共查询到20条相似文献,搜索用时 156 毫秒
1.
Sze-Man Tse 《Annals of the Institute of Statistical Mathematics》2006,58(4):675-686
In this paper, we consider a nonparametric estimator of the Lorenz curve and Gini index when the data are subjected to random
left truncation and right censorship. Strong Gaussian approximations for the associated Lorenz process are established under
appropriate assumptions. A law of the iterated logarithm for the Lorenz curve is also derived. Lastly, we obtain a central
limit theorem for the corresponding Gini index. 相似文献
2.
关于洛伦兹曲线和基尼系数的统计推断 总被引:1,自引:0,他引:1
本文对于洛伦兹曲线的最一般定义,在无任何附加限制条件下,论证了基于样本数据所得到的洛仑兹曲线的通常估计量具有强相合性.在此基础上,证明了基尼系数和Schutz系数的通常估计量均具有强相合性.此外,导出了基尼系数估计量的渐进分布,并在此基础上给出了大样本情形下基尼系数的置信区间. 相似文献
3.
T. S. K. Moothathu 《Annals of the Institute of Statistical Mathematics》1985,37(1):473-479
Summary This paper presents the maximum likelihood estimators (MLEs) of the Lorenz curve and Gini index of the exponential distribution,
their exact distributions and moments. All these MLEs are shown to converge almost surely and in therth mean. Further their asymptotic distributions are obtained. Here we use only very simple arguments to derive certain results
that are very useful in statistical study of ‘inequality’. 相似文献
4.
S. M. Tze 《Mathematical Methods of Statistics》2014,23(2):151-157
Concentration curve is the inverse Lorenz curve. Together, they form the basis for most measures of distributional inequality. In this paper, we consider the empirical estimator of the concentration curve when the data are subjected to random left truncation and/or right censorship. Simultaneous strong Gaussian approximations for the associated Lorenz and normed concentration processes are established under appropriate assumptions. Functional laws of the iterated logarithm for the two processes are established as easy consequences. The construction provides a solid foundation for the study of functional statistics based on the two processes. 相似文献
5.
Two extensions of the univariate Gini index are considered:RD, based on expected distance between two independent vectors from the same distribution with finite meanμ
d; andRV, related to the expected volume of the simplex formed fromd+1 independent such vectors. A new characterization ofRDas proportional to a univariate Gini index for a particular linear combination of attributes relates it to the Lorenz zonoid. TheLorenz zonoidwas suggested as a multivariate generalization of the Lorenz curve.RVis, up to scaling, the volume of the Lorenz zonoid plus a unit cube of full dimension. Whend=1, bothRDandRVequal twice the area between the usual Lorenz curve and the line of zero disparity. Whend>1, they are different, but inherit properties of the univariate Gini index and are related via the Lorenz zonoid:RDis proportional to the average of the areas of some two-dimensioned projections of the lift zonoid, whileRVis the average of the volumes of projections of the Lorenz zonoid over all coordinate subspaces. 相似文献
6.
In this paper, we propose several estimators of Gini index of the two-parameter exponential distribution and obtain distributions and moments of the proposed estimators. The proposed estimators are shown to cosistency and will be compared in terms of the mean squared error (MSE) through Monte Carlo method. 相似文献
7.
This article is concerned with proving the consistency of Efron’s bootstrap for the Kaplan–Meier estimator on the whole support of a survival function. While previous works address the asymptotic Gaussianity of the Kaplan–Meier estimator without restricting time, we enable the construction of bootstrap-based time-simultaneous confidence bands for the whole survival function. Other practical applications include bootstrap-based confidence bands for the mean residual lifetime function or the Lorenz curve as well as confidence intervals for the Gini index. Theoretical results are complemented with a simulation study and a real data example which result in statistical recommendations.
相似文献8.
农村卫生资源配置公平性研究——基于2003-2005年黑龙江省13个地区的数据分析 总被引:1,自引:0,他引:1
运用多种评价指标研究黑龙江省农村卫生资源配置公平性,发现黑龙江省十三个地区各类卫生资源的三种公平性指数高度一致;卫生资源主要是按人口分布配置的,且公平性在逐渐降低;哈尔滨市、绥化市等地区资源配置公平性较高.同时显示政府的认识和重视程度影响资源配置的公平性. 相似文献
9.
Gengsheng Qin Baoying Yang Nelly E. Belinga-Hall 《Annals of the Institute of Statistical Mathematics》2013,65(1):1-21
In this paper, we discuss empirical likelihood-based inferences for the Lorenz curve. The profile empirical likelihood ratio statistics for the Lorenz ordinate are defined under the simple random sampling and the stratified random sampling designs. It is shown that the limiting distributions of the profile empirical likelihood ratio statistics are scaled Chi-square distributions with one degree of freedom. We also derive the limiting processes of the associated empirical likelihood-based Lorenz processes. Hybrid bootstrap and empirical likelihood intervals for the Lorenz ordinate are proposed based on the newly developed empirical likelihood theory. Extensive simulation studies are conducted to compare the relative performances of various confidence intervals for Lorenz ordinates in terms of coverage probability and average interval length. The finite sample performances of the empirical likelihood-based confidence bands are also illustrated in simulation studies. Finally, a real example is used to illustrate the application of the recommended intervals. 相似文献
10.
11.
《Mathematical and Computer Modelling》2006,43(7-8):870-879
The Lorenz curve of a Zipf function describes, graphically, the relation between the fraction of the items and the fraction of the sources producing these items. Hence it generalizes the so-called 80/20-rule to general fractions.In this paper we examine the relation of such Lorenz curves with the size of the system (expressed by the total number of sources). We prove that the height of such a Lorenz curve is an increasing function of the total number of sources.In other words, we show that the share of items as a function of the corresponding share of sources increases with increasing size of the system. This conclusion is opposite (but not in contradiction) to a conclusion of Aksnes and Sivertsen (studied in an earlier paper of Egghe) but where “share of sources” is replaced by “number of sources”. 相似文献
12.
Generalized gini inequality indices 总被引:1,自引:0,他引:1
John A. Weymark 《Mathematical Social Sciences》1981,1(4):409-430
When incomes are ranked in descending order the social-evaluation function corresponding to the Gini relative inequality index can be written as a linear function withthe weights being the odd numbers in increasing order. We generalize this function by allowing the weights to be an arbitrary non-decreasing sequence of numbers. This results in a class of generalized Gini relative inequality indices and a class of generalized Gini absolute inequality indices. An axiomatic characterization of the latter class is also provided. 相似文献
13.
Petr Zizler 《Applications of Mathematics》2014,59(2):167-175
The expected value of the share density of the income distribution can be expressed in terms of the Gini index. The variance of the share density of the income distribution is interesting because it gives a relationship between the first and the second order Gini indices. We find an expression for this variance and, as a result, we obtain some nontrivial bounds on these Gini indices. We propose new statistics on the income distribution based on the higher moments of the share density function. These new statistics are easily computable from the higher order Gini indices. Relating these moments to higher order Ginis suggests new estimates on these quantities. 相似文献
14.
15.
《Stochastic Processes and their Applications》2002,97(2):307-340
We consider semiparametric fractional exponential (FEXP) estimators of the memory parameter d for a potentially non-stationary linear long-memory time series with additive polynomial trend. We use differencing to annihilate the polynomial trend, followed by tapering to handle the potential non-invertibility of the differenced series. We propose a method of pooling the tapered periodogram which leads to more efficient estimators of d than existing pooled, tapered estimators. We establish asymptotic normality of the tapered FEXP estimator in the Gaussian case with or without pooling. We establish asymptotic normality of the estimator in the linear case if pooling is used. Finally, we consider minimax rate-optimality and feasible nearly rate-optimal estimators in the Gaussian case. 相似文献
16.
Philip E Cheng 《Journal of multivariate analysis》1984,15(1):63-72
For a well-known class of nonparametric regression function estimators of nearest neighbor type the uniform measure of deviation from the estimators to the true regression function is studied. Under weak regularity conditions it is shown that the estimators are uniformly consistent with probability one and the corresponding rate of convergence is near-optimal. 相似文献
17.
On the basis of the limit theorem for quadratic variation, we construct a consistent estimator for parameters of a homogeneous Gaussian random field of a certain class. We find confidence ellipsoids for estimators of this sort. 相似文献
18.
In this paper, we study the issue of admissibility in the growth curve model with respect to restricted parameter sets under matrix loss function. We obtain some neces- sary and sufficient conditions that the linear estimators of KBL are admissible in the class of homogeneous linear estimators and in the class of non-homogeneous linear estimators under the growth curve model with respect to restricted parameter sets, respectively. 相似文献
19.
In this paper, we consider the symmetric Gaussian and L-Gaussian quadrature rules associated with twin periodic recurrence relations with possible variations in the initial coefficient. We show that the weights of the associated Gaussian quadrature rules can be given as rational functions in terms of the corresponding nodes where the numerators and denominators are polynomials of degree at most 4. We also show that the weights of the associated L-Gaussian quadrature rules can be given as rational functions in terms of the corresponding nodes where the numerators and denominators are polynomials of degree at most 5. Special cases of these quadrature rules are given. Finally, an easy to implement procedure for the evaluation of the nodes is described. 相似文献
20.
The purpose of this paper is, in the first step, to consider a class of GMM estimators with interesting asymptotic properties and a reasonable number of computations for two dimensionally indexed Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model. In the second step, we use the central limit theorem of Huang (1992) for spatial martingale differences to establish the LAN property for general two-dimensional discrete models on a regular grid with Gaussian errors. We then apply this result to the spatial GARCH model and derive the limit distribution of the maximum likelihood estimators of the parameters. Results of numerical simulations are presented. 相似文献