Inequality restricted linear selection indices

The problem of construction of selection indices with arbitrary linear inequality constraints on covariances is considered. The selection indices suggested by Smith (1936), Kempthorne Nordskog (1959) Tall is (1962) are shown as special cases. A method of solution is presented and prediction errors of various indices are compared. The method is applied to the example given in Kempthorne Nordskog (1959).     

Inequality indices: theoretical and empirical aspects of their asymptotic behaviour

The authors use a Berry-Esseen type bound to identify the factors which influence the speed of convergence to the normal distribution of the indices of Gini, Piesch and Mehran. To empirically confirm the conclusions reached, a Monte Carlo experiment is performed for a log-logistic distribution.     

Inequality indices and the starshaped principle of transfers

The evaluation of income distributions is usually based on the Pigou-Dalton (PD) principle which says that a transfer from any people to people who have less decreases economic inequality, i.e., increases the social evaluation index. We introduce two weaker principles of transfers which refer to a parameter θ. With the new principles, only those PD transfers increase the social evaluation index which take from the class of incomes above θ and give to the class below θ. The relative positions of individuals remain unchanged, and either no individual may cross the line θ (principle of transfers about θ) or some may do who have been situated next to it (starshaped principle of transfers at θ). θ may be a given constant, a function of mean income, or a quantile of the income distribution. The classes of indices which are consistent with these transfers are completely characterized, and examples are given.     

On a generalization of Poisson sampling

In real-time sampling, the units of a population pass a sampler one by one. Alternatively the sampler may successively visit the units of the population. Each unit passes only once and at that time it is decided whether or not it should be included in the sample. The goal is to take a sample and efficiently estimate a population parameter. The list sequential sampling method presented here is called correlated Poisson sampling. The method is an alternative to Poisson sampling, where the units are sampled independently with given inclusion probabilities. Correlated Poisson sampling uses weights to create correlations between the inclusion indicators. In that way it is possible to reduce the variation of the sample size and to make the samples more evenly spread over the population. Simulation shows that correlated Poisson sampling improves the efficiency in many cases.     

On a recent generalization of gamma distribution

In this paper, we investigate a generalized gamma distribution recentIy developed by Agarwal and Kalla (1996). Also, we show that such generalized distribution, like the ordinary gamma distribution, has a unique mode and, unlike the ordinary gamma distribution, may have a hazard rate (mean residual life) function which is upside-down bathtub (bathtub) shaped.     

Efficiency bounds for a generalization of ranked-set sampling

Abstract

Partially rank-ordered set sampling (PROSS) is a generalization of ranked-set sampling (RSS) in which the ranker is not required to give a full ranking in each set. In this paper, we compare the efficiency of the sample mean as an estimator of the population mean under PROSS, RSS, and simple random sampling (SRS). We find that for fixed set size and total sample size, the efficiency of PROSS falls between that of SRS and that of RSS. We also develop a method for finding a sharp upper bound on the efficiency of PROSS relative to SRS for a particular design.     

Depth functions as measures of representativeness

Data depth provides a natural means to rank multivariate vectors with respect to an underlying multivariate distribution. Most existing depth functions emphasize a centre-outward ordering of data points, which may not provide a useful geometric representation of certain distributional features, such as multimodality, of concern to some statistical applications. Such inadequacy motivates us to develop a device for ranking data points according to their “representativeness” rather than “centrality” with respect to an underlying distribution of interest. Derived essentially from a choice of goodness-of-fit test statistic, our device calls for a new interpretation of “depth” more akin to the concept of density than location. It copes particularly well with multivariate data exhibiting multimodality. In addition to providing depth values for individual data points, depth functions derived from goodness-of-fit tests also extend naturally to provide depth values for subsets of data points, a concept new to the data-depth literature.     

On a further generalization of the savage test

A statistic based on the frequencies within the k+1 intervals specified by k arbitrary quantiles is proposed for a LMP test against Lehmann alternatives generalizing the Savage test for the two-sample problem. The maximum efficiency relative to the Savage test for optimally chosen k quantiles is also provided for k=l(2)l5. The asymptotic normality of the statistic follows from the asymptotic multinomial distribution of the frequencies in the classes determined by the k quantiles.     

Markov's Inequality and Chebyshev's Inequality for Tail Probabilities: A Sharper Image

Markov's inequality gives an upper bound on the probability that a nonnegative random variable takes large values. For example, if the random variable is the lifetime of a person or a machine, Markov's inequality says that the probability that an individual survives more than three times the average lifetime in the population of such individuals cannot exceed one-third. Here we give a simple, intuitive geometric interpretation and derivation of Markov's inequality. These results lead to inequalities sharper than Markov's when information about conditional expectations is available, as in reliability theory, demography, and actuarial mathematics. We use these results to sharpen Chebyshev's tail inequality also.     

Pairwise conditional score functions: a generalization of the Mantel–Haenszel estimator

Pairwise conditional score functions are proposed and explored. They provide us with an interpretation on the Mantel–Haenszel estimator, and are applicable to deriving the Mantel–Haenszel-type estimators under the exponential dispersion model with multiple strata. Explicit forms of the estimating functions are presented, and the asymptotic relative efficiency is examined in the cases of the exponential and the geometric distributions. The derivation and the numerical results suggest that the derived estimators are fairly robust and show high efficiency as the Mantel–Haenszel estimator.     

一种反映收入差异程度的新指标——余期望系数

反映收入分配差异大小人们使用最多的指标是基尼系数.但是,基尼系数计算繁杂精度不高而导致不确定性和不可比性.其原因,除了其基础数据采集常常来自抽样调查,精度受样本代表性影响外,还有三个主要原因:一是,精确的洛伦茨曲线难以得到,即一组数据对应的洛伦茨曲线不是唯一的;二是,基尼系数数值等于一个由洛伦茨曲线围成的不规则图形的面积,因此只能采用近似的方法计算;三是,基尼系数计算过程中要将各收入单位进行人为分组,所得出的基尼系数值与分组状况直接相关.     

代际视角下机会不平等与农村居民收入差距

运用中国健康与营养调查(CHNS)1989-2011年的数据,采用夏普里值分解法考察了父代收入对农村子代收入差距的贡献及其变化。研究发现:1989-2011年间,父代收入对子代收入差距的贡献率一直较大。随着中国市场化程度以及经济水平的提高,尽管父代收入对农村子代收入差距的贡献率在2009年前总体上呈现出下降的趋势,但是2009年后其贡献率迅速上升。与此同时,教育因素的贡献率处于较低水平,这表明近年来机会不平等对收入差距的影响有所扩大。     

On a generalization of polynomials in the ballot problem

This work gives two generalizations of polynomials in the ballot problem based on a dual relation for addition formulas by Watanabe (1984, 1985).One is given by solving an interpolation problem in the case of several variables. In the case of one variable, Niederhausen (1981) developed a theory of some rank order statistic based on this problem.On the other hand, Takács' urn model gives a multinomial generalization of the Gould polynomials. Since the Gould polynomials are the special case of basic polynomials, by obtaining a theory of multinomial basic polynomials with several variables, we give a generalization of polynomials in Takács' urn model.     

Generalized ridge regression and a generalization of the CP statistic

We consider a generalization of ridge regression and demonstrate advantages over ridge regression. We provide an empirical Bayes method for determining the ridge constants, using the Bayesian interpretation of ridge estimators, and show that this coincides with a method based on a generalization of the C_P statistic and the non-negative garrote. These provide an automatic variable selection procedure for the canonical variables.     

Log-epsilon-skew normal: A generalization of the log-normal distribution

Abstract

The log-normal distribution is widely used to model non-negative data in many areas of applied research. In this paper, we introduce and study a family of distributions with non-negative reals as support and termed the log-epsilon-skew normal (LESN) which includes the log-normal distributions as a special case. It is related to the epsilon-skew normal developed in Mudholkar and Hutson (2000 Mudholkar, G. S., and A. D. Hutson. 2000. The epsilon-skew-normal distribution for analyzing near-normal data. Journal of Statistical Planning and Inference 83 (2):291–309. doi:10.1016/S0378-3758(99)00096-8.[Crossref], [Web of Science ®] , [Google Scholar]) the way the log-normal is related to the normal distribution. We study its main properties, hazard function, moments, skewness and kurtosis coefficients, and discuss maximum likelihood estimation of model parameters. We summarize the results of a simulation study to examine the behavior of the maximum likelihood estimates, and we illustrate the maximum likelihood estimation of the LESN distribution parameters to two real world data sets.