Abstract. In the model of progressive type II censoring, point and interval estimation as well as relations for single and product moments are considered. Based on two-parameter exponential distributions, maximum likelihood estimators (MLEs), uniformly minimum variance unbiased estimators (UMVUEs) and best linear unbiased estimators (BLUEs) are derived for both location and scale parameters. So...

This article considers the problem of estimating the population variance using auxiliary information. An improved version of Singh’s exponential type ratio estimator has been proposed and its properties have been studied under large sample approximation. It is shown that the proposed exponential type ratio estimator is more efficient than that considered by the Singh estimator, conventional rat...

• In the present paper we study the performance of the Bayes Shrinkage estimators for the scale parameter of the Weibull distribution under the squared error loss and the LINEX loss functions in the presence of a prior point information of the scale parameter when Type-II censored data are available. The properties of the minimax estimators are also discussed. Key-Words: • Bayes shrinkage estim...

A new method is developed for the state estimation of linear discrete-time stochastic system in the presence of unknown disturbance. The obtained filter is optimal in the unbiased minimum variance sense. The necessary and sufficient conditions for the existence and the stability of the filter are given.

Estimators of the conditional expectation, i.e., prediction, function involve a global bias-variance trade off. In some cases, an estimator that yields unbiased estimates of the conditional expectation for a particular partitioning of the data may be desirable. Such estimators are calibrated with respect to the partitioning. We identify the conditional expectation given a particular partitionin...

In this paper, we propose a new componentwise estimator of a dispersion matrix, based on a highly robust estimator of scale. The key idea is the elimination of a location estimator in the dispersion estimation procedure. The robustness properties are studied by means of the influence function and the breakdown point. Further characteristics such as asymptotic variance and efficiency are also an...

Analytic expressions for the first order bias and second order covariance of a general maximum likelihood estimate (MLE) are presented. These expressions are used to determine general analytic conditions on sample size, or signal-to-noise ratio (SNR), that are necessary for a MLE to become asymptotically unbiased and attain minimum variance as expressed by the Cramer-Rao lower bound (CRLB). The...

Let X be our data. Let θ̂ = T (X) be an estimator where T is some function. We say that θ̂ is unbiased for θ if Eθ[T (X)] = θ for all possible values of θ where Eθ denotes the expectation when θ is the true parameter value. Thus, the concept of unbiasness means that we are on average right. The bias of θ̂ is de ned by Bias(θ̂) = Eθ[θ̂] − θ. Thus, θ̂ is unbiased if and only if its bias equals 0. For e...

This article considers a linear regression model with some missing observations on the response variable and presents two estimators of regression coefficients employing the approach of minimum risk estimation. Asymptotic properties of these estimators along with the traditional unbiased estimator are analyzed and conditions, that are easy to check in practice, for the superiority of one estima...

This article considers a linear regression model with some missing observations on the response variable and presents two estimators of regression coefficients employing the approach of minimum risk estimation. Asymptotic properties of these estimators along with the traditional unbiased estimator are analyzed and conditions, that are easy to check in practice, for the superiority of one estima...