Econometric applications of kernel estimators are proliferating, suggesting the need for convenient variance estimates and conditions for asymptotic normality. This paper develops a general “delta-method” variance estimator for functionals of kernel estimators. Also, regularity conditions for asymptotic normality are given, along with a guide to verify them for particular estimators. The general results are applied to partial means, which are averages of kernel estimators over some of their arguments with other arguments held fixed. Partial means have econometric applications, such as consumer surplus estimation, and are useful for estimation of additive nonparametric models.

We consider a system of m general linear models, where the system error vector has a singular covariance matrix owing to various “adding up” requirements and, in addition, the error vector obeys an autoregressive scheme. The paper reformulates the problem considered earlier by Berndt and Savin [8] (BS), as well as others before them; the solution, thus obtained, is far simpler, being the natural extension of a restricted least-squares-like procedure to a system of equations. This reformulation enables us to treat all parameters symmetrically, and discloses a set of conditions which is different from, and much less stringent than, that exhibited in the framework provided by BS.

Finally, various extensions are discussed to (a) the case where the errors obey a stable autoregression scheme of order r; (b) the case where the errors obey a moving average scheme of order r; (c) the case of “dynamic” vector distributed lag models, that is, the case where the model is formulated as autoregressive (in the dependent variables), and moving average (in the explanatory variables), and the errors are specified to be i.i.d.

This paper proposes a new approach to modeling heteroskedastidty which enables the modeler to utilize information conveyed by data plots in making informed decisions on the form and structure of heteroskedasticity. It extends the well-known normal/linear/homoskedastic models to a family of non-normal/linear/heteroskedastic models. The non-normality is kept within the bounds of the elliptically symmetric family of multivariate distributions (and in particular the Student's t distribution) that lead to several forms of heteroskedasticity, including quadratic and exponential functions of the conditioning variables. The choice of the latter family is motivated by the fact that it enables us to model some of the main sources of heteroskedasticity: “thicktails,” individual heterogeneity, and nonlinear dependence. A common feature of the proposed class of regression models is that the weak exogeneity assumption is inappropriate. The estimation of these models, without the weak exogeneity assumption, is discussed, and the results are illustrated by using cross-section data on charitable contributions.

Let F denote a distribution function defined on the probability space (Ω,,P), which is absolutely continuous with respect to the Lebesgue measure in Rd with probability density function f. Let f0(·,β) be a parametric density function that depends on an unknown p × 1 vector β. In this paper, we consider tests of the goodness-of-fit of f0(·,β) for f(·) for some β based on (i) the integrated squared difference between a kernel estimate of f(·) and the quasimaximum likelihood estimate of f0(·,β) denoted by In and (ii) the integrated squared difference between a kernel estimate of f(·) and the corresponding kernel smoothed estimate of f0(·, β) denoted by Jn. It is shown in this paper that the amount of smoothing applied to the data in constructing the kernel estimate of f(·) determines the form of the test statistic based on In. For each test developed, we also examine its asymptotic properties including consistency and the local power property. In particular, we show that tests developed in this paper, except the first one, are more powerful than the Kolmogorov-Smirnov test under the sequence of local alternatives introduced in Rosenblatt [12], although they are less powerful than the Kolmogorov-Smirnov test under the sequence of Pitman alternatives. A small simulation study is carried out to examine the finite sample performance of one of these tests.

This paper compares the local power of tests for a nonlinear transformation of the dependent variable in a regression model against the alternative hypothesis of a linear transformation. It is shown that the local power of the Cox test is higher than those of the extended projection test of MacKinnon, White, and Davidson, and Bera and McAleer's test. The theoretical result is supported by a Monte-Carlo experiment in testing for a regression model with a logarithmically transformed dependent variable against a linear regression model.

We prove -consistency and asymptotic normality of a generalized semiparametric regression estimator that includes as special cases Ichimura's semiparametric least-squares estimator for single index models, and the estimator of Klein and Spady for the binary choice regression model. Two function expansions reveal a type of U-process structure in the criterion function; then new U-process maximal inequalities are applied to establish the requisite stochastic equicontinuity condition. This method of proof avoids much of the technical detail required by more traditional methods of analysis. The general framework suggests other -consistent and asymptotically normal estimators.

This paper provides a simple estimation method for an error component regression model with general MA(q) remainder disturbances. The estimation method utilizes the transformation derived by Baltagi and Li [3] for an error component model with autoregressive remainder disturbances, and a standard orthogonalizing algorithm for the general MA(q) model. This estimation method is computationally simple utilizing only least-squares regressions. This is important for panel data regressions where brute force GLS is in many cases not feasible.This estimation method performs well relative to true GLS in Monte-Carlo experiments.

In this comment on Gurmu and Trivedi's “Variable Augmentation Specification Tests in the Linear Exponential Family,” I show how their generalized linear model (GLM) approach relates to other work in econometrics on specification testing in the linear exponential family. In addition to shedding light on the relationship between the statistics and econometrics literatures on testing in quasi-likelihood frameworks, this comparison reveals some important limitations of GLM as a general framework for devising specification tests.