an arbitrary signal corrupted by additive Gaussian noise, the optimum minimum-variance estimator is always a simple linear transformation of the logarithmic gradient of the average likelihood ratio which is obtained in the optimum detection of the same signal. Conversely, the average likelihood ratio can always be expressed in a simple functional form conta...

In this paper, we consider identification in a correlated random effects model for panel data. We assume that the likelihood for each individual in the panel is known up to a finite dimensional common parameter and an individual specific parameter. We allow the distribution of unobserved individual specific effects to depend on observed explanatory variables and make no assumptions about the pa...

In this paper, we consider identification and estimation of average marginal effects in a correlated random effects model without imposing strong functional form assumptions on the structural likelihood or the mixing distribution. Identification is achieved through imposing that the mixing distribution depends on observed covariates only through an index function and the assumption that at leas...

This paper examines the relationship between child labor and access to credit at a crosscountry level. Even though this link is theoretically central to child labor, so far there has been little work done to assess its importance empirically. We measure child labor as a country aggregate, and credit constraints are proxied by the extent of financial development. These two variables display a st...