An approximation method to derive confidence intervals for quantiles with some applications

Standard jackknife confidence intervals for a quantile Q _y (β) are usually preferred to confidence intervals based on analytical variance estimators due to their operational simplicity. However, the standard jackknife confidence intervals can give undesirable coverage probabilities for small samples sizes and large or small values of β. In this paper confidence intervals for a population quantile based on several existing estimators of a quantile are derived. These intervals are based on an approximation for the cumulative distribution function of a studentized quantile estimator. Confidence intervals are empirically evaluated by using real data and some applications are illustrated. Results derived from simulation studies show that proposed confidence intervals are narrower than confidence intervals based on the standard jackknife technique, which assumes normal approximation. Proposed confidence intervals also achieve coverage probabilities above to their nominal level. This study indicates that the proposed method can be an alternative to the asymptotic confidence intervals, which can be unknown in practice, and the standard jackknife confidence intervals, which can have poor coverage probabilities and give wider intervals.     

Estimation of poverty measures with auxiliary information in sample surveys

The analysis of poverty measures has been receiving increased attention in recent years. This paper contributes to the literature by developing percentile ratio estimators based on the pseudo empirical likelihood method. In practice, variances of poverty measures could be not expressible by simple formulae and consequently other techniques should be used in the variance estimation stage. Assuming percentile ratios, resampling techniques are investigated in this paper. A numerical example based on data from the Spanish Household Panel Survey is taken up to illustrate how suggested procedures can perform better than existing ones. The effect of a model-misspecification on the proposed estimators is also evaluated by using simulated populations.     

Pseudo empirical likelihood method in the presence of missing data

In this paper, we propose an estimator for the population mean when some observations on the study and auxiliary variables are missing from the sample. The proposed estimator is valid for any unequal probability sampling design, and is based upon the pseudo empirical likelihood method. The proposed estimator is compared with other estimators in a simulation study.     

A mixed-mode sensitive research on cannabis use and sexual addiction: improving self-reporting by means of indirect questioning techniques

In this article, we describe the methods employed and the results obtained from a mixed-mode “sensitive research” conducted in Spain to estimate certain aspects concerning patterns of cannabis consumption and sexual addiction among university students. Three different data-collection methods are considered and compared: direct questioning, randomized response technique and item sum technique. It is shown that posing direct questions to obtain sensitive data produces significantly lower estimates of the surveyed characteristics than do indirect questioning methods. From the analysis, it emerges that male students seem to be more affected by sex addiction than female students while for cannabis consumption there is no evidence of a predominant gender effect.     

Nonparametric methods in sample surveys. Application to the estimation of cancer prevalence

We address the problem of the estimation of the population mean and the distribution function using nonparametric regression. These methods are being used in a wide range of settings and areas of research. In particular, they are a good alternative to other classical methods in the survey sampling context, since they work under the assumption that the underlying regression function is smooth. Some relevant nonparametric regression methods in survey sampling are presented. Data on breast cancer prevalence derived from 40 European countries are used to study the application of the nonparametric estimators to the estimation of cancer prevalence. Result derived from an empirical study show that nonparametric estimators have a good empirical performance in this study on cancer prevalence.     

Successive Sampling to Estimate Quantiles with P-Auxiliary Variables

The successive sampling is a known technique that can be used in longitudinal surveys to estimate population parameters and measurements of difference or change of a study variable. The paper discusses the estimation of quantiles for the current occasion based on sampling in two successive occasions and using p-auxiliary variables obtained of the previous occasion. A multivariate ratio estimator from the matched portion is used to provide the optimum estimate of a quantile by weighting the estimates inversely to derived optimum weights. Its properties are studied under large–sample approximation and the expressions of the variances are established. The behavior of these asymptotic variances is analyzed on the basis of data from natural populations. A simulation study is also used to measure the precision of the proposed estimator.