I= SAMPLING WITH UNEQUAL PROBABILITIES AND WITHOUT REPLACEMENT
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Title of Thesis
SAMPLING WITH UNEQUAL PROBABILITIES AND WITHOUT REPLACEMENT

Author(s)
Muhammad Qaiser Shahbaz
Institute/University/Department Details
National College Of Business Administration And Economics
Session
2003
Subject
Economics
Number of Pages
183
Keywords (Extracted from title, table of contents and abstract of thesis)
unequal probability sampling , unbiasedness, survey sampling, inclusion probabilities, estimator

Abstract
After describing the basic theory of survey sampling with reference to equal and unequal probability sampling, some selected selection procedures have been discussed, which can be used with Horvitz and Thompson estimator. Some of the popular estimators of population total (other than the Horvitz – Thompson estimator) have been discussed. The Model based sampling inference has been presented along with the famous model based estimators.

Some approximate formulae for variance of the Horvitz – Thompson estimator that use only the first order inclusion probabilities have been obtained. Some special cases of these approximations have been given. Three new selection procedures for use with Horvitz – Thompson estimator have been developed. These selection procedures are applicable for a sample of size two and are strictly without replacement. Some fundamental results related to inclusion probabilities and joint inclusion probabilities have been verified for these newly developed selection procedures. Empirical study for these new selection procedures have been carried out in order to see their performance for various types of populations. The regression analysis has been carried out in order to see the effect of coefficient of variation and correlation coefficient on the variance of these estimators. It has been found that these two coefficients have significant effect on the variance of Horvitz – Thompson estimator under the newly developed selection procedures.

A general procedure has been developed by introducing a constant in the revised probabilities of selection that helps in developing a number of other selection procedures. It has been found that the Yates – Grundy draw-by-draw (1953) and the Brewer (1963a) procedures are special cases of the general selection procedure Empirical study has been conducted to obtain a suitable value of the constant for various sorts of populations.

A series of modified Murthy estimators has been developed by using the general Murthy (1957) estimator. These estimators have been developed by using various selection procedures in the general Murthy (1957) estimator. It has been found that the estimator used by Durbin (1953) for his rejective procedure is a special case of Murthy (1957) estimator under the Durbin (1967) draw-by-draw procedure. The unbiasedness of the new estimators has been verified and their design-based variances have been obtained. Empirical study has been carried out in order to see the performance of the new estimators. The model based study of the modified Murthy estimator under the Durbin (1953) draw-by-draw procedure has been conducted and it is found that this estimator achieves the Godambe – Joshi (1965) lower bound to the variance of any estimator in unequal probability sampling.

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1230.45 KB
S. No. Chapter Title of the Chapters Page Size (KB)
1 0 Contents
86.83 KB
2 1 Basic Theory And Survey Of Literature 1
271.89 KB
  1.1 Introduction 1
  1.2 Unequal Probability Sampling With Replacement 5
  1.3 Unequal Probability Sampling Without Replacement – Using Horvitz – Thompson Estimator 6
  1.4 Description Of Selected Selection Procedures 14
  1.5 Unequal Probability Sampling Without Replacement – Using Special Estimators 18
  1.6 The Model Based Inference In Sampling 22
  1.7 Chronological Development 24
3 2 First Order Inclusion Probabilities 35
57.08 KB
  2.1 Introduction
  2.2 An Alternative Expression For Variance Of Horvitz – Thompson Estimator 35
  2.3 Approximations For 38
4 3 The New Selection Procedures 43
322.27 KB
  3.1 Introduction 43
  3.2 The New Selection Procedures 43
  3.3 Some Useful Results For The New Selection Procedures 50
  3.4 Empirical Study 59
  3.5 Conclusions 79
5 4 The General Selection Procedure 83
195.22 KB
  4.1 Introduction 83
  4.2 The General Selection Procedure 83
  4.3 Some Useful Results For The General Selection Procedure 85
  4.4 Two Special Cases For The General Selection Procedure 88
  4.5 Empirical Study 90
  4.6 Conclusions 109
6 5 Series Estimators 113
84.42 KB
  5.1 Introduction 113
  5.2 Modified Murthy Estimators 113
  5.3 Unbiasedness Of The Modified Estimators 117
7 6 Design Based Study 125
240.6 KB
  6.1 Introduction 125
  6.2 Design Based Variances 125
  6.3 Empirical Study 135
  6.4 Conclusions 153
8 7 The Model Based Study 157
107.11 KB
  7.1 Introduction 157
  7.2 Model Based Study Of New Estimator – II 157
  7.3 Empirical Study 160
  7.4 Conclusions 171
9 8 References 172
98.96 KB