We establish valid Edgeworth expansions for the distribution of smoothed nonparametric spectral estimates, and of studentized versions of linear statistics such as the sample mean, where the studentization employs such a nonparametric spectral estimate. Particular attention is paid to the spectral estimate at zero frequency and, correspondingly, the studentized sample mean, to reflect econometric interest in autocorrelation-consistent or long-run variance estimation. Our main focus is on stationary Gaussian series, though we discuss relaxation of the Gaussianity assumption. Only smoothness conditions on the spectral density that are local to the frequency of interest are imposed. We deduce empirical expansions from our Edgeworth expansions designed to improve on the normal approximation in practice and also deduce a feasible rule of bandwidth choice.

In this paper we study the properties of a pth-order Markovian local resampling procedure in approximating the distribution of nonparametric (kernel) estimators of the conditional expectation m(x;φ). Under certain regularity conditions, asymptotic validity of the proposed resampling scheme is established for a class of stochastic processes that is broader than the class of stationary Markov processes. Some simulations illustrate the finite sample performance of the proposed resampling procedure.

In this paper we propose an estimation procedure for a censored regression model where the latent regression function has a partially linear form. Based on a conditional quantile restriction, we estimate the model by a two stage procedure. The first stage nonparametrically estimates the conditional quantile function at in-sample and appropriate out-of-sample points, and the second stage involves a simple weighted least squares procedure. The proposed procedure is shown to have desirable asymptotic properties under regularity conditions that are standard in the literature. A small scale simulation study indicates that the estimator performs well in moderately sized samples.

The finite sample performance of spectral regression estimators in temporally aggregated cointegrated systems is investigated via the use of simulation experiments. The simulations address issues such as “optimal” choice of bandwidth parameter and effects of smoothing kernel in constructing estimates of spectral densities that are used by the spectral regression estimators; the effects of stock and flow variables and mixtures of the two, including the relative finite sample efficiency of the estimators under different combinations of stock and flow variables; and the effects of conducting iterations of the spectral estimators. A striking feature of the results is the crucial role that correct choice of bandwidth and kernel function plays in producing accurate estimates of the unknown parameters. Furthermore, estimates obtained using flow data alone are found to be more efficient, in the sense of having smaller variance, than those obtained using stock data alone or mixtures of stocks and flows, thereby confirming in finite samples their relative asymptotic properties.

For a class of parametric ARCH models, Whittle estimation based on squared observations is shown to be [square root of n]-consistent and asymptotically normal. Our conditions require the squares to have short memory autocorrelation, by comparison with the work of Zaffaroni (1999, “Gaussian Inference on Certain Long-Range Dependent Volatility Models,” Preprint), who established the same properties on the basis of an alternative class of models with martingale difference levels and long memory autocorrelated squares.

Joseph B. Kadane, usually known as Jay among his friends and colleagues, is a well-known figure among statisticians and econometricians. He has made substantial contributions to the fields of Bayesian statistics, econometrics, and many applied areas. He is well known for his work in applying statistics to how people make decisions and draw conclusions from data.