On the hidden truncated bivariate Pareto (IV) model and associated inferential issues

Income and wealth data are typically modelled by some variant of the classical Pareto distribution. Often, in practice, the observed data are truncated with respect to some unobserved covariate. In this paper, a hidden truncation formulation of this scenario is proposed and analysed. For this purpose, a bivariate Pareto (IV) distribution is assumed for the variable of interest and the unobserved covariate. Some important distributional properties of the resulting model as well as associated inferential methods are studied. An example is used finally to illustrate the results developed here. In this case, it is noted that hidden truncation on the left does not result in any new model, but the hidden truncation on the right does. The properties and fit of such a model pose a challenging problem and that is what is focused here in this work.     

On some robust estimation procedures for quantiles based on data

This paper introduces some robust estimation procedures to estimate quantiles of a continuous random variable based on data, without any other assumptions of probability distribution. We construct a reasonable linear regression model to connect the relationship between a suitable symmetric data transformation and the approximate standard normal statistics. Statistical properties of this linear regression model and its applications are studied, including estimators of quantiles, quartile mean, quartile deviation, correlation coefficient of quantiles and standard errors of these estimators. We give some empirical examples to illustrate the statistical properties and apply our estimators to grouping data.     

关于等比分位抽样的有关结果

在概率空间的基础上,提出了比等距抽样更广泛的等比分位抽样的概念,依据等比抽样样本,构造出总体均值估计的统计量。通过对其性质的讨论,证明了该统计量为总体均值的无偏估计,在适当的条件下,得出了该估计量的抽样精度高于简单随机抽样的结论。     

Estimating the population mean in the case of missing data using simple random sampling

In this paper, we suggest three new ratio estimators of the population mean using quartiles of the auxiliary variable when there are missing data from the sample units. The suggested estimators are investigated under the simple random sampling method. We obtain the mean square errors equations for these estimators. The suggested estimators are compared with the sample mean and ratio estimators in the case of missing data. Also, they are compared with estimators in Singh and Horn [Compromised imputation in survey sampling, Metrika 51 (2000), pp. 267–276], Singh and Deo [Imputation by power transformation, Statist. Papers 45 (2003), pp. 555–579], and Kadilar and Cingi [Estimators for the population mean in the case of missing data, Commun. Stat.-Theory Methods, 37 (2008), pp. 2226–2236] and present under which conditions the proposed estimators are more efficient than other estimators. In terms of accuracy and of the coverage of the bootstrap confidence intervals, the suggested estimators performed better than other estimators.     

Bootstrap confidence intervals for the coefficient of quartile variation

ABSTRACT

In non-normal populations, it is more convenient to use the coefficient of quartile variation rather than the coefficient of variation. This study compares the percentile and t-bootstrap confidence intervals with Bonett's confidence interval for the quartile variation. We show that empirical coverage of the bootstrap confidence intervals is closer to the nominal coverage (0.95) for small sample sizes (n = 5, 6, 7, 8, 9, 10 and 15) for most distributions studied. Bootstrap confidence intervals also have smaller average width. Thus, we propose using bootstrap confidence intervals for the coefficient of quartile variation when the sample size is small.