<p style='text-indent:20px;'>Unbiased estimation for parameters of maximal distribution is a fundamental problem in the statistical theory sublinear expectations. In this paper, we proved that maximum estimator largest unbiased upper mean and minimum smallest lower mean.</p>

Rousseeuw’s minimum covariance determinant (MCD) method is a highly robust estimator of multivariate mean and covariance. In practice, the MCD covariance estimator may be singular. However, a nonsingular covariance estimator is required to calculate the Mahalanobis distance. In order to fix this singular problem, we propose an improved version of the MCD estimator, which is a combination of the...

Loran-C is a navigational aid that relies on the ability to make correct estimates of the Times of Arrival (TOAs) of signals received over a noisy radio channel. How good is the performance of Loran-C in this respect? Is it close to optimal? Are there perhaps better estimation techniques available than we currently employ? In this paper we use Estimation Theory to find the optimal limit of the ...

Optimal or unbiased estimators are widely used for state estimation and tracking. We propose a new minimum variance unbiased (MVU) finite impulse response (FIR) filter which minimizes the estimation error variance in the unbiased FIR (UFIR) filter. The relationship between the filter gains of the MVU FIR, UFIR and optimal FIR (OFIR) filters is found analytically. Simulations provided using a po...

Appropriate imputation inference requires both an unbiased imputation estimator and an unbiased variance estimator. The commonly used variance estimator, proposed by Rubin, can be biased when the imputation and analysis models are misspecified and/or incompatible. Robins and Wang proposed an alternative approach, which allows for such misspecification and incompatibility, but it is considerably...

Motivated by steady-state simulation experiments, we consider the problem of estimating the marginal variance of a stationary time series. The usual estimator, the sample variance is biased for autocorrelated data. To reduce bias, other authors have suggested interlaced estimators. These estimators which like the sample variance are sums of squares are a generalization of the sample variance an...

In vision science the currently most popular models for depth perception are weak fusion models in which the final depth estimate results from a weighted average of the independent depth estimates obtained from each cue [2]. In these models a more reliable cue has a larger weight in the combined estimate. Furthermore, recent studies report that human observes combine depth cues as to obtain the...

We introduce a robust and asymptotically unbiased estimator for the coefficient of tail dependence in multivariate extreme value statistics. The estimator is obtained by fitting a second order model to the data by means of the minimum density power divergence criterion. The asymptotic properties of the estimator are investigated. The efficiency of our methodology is illustrated on a small simul...