This paper proposes tests on semiparametric models based on the sum of squared residuals from a least-squares procedure. Smoothness conditions are imposed on the nonparametric portion of the model to obtain asymptotic normality of the sum of squared residuals. The approach yields tests of specification, significance, smoothness and concavity and allows for heteroskedastic residuals.

A test for neglected nonlinearities in regression models is proposed. The test is of the Davidson-MacKinnon type against an increasingly rich set of non-nested alternatives, and is based on sieve estimation of the alternative model. For the case of a linear parametric model, the test statistic is shown to be asymptotically standard normal under the null, while rejecting with probability going to one if the linear model is misspecified. A small simulation study suggests that the test has adequate finite sample properties, but one must guard against over fitting the nonparametric alternative.

The size distributions of net income in Great Britain changed systematically in the 1970s. This can be shown by visual comparison of nonparametric density estimates. Typical bandwidth selection methods, such as least squares and biased cross-validation, tend to hinder comparison, because of too much variability across curves. Hence, a method for finding an appropriate pooled bandwidth is developed. It is seen that this method is much more reliable than single curve cross-validation.

This paper provides conditions to establish the weak convergence of stochastic integrals. The theorems are proved under the assumption that the innovations are strong mixing with uniformly bounded 2-h moments. Several applications of the results are given, relevant for the theories of estimation with I(1) processes, I(2) processes, processes with nonstationary variances, near-integrated processes, and continuous time approximations.

The locally best invariant statistic to test for the constancy of regression coefficients under a random walk alternative is shown to be the same as a Bayesian-type statistic derived under a change-point alternative. Asymptotic theory for this and more general statistics is discussed.

This article considers methods of simulated moments for estimation of discrete response models. It is possible to use the same set of random numbers to simulate the choice probabilities for each individual in the sample. In addition to the method of simulated moments of McFadden, we have considered also maximum simulated likelihood estimation methods. An asymptotic theory for such procedures is provided. The estimators are shown to be consistent and asymptotically normal by the theory of generalized U-statistics. Asymptotic efficiency is discussed. Monte Carlo experiments on the finite sample performance of the estimators are reported.

It is shown that the Cox modified likelihood-ratio statistic for testing partially non-nested hypotheses H0 and H1 is asymptotically equivalent to a bilinear form in nondegenerate asymptotically normal random vectors for sequences of data-generating processes converging to the intersection of H0 and H1 but not necessarily belonging to either H0 or H1. One of the asymptotically normal vectors is the complete parametric encompassing vector of Mizon and Richard, while the other is a close relative. The results are valid regardless of whether or not the data-generating process is exponential and imply that the Cox statistic is not generally asymptotically locally normal. This corrects an assumption made in recent literature.