We show that that the jackknife variance estimator vjack and the the infinitesimal jackknife variance estimator are asymptotically equivalent if the functional of interest is a smooth function of the mean or a smooth trimmed L-statistic. We calculate the asymptotic variance of vjack for these functionals.

A positive linear recurrence sequence is of the form Hn+1 = c1Hn + · · · + cLHn+1−L with each ci ≥ 0 and c1cL > 0, with appropriately chosen initial conditions. There is a notion of a legal decomposition (roughly, given a sum of terms in the sequence we cannot use the recurrence relation to reduce it) such that every positive integer has a unique legal decomposition using terms in the sequence;...

We consider the problem of estimating passage times in stochastic simulations of Markov chains+ Two types of estimator are considered for this purpose: the “simple” and the “overlapping” estimator; they are compared in terms of their asymptotic variance+ The analysis is based on the regenerative structure of the process and it is shown that when estimating the mean passage time, the simple esti...

Subspace identification for closed loop systems has been recently studied by several authors. Recent results are available which express the asymptotic variance of the estimated parameters (and hence of any system invariant) as a function of the “true” underlying system parameters and of certain conditional covariance matrices. When it comes to using these formulas in practice one is faced with...

The variance ratio test statistic, which is based on k-period differences of the data, is commonly used in empirical finance and economics to test the random walk hypothesis. We obtain the asymptotic power function of the variance ratio test statistic when the differencing period k is increasing with the sample size n such that k/n→ δ > 0. We show that the test is inconsistent against a variety...

In recent papers it has been demonstrated that sampling a Gibbs distribution from an appropriate time-irreversible Langevin process is, from several points of view, advantageous when compared to sampling from a time-reversible one. Adding an appropriate irreversible drift to the overdamped Langevin equation results in a larger large deviations rate function for the empirical measure of the proc...

Importance sampling is a widely used variance reduction technique to compute sample quantiles such as value at risk. The variance of the weighted sample quantile estimator is usually a difficult quantity to compute. In this paper we present the exact convergence rate and asymptotic distributions of the bootstrap variance estimators for quantiles ofweighted empirical distributions. Under regular...

New formulas for the asymptotic variance of the parameter estimates in subspace identi)cation, show that the accuracy of the parameter estimates depends on certain indices of ‘near collinearity’ of the state and future input subspaces of the system to be identi)ed. This complements the numerical conditioning analysis of subspace methods presented in the companion paper (On the ill-conditioning ...

Abstract: This paper establishes that when using a least squares criterion to estimate an output error type model structure, then the measurement noise induced variability of the frequency response estimate depends on the estimated (and hence also on the true) pole positions. This dependence on pole position is perhaps counter to prevailing wisdom that for any ‘shift invariant’ model structure,...

We derive the asymptotic distribution of the eigenvalues of a sample covariance matrix with distinct roots. Our theorem can accommodate the situation in which the population covariance matrix is estimated via its sample analogue as well as the more general case in which it is estimated via a √ N -consistent extremum estimator. The sample roots will have a Normal distribution in ∗Address: 2424 M...