scholarly journals Confidence Intervals of Gini Coefficient Under Unequal Probability Sampling

2020 ◽  
Vol 36 (2) ◽  
pp. 237-249
Author(s):  
Yves G. Berger ◽  
İklim Gedik Balay
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Empirical Likelihood ◽  
Simulation Study ◽  
Gini Coefficient ◽  
Probability Sampling ◽  
Unequal Probability Sampling ◽  
Unequal Probability ◽  
The Gini Coefficient

AbstractWe propose an estimator for the Gini coefficient, based on a ratio of means. We show how bootstrap and empirical likelihood can be combined to construct confidence intervals. Our simulation study shows the estimator proposed is usually less biased than customary estimators. The observed coverages of the empirical likelihood confidence interval proposed are also closer to the nominal value.

scholarly journals Inference under unequal probability sampling with the Bayesian exponentially tilted empirical likelihood

Biometrika ◽  
2020 ◽  
Vol 107 (4) ◽  
pp. 857-873
Author(s):  
A Yiu ◽  
R J B Goudie ◽  
B D M Tom
Keyword(s):  
Bayesian Inference ◽  
Empirical Likelihood ◽  
Evidence Synthesis ◽  
Asymptotic Variance ◽  
Small Sample ◽  
Superior Performance ◽  
Probability Sampling ◽  
Unequal Probability Sampling ◽  
Unequal Probability ◽  
Von Mises

Summary Fully Bayesian inference in the presence of unequal probability sampling requires stronger structural assumptions on the data-generating distribution than frequentist semiparametric methods, but offers the potential for improved small-sample inference and convenient evidence synthesis. We demonstrate that the Bayesian exponentially tilted empirical likelihood can be used to combine the practical benefits of Bayesian inference with the robustness and attractive large-sample properties of frequentist approaches. Estimators defined as the solutions to unbiased estimating equations can be used to define a semiparametric model through the set of corresponding moment constraints. We prove Bernstein–von Mises theorems which show that the posterior constructed from the resulting exponentially tilted empirical likelihood becomes approximately normal, centred at the chosen estimator with matching asymptotic variance; thus, the posterior has properties analogous to those of the estimator, such as double robustness, and the frequentist coverage of any credible set will be approximately equal to its credibility. The proposed method can be used to obtain modified versions of existing estimators with improved properties, such as guarantees that the estimator lies within the parameter space. Unlike existing Bayesian proposals, our method does not prescribe a particular choice of prior or require posterior variance correction, and simulations suggest that it provides superior performance in terms of frequentist criteria.

Evaluation of sampling alternatives to quantify tree leaf area

2003 ◽  
Vol 33 (1) ◽  
pp. 82-95 ◽  
Author(s):  
H Temesgen
Keyword(s):  
Leaf Area ◽  
Poor Performance ◽  
Tree Crown ◽  
Two Stage ◽  
Zero Bias ◽  
Probability Sampling ◽  
First Order ◽  
Unequal Probability Sampling ◽  
Unequal Probability ◽  
Tree Leaf

High within- and among-tree crown variation have contributed to the difficulty of tree-crown sampling and single-tree leaf area (area available for photosynthesis) estimation. Using reconstructed trees, simulations were used to compare five sampling designs for bias, mean square error (MSE), and distribution of the estimates. All sampling designs showed nearly zero bias. For most sample trees, stratified random sampling resulted in the lowest MSE values, followed by ellipsoidal, two-stage systematic, simple random, and then by two-stage unequal probability sampling. The poor performance of two-stage unequal probability sampling can be ascribed to the unequal probability of inclusion of first-order branches and twigs.

scholarly journals A comparative study of the Gini coefficient estimators based on the linearization and U-statistics Methods

2017 ◽  
Vol 40 (2) ◽  
pp. 205-221 ◽  
Author(s):  
Shahryar Mirzaei ◽  
Gholam Reza Mohtashami Borzadaran ◽  
Mohammad Amini
Keyword(s):  
Comparative Study ◽  
Simulation Study ◽  
Gini Coefficient ◽  
Gini Index ◽  
Real Data ◽  
Linearization Method ◽  
U Statistics ◽  
The Gini Coefficient

In this paper, we consider two well-known methods for analysis of the Gini index, which are U-statistics and linearization for some incomedistributions. In addition, we evaluate two different methods for some properties of their proposed estimators. Also, we compare two methods with resampling techniques in approximating some properties of the Gini index. A simulation study shows that the linearization method performs 'well' compared to the Gini estimator based on U-statistics. A brief study on real data supports our findings.

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