Exact small sample properties of an operational variant of the minimum mean squared error estimator

The dispersion parameter of a chi-distributed radial error is of interest in numerous target analysis problems as a measure of weapon-system accuracy, and it is often of practical importance to estimate it. This paper presents a few classical estimators including the maximum likelihood estimator, an unbiased estimator and a minimum mean squared error estimator of this dispersion for both when the origin or “center of impact” is knownor can be assumed as known and when it is unknown. Some families of shrinkage estimators have also been suggested when a prior point estimate of the dispersion parameter is available in addition to sample information. The estimators of circular error probable and spherical error probable have been obtained as well. A simulation study has been carried out to demonstrate the performance of the proposed estimators.

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An Improved Estimation of Parameter of Morgenstern-Type Bivariate Exponential Distribution Using Ranked Set Sampling

10.4018/978-1-7998-7556-7.ch001 ◽

2022 ◽

pp. 1-25

Author(s):

Vishal Mehta

Keyword(s):

Exponential Distribution ◽

Mean Squared Error ◽

Ranked Set Sampling ◽

Error Estimator ◽

Bivariate Exponential Distribution ◽

Ranked Set Sample ◽

Minimum Mean Squared Error ◽

Squared Error ◽

Bivariate Exponential ◽

Special Cases

In this chapter, the authors suggest some improved versions of estimators of Morgenstern type bivariate exponential distribution (MTBED) based on the observations made on the units of ranked set sampling (RSS) regarding the study variable Y, which is correlated with the auxiliary variable X, where (X,Y) follows a MTBED. In this chapter, they firstly suggested minimum mean squared error estimator for estimation of 𝜃2 based on censored ranked set sample and their special case; further, they have suggested minimum mean squared error estimator for best linear unbiased estimator of 𝜃2 based on censored ranked set sample and their special cases; they also suggested minimum mean squared error estimator for estimation of 𝜃2 based on unbalanced multistage ranked set sampling and their special cases. Efficiency comparisons are also made in this work.

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Evaluation of Synthetic Small-area Estimators Using Design-based Methods

Austrian Journal of Statistics ◽

10.17713/ajs.v48i4.790 ◽

2019 ◽

Vol 48 (4) ◽

pp. 43-57

Author(s):

Partha Lahiri ◽

Santanu Pramanik

Keyword(s):

Sample Size ◽

Mean Squared Error ◽

Small Sample Size ◽

Small Sample ◽

Error Estimator ◽

Specific Design ◽

Small Areas ◽

Model Free ◽

Squared Error ◽

Better Than

The use of area-specific design-based mean squared error (MSE) to measure the uncertainty associated with synthetic and direct estimators is appealing since the same model-free criterion is applied. However, the small sample size is often a difficulty in obtaining a reliable estimator of the area-specific design-based MSE. Moreover, the area-specific design-based mean squared error estimator might yield undesirable negative values under certain circumstances. The existing solution to overcome the problem of small sample size is to consider average design-based MSE, average being taken over the available small areas. This may not solve the other problem of negative MSE. An alternative average design-based mean squared error estimator is proposed which always produces positive estimates. Simulation shows that this estimator performs better than the existing average design-based MSEs as it always produces positive estimates and accounts for the bias component usually present in synthetic estimators.

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