We consider pointwise mean squared errors of several known Bayesian wavelet estimators, namely, posterior mean, posterior median and Bayes Factor, where the prior imposed on wavelet coefficients is a mixture of an atom of probability zero and a Gaussian density. We show that for the properly chosen hyperparameters of the prior, all the three estimators are (up to a log-factor) asymptotically mi...

A moment bound for the normalized conditional-sum-of-squares (CSS) estimate of a general autoregressive fractionally integrated moving average (ARFIMA) model with an arbitrary unknown memory parameter is derived in this paper. To achieve this goal, a uniform moment bound for the inverse of the normalized objective function is established. An important application of these results is to establis...

We consider benchmarked empirical Bayes (EB) estimators under the basic area-level model of Fay and Herriot while requiring the standard benchmarking constraint. In this paper we determine the excess mean squared error (MSE) from constraining the estimates through benchmarking. We show that the increase due to benchmarking is O(m−1), where m is the number of small areas. Furthermore, we find an...

This paper gives an expression for the minimum mean squared error predictor of the single equation ARMAX model when all the parameters are known. A formula is then derived for the asymptotic prediction mean squared error when the parameters are replaced by their maximum likelihood estimates. These general results are then specialised to the regression model with ARMA errors; for this case we al...

Humans can learn to overcome the 150 msec delay of the eye movement system and track predictable targets with no latency. The mean squared error between the target and eye position was used as a measure of the goodness of tracking. For typical subjects, this error decreased from 0.5 deg2 to 0.1 deg2 after 100-200 sec of viewing the target. Professional athletes had much smaller mean squared err...