The restricted maximum likelihood is preferred by many to the full maximum likelihood for estimation with variance component and other random coefficient models, because the variance estimator is unbiased. It is shown that this unbiasedness is accompanied in some balanced designs by an inflation of the mean squared error. An estimator of the cluster-level variance that is uniformly more efficie...

In this paper, the problem of interest is efficient estimation of log-normal means. Several existing estimators are reviewed first, including the sample mean, the maximum likelihood estimator, the uniformly minimum variance unbiased estimator and a conditional minimal mean squared error estimator. A new estimator is then proposed, and we show that it improves over the existing estimators in ter...

This paper presents mathematically novel estimator for the linear regression model named Minimum-Variance Pseudo-Unbiased Reduced-Rank Estimator (MV-PURE), designed specially for applications where the model matrix under consideration is ill-conditioned, and auxiliary knowledge on the unknown deterministic parameter vector is available in the form of linear constraints. We demonstrate closed al...

we develop a two phase sampling procedure to determine the sample size necessary to estimatethe population mean of a normally distributed random variable and show that the resulting estimator has preassigned variance and is unbiased under a regular condition. we present a necessary and sufficient condition under which the final sample mean is an unbiased estimator for the population mean.

In this thesis, the problem of minimum-variance unbiased (MVU) parameter estimation in low signal-to-noise ratios (SNRs) or few number of samples was studied. Performance lower bounds are commonly used in statistical signal processing for system design and analysis. In most practical problems there exists a threshold SNR below which the performance of the estimators, such as the maximum likelih...

Shrinkage preliminary test estimation in exponential distribution under a precautionary loss function is considered. The minimum risk-unbiased estimator is derived and some shrinkage preliminary test estimators are proposed. We apply our results on censored data and records. The relative efficiencies of proposed estimators with respect to the minimum ‎risk-unbiased‎&...

This paper is concerned with the problem of state estimation for discrete-time linear systems in presence additional (equality or inequality) constraints on (or estimate). By use minimum variance duality, converted into an optimal control problem. Two algorithmic solutions are described: full information estimator (FIE) and moving horizon (MHE). The main result to show that proposed stable sens...