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Title of Thesis

Muhammad Hanif Mian
Institute/University/Department Details
University of the Punjab
Number of Pages
Keywords (Extracted from title, table of contents and abstract of thesis)
sampling, unequal probabilities, design and model based inference, estimator, design €“ based estimator, model-based variance estimator

After describing the basic theory of design- and model-based sampling inference and literature review, the controversy between those who accept Royall's model-based (prediction approach) to inference in finite population sampling and those who continue to use the design-based (randomization) principle even after twenty four years with special reference to Neyman (1934) is discussed. While discussing the controversy, the author has presented his own point of view.

A general estimator is introduced. The derivation of this estimator using a strictly design-based approach is given. Empirical and semi-empirical studies have been conducted to compare this new strictly design-based estimator with the existing design-based and model-based estimators.

The design- and model-based properties of this general class of estimators have also been discussed. An anticipated variance (Isaki and Fuller, 1982) is derived. It is also proved that the asymptotic form of the estimator under investigation is the Generalized Regression of Cassel, Sarndal and Wretman (1976). The predictive form of this estimator, like Basu (1971), is, presented. An exact and approximate lower bound of the mean square of this general class of estimators is derived and compared with the Godambe Joshi (1965) lower bound of variance. For this purpose, a natural course of action is to limit the class of estimators which are design and model-unbiased. Within this class, we have found the optimum estimator and then derived the lower bound. An approximation to an exact lower bound of mean square error is derived by using Brewer's (1979) concept of asymptotic unbiased ness.

A new model-based variance estimator is derived and compared with the existing design-based and model-based variance estimators. Some properties of the existing model-based estimators which remain unexplained so far are also discussed. Finally, a new selection procedure is introduced and using this selection procedure, the Generalized Murthy estimator (or revised ratio estimator) is de rived. The Generalized Murthy estimator is both design- and model-unbiased. A small sample performance of this new estimator is studied and it is found to be more stable than the Lahiri's (1951) ratio estimator, and it is as good as those of Horvitz and Thompson (1952) and Murthy (1957).

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2150.84 KB
S. No. Chapter Title of the Chapters Page Size (KB)
1 0 Contents
109.78 KB
2 1 Basic Theory And Survey Of Literature 1
483.97 KB
  1.1 Introduction 1
  1.2 Sampling With Unequal Probabilities 3
  1.3 Basic Theory Of Design €“ And Model €“ Based Inference 6
  1.4 Survey Of Literature 21
3 2 Design €“ And Model-Based Sampling Inference 46
288.71 KB
  2.1 Introduction 46
  2.2 The Establishment Of Probability Sampling Paradigm By Neyman 47
  2.3 Population Modeling 53
  2.4 The Present Situation 63
  2.5 Concluding Remarks 70
4 3 A Design €“ Based Estimator For Unequal Probability Sampling 72
277.16 KB
  3.1 Introduction 72
  3.2 Derivation Of Estimator Using A Strictly Design €“ Based Approach 77
  3.3 Unbiased Ness , Variance And Expected Variance Of The Design €“ Based Estimator 81
  3.4 Semi And Empirical Studies 84
  3.5 General Conclusion 89
5 4 A Design €“ And Model-Based Estimator 102
101.56 KB
  4.1 Introduction 102
  4.2 Design €“ And Model-Based Estimator 102
  4.3 Anticipated Variance Of Design-And Model-Unbiased Estimator (Y€™s ) 104
  4.4 Predictive From Of Estimator 110
6 5 A Model-Based Variance Estimator 113
246.28 KB
  5.1 Introduction 113
  5.2 Some Useful New Results 121
  5.3 A New Model-Based Variance Estimator 128
  5.4 Empirical Studies 130
  5.5 General Conclusion 133
7 6 Design €“ And Model Revised Ratio Estimator 140
157.39 KB
  6.1 Introduction 140
  6.2 The Class Of Generalized Murthy Estimator 143
  6.3 The New Selection Procedure 144
  6.4 The Revised Ratio Estimator 146
  6.5 Small Sample Performance Of The Revised Ratio Estimator 149
8 7 Lower Bound To Mean Square Error Of An Estimator 157
755.84 KB
  7.1 Introduction 157
  7.2 A Design €“And Model-Unbiased Estimator 160
  7.3 An Approximation To The Lower Bound 167
  7.4 Numerical Comparison 170
  7.5 References 187
  7.6 Appendix-1: Derivation Of Formula For Σ n j±1 1j When The Sample Size Is A Random Variable 204