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1 edition of A model approach to estimating the finite population Gini coefficient found in the catalog.

A model approach to estimating the finite population Gini coefficient

Arne Sandstrom

# A model approach to estimating the finite population Gini coefficient

## by Arne Sandstrom

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• 4 Currently reading

Published by Department of Statistics, University of Stockholm in Stockholm .
Written in English

The Physical Object
Pagination65 p.
Number of Pages65
ID Numbers
Open LibraryOL24715256M

The second measure, employed to make sure that any results were not sensitive to the use of the Gini coefficient as a measure of inequality (Messner et al. ), was the ratio of the income or consumption share of the top 20 per cent of the population relative to the bottom 20 per cent of the population. When using y to estimate the superpopulation mean |i, there is no finite population correction (f.p.c,) in the variance, but when using y to estimate the finite population mean Y, there is a finite population correction in the variajice. This point has been made by Deming [, p. ] aoid Cochran [, p. 37], Cochran says, in reference.

Measuring inequality in finite population sampling of the QSR can be estimated by means of the linearization approach without applying a kernel smoothing, and that a simple transformation enhances the Keywords survey sampling, variance estimation, Gini index, Lorenz curve, lin-earization, income, balanced sampling. (). An Empirical Likelihood Estimate of the Finite Population Correlation Coefficient. Communications in Statistics - Simulation and Computation: Vol. 43, No. 6, pp.

The Gini coefficient is sometimes used in classification problems. Gini = 2*AUC - 1, where AUC is the area under the curve (see the ROC curve entry above). A Gini ratio above 60% corresponds to a good model. The Gini coefficient (Gini ) has proved valuable as a measure of income inequality. In cross-sectional studies of the Gini coefficient, information about the accuracy of its estimates is crucial. We show how to use jackknife and linearization to estimate the variance of the Gini coefficient, allowing for the effect of the sampling design.

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### A model approach to estimating the finite population Gini coefficient by Arne Sandstrom Download PDF EPUB FB2

A generalised regression estimation procedure is proposed that can lead to much improved estimation of population characteristics, such as quantiles, variances and coefficients of variation.

The method involves conditioning on the discrepancy between an estimate of an auxiliary parameter and its known population : James G. Booth, Alan H. Welsh. The Gini coefficient and other standard inequality indices reduce to a common form. Perfect equality—the absence of inequality—exists when and only when the inequality ratio, = / ¯, equals 1 for all j units in some population (for example, there is perfect income equality when everyone's income equals the mean income ¯, so that = for everyone).).

Measures of inequality, then, are. This paper proposes a new model-based approach to small area estimation of general finite-population parameters based on grouped data or frequency data, which is often available from sample surveys.

Grouped data contains information on frequencies of some pre-specified groups in each area, for example the numbers of households in the income classes, Cited by: 2. In a total survey of a finite population, cf. Section 3, with the finite population df F., () becomes () and an estimate of () based on a sample survey is obtained by (i) estimating F., and (ii) changing FN for its estimate, sayN F, i.e.

() The last procedure is. 7. Conclusion. The regression approach is the simplest way to estimate the Gini coefficient and its SE; however, this analysis of the Gini estimator can produce weaker results because it does not account for potential shortcomings introduced in the proposed regression model.

It is important to note that actual data has defects when this method is used, despite the known shortcomings. The Gini. T o cite this article: W eidong Huang (): Numerical method to calculate Gini coefficient from limited data of subgroups, Applied Economics.

studying Gini estimation from ﬁnite population. F ollowing Langel and Till´ e (), the expression of the Gini index in case of a ﬁnite population U of size M is given by. In some finite sampling situations, there is a primary variable that is sampled, and there are measurements on covariates for the entire population.

A Bayesian hierarchical model for estimating totals for finite populations is proposed. A nonparametric linear model is assumed to explain the relationship between the dependent variable of interest and covariates. The regression coefficients. The original Gini coefficient given in corresponds to ψ {F (y)} = 2 F (y) − 1.

The finite population Gini coefficient is defined as θ N = N − 1 ∑ i = 1 N μ N − 1 ψ {F N (Y i)} Y i, which is the solution to the census estimating equation U N (θ, F N) = 1 N ∑ i = 1 N g (Y i, θ, F N (Y i)) = 0, where g (Y, θ, F) = ψ {F} Y − θ Y.

Sections through consider design-based, model-based and Bayes prediction of a finite population variance. Section considers some asymptotic properties of a sample regression coefficient. The next section considers pm -unbiased prediction of the slope parameter in the linear regression model.

We will be concerned with estimation of the finite population Gini coefficient RN, as defined by (), us-ing data from a probability sample s. An estimator, denoted by RN, is obtained in the fol-lowing way: In () we replace F with the estimated finite population DF.

primary interest if the finite population Gini coefficient is to be estimated. Point estimators of the Gini coefficient are given in Tablecf, Nygård and Sandströ (a)m, (b) where IT. deonote s the inclusion probability of unit i, ies, and s denotes the sample of fixed size n. But the principal aim is to make inference about the finite population inequality.

In a design approach it seems necessary to introduce assumptions on the asymptotic properties on the inclusion probabilities.

To avoid this, we introduce a superpopulation model within which the inference of the finite population inequalities is supposed to be made. o Scale independence: the Gini coefficient does not consider the size of the economy, the way it is measured, or whether it is a rich or poor country on average.

o Population independence: it does not matter how large the population of the country is. o Transfer principle: if income (less than the difference), is transferred from a rich person to a poor person the resulting distribution.

This paper proposes the κ-generalized distribution as a model for describing the distribution and dispersion of income within a population. Formulas for the shape, moments and standard tools for inequality measurement–such as the Lorenz curve and the Gini coefficient–are given. A method for parameter estimation is also discussed.

estimation of the Gini index have prompted a great amount of research in statistics and economics. The main contributions of this section is to present and compare some di erent approaches to ariancev estimation of the Gini index.

The linearization technique. The linearization combines a range of tech. On estimating variances for Gini coefficients with complex surveys: theory and application we explore two finite sample properties of the Gini coefficient estimator: bias of the estimator and empirical coverage probabilities of interval estimators for the Gini coefficient.

Although the bootstrap approach often generates slightly smaller. Abstract: In this paper, nonparametric regression is employed which provides an estimation of unknown finite population totals.

A robust estimator of finite population totals in model based inference is constructed using the procedure of local linear regression. In Section 2, we describe the finite population mixed model.

In Section 3, we derive estimators of linear combinations of the latent values (of which B is a special case). In Section 4, we present numerical examples to compare the performance of the proposed estimator of B with that of the ordinary least squares estimator, B ̂ also include results from a.

Downloadable (with restrictions). In this paper we estimate income distributions, Lorenz curves and the related Gini index using a Bayesian nonparametric approach based on Polya tree priors.

In particular, we propose an alternative approach for dealing with contaminated observations and extreme income values: avoiding the common practise that removes these critical data, we.

(). Numerical method to calculate Gini coefficient from limited data of subgroups. Applied Economics Letters: Vol. 20, No. 13, pp. Complete coverage of the prediction approach to survey sampling in a single resource Prediction theory has been extremely influential in survey sampling for nearly three decades, yet research findings on this model-based approach are scattered in disparate areas of the statistical literature.

Finite Population Sampling and Inference: A Prediction Approach presents for the. The standard errors of Gini and Zenga coefficients were estimated by means of the bootstrap and the parametric approach based on the Dagum model. Keywords Income distribution * Income inequality * Variance estimation JEL C10 * J30 Introduction Measures of inequality are widely used to study income, welfare, and poverty issues.