Handling Missing Data in Ranked Set Sampling

verfasst von: Carlos N. Bouza-Herrera

Verlag: Springer Berlin Heidelberg

Buchreihe : SpringerBriefs in Statistics

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

Einloggen, um Zugang zu erhalten

Über dieses Buch

The existence of missing observations is a very important aspect to be considered in the application of survey sampling, for example. In human populations they may be caused by a refusal of some interviewees to give the true value for the variable of interest. Traditionally, simple random sampling is used to select samples. Most statistical models are supported by the use of samples selected by means of this design. In recent decades, an alternative design has started being used, which, in many cases, shows an improvement in terms of accuracy compared with traditional sampling. It is called Ranked Set Sampling (RSS). A random selection is made with the replacement of samples, which are ordered (ranked). The literature on the subject is increasing due to the potentialities of RSS for deriving more effective alternatives to well-established statistical models. In this work, the use of RSS sub-sampling for obtaining information among the non respondents and different imputation procedures are considered. RSS models are developed as counterparts of well-known simple random sampling (SRS) models. SRS and RSS models for estimating the population using missing data are presented and compared both theoretically and using numerical experiments.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Missing Observations and Data Quality Improvement

Abstract

Missing data is a well-recognized problem which arises in statistical inferences and data analysis. We address different possible ways to handle missing data, to ameliorate its effect on the reliability and accuracy of survey-based inferences. Subsampling the non-respondents and imputation of missing values, are considered as methods for dealing with non-responses. This book presents the work developed on Ranked Set Sampling (RSS) in dealing with missing data. RSS is a relatively new sampling design. This chapter may be considered as an introduction to the rest of the oeuvre.

Carlos N. Bouza-Herrera

Chapter 2. Sampling Using Ranked Sets: Basic Concepts

Abstract

Simple random sampling is the kernel of sampling theory. The basic theory of statistical inference is supported by the assumption of using samples selected by means of this design. During the last decade Ranked Set Sampling has appeared as a challenge to this design. It is implemented by selecting units with replacement and the sampled units are ordered (ranked). Each order statistic is observed once. This process can be repeated if needed to observe various realizations of each order statistic. A review of the most significant results is developed in this chapter, taking into account the modeling of missing data.

Carlos N. Bouza-Herrera

Chapter 3. The Non-response Problem: Subsampling Among the Non-respondents

Abstract

The existence of missing observations in the estimation problems present in random sampling can be considered unimportant. But the risk of misunderstanding is high because the non-responses may be generated by the existence of a very different behavior of a group of units. This is especially important when human populations are sampled. The solution of subsampling among the non-respondents is the most intelligent approach in such cases. The usual simple random sampling models are revisited and their ranked set sample counterpart developed. Generally they are more accurate.

Carlos N. Bouza-Herrera

Chapter 4. Imputation of the Missing Data

Abstract

We may consider the existence of missing observations as unimportant, considering that the risk of misunderstanding is negligible. The surveyor assumes some model that allows adequately explaining the variable of interest. In such cases, we are able to predict the unknown values and to plug them into some estimator. Generally, the models used for imputing in sampling are not complicated and rely on simple ideas. Imputation in simple random sampling has been developed for decades; the literature is increased yearly. Ranked Set Sampling (RSS) alternatives are presented in this chapter. The efficiency of this approach is supported for the different models. On some occasions the preference of RSS is doubtful and needs numerical comparisons.

Carlos N. Bouza-Herrera

Chapter 5. Some Numerical Studies of the Behavior of RSS

Abstract

The superiority of Ranked Set Sampling (RSS) models is measured by the comparison of the Mean Square Errors of the models with respect to their alternatives. The expressions support general evaluations of the gains in accuracy but their values depend on the underlying distribution or the characteristics of the studied population. We present some numerical studies for illustrating the behavior of RSS strategies.

Carlos N. Bouza-Herrera

Backmatter

Titel: Handling Missing Data in Ranked Set Sampling
verfasst von: Carlos N. Bouza-Herrera
Verlag: Springer Berlin Heidelberg
Electronic ISBN: 978-3-642-39899-5
Print ISBN: 978-3-642-39898-8
DOI: https://doi.org/10.1007/978-3-642-39899-5