The expectation of a function can be estimated by the empirical estimator based on the output of a Markov chain Monte Carlo method. We review results on the asymp-totic variance of the empirical estimator, and on improving the estimator by exploiting knowledge of the underlying distribution or of the transition distribution of the Markov chain.

Expressions for the variance of an estimated frequency function are necessary for many issues in model validation and experiment design. A general result is that a simple expression for this variance can be obtained asymptotically as the model order tends to infinity. This expression shows that the variance is inversely proportional to the signal-to-noise ratio frequency by frequency. Still, fo...

Asymptotics of the variances of many cost measures in random digital search trees are often notoriously messy and involved to obtain. A new approach is proposed to facilitate such an analysis for several shape parameters on random symmetric digital search trees. Our approach starts from a more careful normalization at the level of Poisson generating functions, which then provides an asymptotica...

We show that there is no batch-means estimation procedure for consistently estimating the asymptotic variance when the number of batches is held fixed as the run length increases. This result suggests that the number of batches should increase as the run length increases for sequential stopping rules based on batch means.

We give new simple general expressions for the asymptotic covariance of the estimated system parameters (A,B,C,D) in subspace identification. The formulas can be applied to a whole class of subspace methods including N4SID, MOESP, CVA etc. The asymptotic expressions highlight how the conditioning of the estimation problem influences the accuracy of the estimates. Journal of Economic Literature ...

This paper develops the methodology and asymptotic theory for the estimation of longrun variance of continuous time process. We analyze the asymptotic bias and variance of the longrun variance estimator in continuous time, and provide the optimal bandwidth balancing them o↵ and minimizing the asymptotic mean squared error. In the paper, we present not only how to consistently estimate the longr...

Most epidemiological studies suffer from misclassification in the response and/or the covariates. Since ignoring misclassification induces bias on the parameter estimates, correction for such errors is important. For measurement error, the continuous analog to misclassification, a general approach for bias correction is the SIMEX (simulation extrapolation) originally suggested by Cook and Stefa...

We present a general transfer theorem for random sequences with independent random indexes in the double array limit setting. We also prove its partial inverse providing necessary and sufficient conditions for the convergence of randomly indexed random sequences. Special attention is paid to the cases of random sums of independent not necessarily identically distributed random variables and sta...

Some aspects of the source separation problem is studied in this paper. Unmeasurable source signals are mixed by means of a channel system resulting in measurable output signals. These output signals can be used to determine a separation structure in order to extract the sources. When solving the source separation problem the channel lter parameters have to be estimated. This paper presents a c...