The method of using Global Positioning System-leveling data to obtain orthometric heights has been well studied. A simple formulation for the weighted least squares problem has been presented in an earlier work. This formulation allows one directly employing the errors-in-variables models which completely descript the covariance matrices of the observables. However, an important question that w...

Agencies and policy makers are interested in constructing reliable estimates for areas with small sample sizes, where areas often refer to geographic areas and demographic groups. The estimation for such areas is known as small area estimation. Procedures based on models have been used to construct estimates for the small area means, by exploiting auxiliary information. Mixed models are suitabl...

Assessing the variability of an estimator is a key component of the process of statistical inference. In nonparametric regression, estimating observation-error variance is the principal ingredient needed to estimate the variance of the regression mean. Although there is an extensive literature on variance estimation in nonparametric regression, the techniques developed in conventional settings ...

We examine how the estimation error grows with time when a mobile robot estimates its location from relative pose measurements without global position or orientation sensors. We show that in both 2-D or 3-D space, both the bias and variance of the position estimation error grows at most linearly with time (or distance traversed) asymptotically. The bias is crucially dependent on the trajectory ...

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...

This paper is concerned with the variance-constrained state estimation problem for a class of networked multi-rate systems (NMSs) with network-induced probabilistic sensor failures and measurement quantization. The stochastic characteristics of the sensor failures are governed by mutually independent random variables over the interval [0, 1]. By applying the lifting technique, an augmented syst...

In the context of binary classification, we define disagreement as a measure of how often two independently-trained models differ in their classification of unlabeled data. We explore the use of disagreement for error estimation and model selection. We call the procedure co-validation, since the two models effectively (in)validate one another by comparing results on unlabeled data, which we ass...