In this paper the asymptotic behavior of penalized spline estimators is studied using bivariate splines over triangulations and an energy functional as the penalty. The rate of L2 convergence is derived, which achieves the optimal nonparametric convergence rate established by Stone (1982). The asymptotic normality of the penalized spline estimators is established, which is shown to hold uniform...

The covariance ordering, for discrete and continuous time Markov chains, is defined and studied. This partial ordering gives a necessary and sufficient condition for MCMC estimators to have small asymptotic variance. Connections between this ordering, eigenvalues, and suprema of the spectrum of the Markov transition kernel, are provided. A representation of the asymptotic variance of MCMC estim...

If we wish to eeciently estimate the expectation of an arbitrary function on the basis of the output of a Gibbs sampler, which is better: deterministic or random sweep? In each case we calculate the asymptotic variance of the empirical estimator, the average of the function over the output, and determine the minimal asymptotic variance for estimators that use no information about the underlying...

For any given number of factors, Minimum Rank Factor Analysis yields optimal communalities for an observed covariance matrix in the sense that the unexplained common variance with that number of factors is minimized, subject to the constraint that both the diagonal matrix of unique variances and the observed covariance matrix minus that diagonal matrix are positive semidefinite. As a result, it...

Long-run variance estimation can typically be viewed as the problem of estimating the scale of a limiting continuous time Gaussian process on the unit interval. A natural benchmark model is given by a sample that consists of equally spaced observations of this limiting process. The paper analyzes the asymptotic robustness of long-run variance estimators to contaminations of this benchmark model...

An ordered tree with height h is b-balanced if all its leaves have a level l with h − b <= l <= h, where at least one leaf has a level equal to h − b. For large n, we shall compute asymptotic equivalents to the number of all b-balanced ordered trees with n nodes and of all such trees with height h. Furthermore, assuming that all b-balanced ordered trees with n nodes are equally likely, we shall...

This study considers variance estimation when estimating the asymptotic variance of a propensity score matching estimator for the average treatment effect. We investigate the role of smoothing parameters in a variance estimator based on matching. We also study the properties of estimators using local linear estimation. Simulations demonstrate that large gains can be made in terms of mean square...

The asymptotic variance is a natural indicator of the efficiency for Markov Chain Monte Carlo algorithm. In this note, we prove that drift accelerated diffusion converges to zero uniformly if and only there are no non-trivial first order Sobolev functions in kernel generating operator. Its proof based on spectral analysis space mean functions.