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2003 | Buch

Basic Concepts and Mathematical Notation Kapitel lesen Erstes Kapitel lesen

Advanced Sampling Theory with Applications

How Michael ‘ selected’ Amy Volume I

verfasst von: Sarjinder Singh

Verlag: Springer Netherlands

Enthalten in: Professional Book Archive

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Über dieses Buch

This book is a multi-purpose document. It can be used as a text by teachers, as a reference manual by researchers, and as a practical guide by statisticians. It covers 1165 references from different research journals through almost 1900 citations across 1194 pages, a large number of complete proofs of theorems, important results such as corollaries, and 324 unsolved exercises from several research papers. It includes 159 solved, data-based, real life numerical examples in disciplines such as Agriculture, Demography, Social Science, Applied Economics, Engineering, Medicine, and Survey Sampling. These solved examples are very useful for an understanding of the applications of advanced sampling theory in our daily life and in diverse fields of science. An additional 173 unsolved practical problems are given at the end of the chapters. University and college professors may find these useful when assigning exercises to students. Each exercise gives exposure to several complete research papers for researchers/students.

Inhaltsverzeichnis

Frontmatter
1. Basic Concepts and Mathematical Notation
Abstract
In this chapter we introduce some basic concepts and mathematical notation, which should be known to every survey statistician. The meaning and the use of these terms is supported by using them in the subsequent chapters.
Sarjinder Singh
2. Simple Random Sampling
Abstract
Simple Random Sampling (SRS) is the simplest and most common method of selecting a sample, in which the sample is selected unit by unit, with equal probability of selection for each unit at each draw. In other words, simple random sampling is a method of selecting a sample s of n units from a population Ω of size N by giving equal probability of selection to all units. It is a sampling scheme in which all possible combinations of n units may be formed from the population of N units with the same chance of selection.
Sarjinder Singh
3. Use of Auxiliary Information: Simple Random Sampling
Abstract
It is well known that suitable use of auxiliary information in probability sampling results in considerable reduction in the variance of the estimators of population parameters viz. population mean (or total), median, variance, regression coefficient, and population correlation coefficient, etc.. In this chapter we will consider the problem of estimation of different population parameters of interest to survey statisticians using known auxiliary information under SRSWOR and SRSWR sampling schemes only. Before proceeding further it is necessary to define some notation and expected values, which will be useful throughout this chapter.
Sarjinder Singh
4. Use of Auxiliary Information: Probability Proportional to Size and with Replacement (PPSWR) Sampling
Abstract
Through the previous chapter we have seen that the proper use of auxiliary information at the estimation stage for estimating any population parameter results in a gain in the efficiency of the resultant estimators. For example, the product and ratio estimators of the population mean remain better than the sample mean when the correlation between the study variable and the auxiliary variable lies in the interval [−1.0,−0.5) and (+0.5, + 1.0], respectively. In this chapter we shall show that the auxiliary information can also be used to select a sample which can provide better estimators of population parameters. In other words, the auxiliary information can be used at the sample selection stage as well as at the estimation stage. A sampling scheme with replacement in which each sampling unit has unequal probability of selection, the probability being proportional to the size of the auxiliary variable associated with the particular unit, is called probability proportional to size and with replacement (PPSWR) sampling scheme.
Sarjinder Singh
5. Use of Auxiliary Information: Probability Proportional to Size and Without Replacement (PPSWOR) Sampling
Abstract
In probability proportional to size and without replacement (PPSWOR) sampling scheme, we will discuss the Horvitz and Thompson (1952) estimator, two forms of the variance of the Horvitz and Thompson (1952) estimator and their estimators, superpopulation model, construction of inclusion probabilities, calibrated estimators of population total and calibrated estimators of variance of the estimators of total like ratio estimator, linear regression estimator, regression predictor, distribution function, Rao, Hartley, and Cochran (1962) sampling scheme, unbiased estimation strategies under IPPS sampling and unified approach. At the end, we will celebrate Golden Jubilee Year 2003 of the traditional linear regression estimator owed to Hansen, Hurwitz, and Madow (1953). Before going further we would like to define a few important symbols and mathematical relations.
Sarjinder Singh
6. Use of Auxiliary Information: Multi-Phase Sampling
Abstract
In the previous chapters we have seen that use of known auxiliary information at the estimation stage as well as at the selection stage leads to improved estimation strategies in survey sampling. When such information is not completely known or lacking and it is relatively cheaper to obtain information on the auxiliary variable(s), one can consider taking a large preliminary sample for estimating population mean(s) of the auxiliary variable(s) to be used at the estimation or selection stage of the ultimate estimation strategies. For example, in the case of single auxiliary variable X, since it is cheaper to obtain information on X, we consider taking a large preliminary sample for estimating population mean. \( \bar X \) or distribution of X as the case may be, and only a small sample (some times a subsample) for measuring the study variable Y.
Sarjinder Singh
7. Systematic Sampling
Abstract
Sampling scheme in which only the first unit is selected at random, the rest being automatically selected according to a predetermined pattern is known as systematic sampling. Systematic sampling provides a very simple sampling design in practice to select a sample of size n from a population of size N. Systematic sampling is both operationally convenient and efficient in sampling some natural populations like forest areas for estimating the volume of timber and hardwood seedlings, etc..
Sarjinder Singh
8. Stratified and Post-Stratified Sampling
Abstract
Stratified and post-stratified sampling schemes are useful survey techniques commonly used by government agencies, private consultants, and applied statisticians. Let us differentiate between stratified and post-stratified sampling.
Sarjinder Singh
9. Non-Overlapping, Overlapping, Post, and Adaptive Cluster Sampling
Abstract
In survey sampling the basic assumption is that the population consists of a finite number of distinct and identifiable units. A group of such units is called a cluster. If, instead of randomly selecting a unit for sample, a group of units is selected as a single unit in the sample, it is called cluster sampling. If the entire area containing the population under study is divided into smaller segments, and if each unit of the population belongs to only one segment, the procedure is called area sampling or non-overlapping cluster sampling. If one or a few units appears in more than one segment or cluster, then such a procedure is called overlapping cluster sampling. The main purpose of cluster sampling is to divide the population into small groups with each group serving as a sample unit. Clusters are generally made up of neighbouring elements; therefore the elements within a cluster tend to be homogeneous. However at some stage in the research we become interested in heterogeneous clusters rather than homogeneous. More broadly, the concept of forming strata in the previous chapter was to form homogeneous groups, whereas in this chapter the concept of forming clusters will be to form groups of a heterogeneous nature. After dividing the population into clusters the sample of clusters can be selected with either equal or unequal probability. The concept of unequal probability may be based on the size of the cluster; that is, the larger the cluster, the larger the probability of its being selected in the sample. All the units in the selected cluster will be enumerated. As a simple rule the number of units in a cluster should be small and the number of clusters should be large.
Sarjinder Singh
10. Multi-Stage, Successive, and Re-Sampling Strategies
Abstract
The meaning of multi-stage sampling is clear from its name. Here we have several stages for the sample selection. In fact it is an extension of the concept of cluster sampling. Similar to cluster sampling first we divide the population into M clusters or heterogeneous groups. We select m clusters and use the estimates of cluster means or totals to form population estimate. For example, in two-stage sampling we again divide our population into M groups and select a sample of groups, which form the first stage sample. The units so selected are called first stage units (FSU).
Sarjinder Singh
11. Randomized Response Sampling: Tools For Social Surveys
Abstract
The randomized response technique (RRT) is useful for reducing response error problems when potentially sensitive questions such as the illegal use of drugs, sexual practice, illegal earning, or incidence of acts of domestic violence are included in surveys of human populations. Direct questioning of respondents about sensitive issues often results in either refusal of falsification of the answers. Social stigma and fear of reprisals sometimes result in untruthful, exaggerated, or misleading responses by respondents when apporached with conventional survey methods. Warner (1965) was the first to suggest an ingenious mehtod of counteracting fears in response to sensitive questions.
Sarjinder Singh
12. Non-Response and Its Treatments
Abstract
Incompleteness or non-response in the form of absence, censoring, or grouping is a troubling issue of many data sets. Statisticians have recognized for some time that failure to account for the stochastic nature of incompleteness or non-response can spoil the nature of data. There are several factors which effect the non-response rate in any particular inquiry. Some of these factors are the type of information being collected, the official status of the surveying agency, the extent of publicity, the legal obligations of the respondents, the time of visit by the enumerator and length of the schedule, etc.. Hansen and Hurwitz (1946) were the first to deal with the problem of incomplete samples in mail surveys. It is a well known fact that mail surveys or telephone surveys are most commonly used by most of the bureaucratic or business organisations because of their low cost. Rubin (1976) has defined three key concepts: Missing at random (MAR), Observed at random (OAR), and parameter distinctness (PD).
Sarjinder Singh
13. Miscellaneous Topics
Abstract
The main purpose of this chapter is to keep this book open to the new topics coming in the recent years or which have not been touched upon by the author in the present version of the book. In this chapter we shall introduce a few miscellaneous topics namely:
(a)
Estimation of Measurement Errors; (b) Raking Ratio Estimators;
 
(c)
Continuous Populations; and (d) Small Area Estimation.
 
Sarjinder Singh
Backmatter
Metadaten
Titel
Advanced Sampling Theory with Applications
verfasst von
Sarjinder Singh
Copyright-Jahr
2003
Verlag
Springer Netherlands
Electronic ISBN
978-94-007-0789-4
Print ISBN
978-94-010-3728-0
DOI
https://doi.org/10.1007/978-94-007-0789-4