T-Classes of Linear Estimators and the Thoery of Successive Sampling

Scientific Publishers India, 2010. Hardcover. New. 1. T-Classes Of Linear Estimators And Techniques Of Unordering And Combined Unordering (A) Definition Of T-Classes Of Linear Estimators Definition Of Ordered Set, Definition Of Sample 1.1 Tikkiwal'-S Partition Of Sample Space 1.2 Set Of T-Classes Of Linear Estimators 1.3 Wideness Of The Set Of Seven Classes Of Linear Estimators (B) Techniques Of Unordering And Combined Unordering 1.4 Unordering Of Estimators For Sampling With Varying Probabilities With Or Without Replacement - A Unified Approach 1.5 Murthy'-S Results Of Unordering Of Ordered Estimators For Sampling With Varying Probabilities Without Replacement 1.6 The Technique Of Combined Unordering 1.7 Applications Of Unordering And Combined Unordering 1.8 Unordering Of -Class Of Linear Estimators 1.9 Combined Unordering Of The Classical Srswr Estimator Exercises 2. -Class Estimators 2.1 Introduction 2.2 Estimators In -Class For Some Well Known Sampling Schemes: (A) Simple Random Sampling Schemes: Srswor And Srswr (B) Midzuno Scheme Of Sampling With Or Without Replacement Exercises 3. -Class Estimators 3.1 Introduction 3.2 A General Discussion Of -Class Estimators 3.3 Sampling With Varying Probabilities And Without Replacement : 3.3.1 The Variance Of Horvitz-Thompson Estimator 3.3.2 The Three Unbiased Estimators Of The Variance Of And Their Relative Merits 3.3.3 Non-Negative Variance Estimators 3.3.4 Calculation Of Probabilities Of Inclusion For Certain Sampling Schemes 3.4 Sampling With Varying Probabilities And With Replacement 3.5 Unequal Probability Sampling Without Replacement Due To Rao, Hartley And Cochran (A) Certain Preliminaries- (B) Rao-Hartley-Cochran Results 3.6 The Theory Of Multistage Sampling With Varying Probabilities And With Or Without Replacement 3.7 Comparison Of The Efficiency Of Estimators For Sampling With Varying Probabilities Without Replacement And With Replacement In Case Of Multistage Designs Exercises 4. Estimation In -Class 4.1 Introcuction 4.2 A Lemma In Quadratic Equation 4.3 Non-Existence Of Mvlue In The Class For Sampling Without Replacement 4.4 An Estimator In -Class For Midzuno Scheme Of Sampling Without Replacement 4.5 Non-Existence Of Mvlue In The Class For Sampling With Replacement 4.6 An Estimator In The Class For Midzuno Scheme Of Sampling With Replacement 4.7 A Unified Proof Of Non-Existence Of Mvlue In The Class For Sampling With Or Without Replacement Exercises 5. Estimation In -Class 5.1 Introduction 5.2 Non-Emptiness Of &Not-&Not--Class 5.3 Non-Existence Of Mvlue In The Class For Swor 5.4 Non-Existence Of Mvlue In The Class For Swr 5.5 Des Raj Ordered Estimator Exercises 6. Estimation In And -Classes 6.1 Introduction 6.2 Estimation In -Class For Sampling With Or Without Replacement 6.3 Estimation In -Class For Sampling With Or Without Replacement 6.4 Mvlue In -Class For Srswor 6.5 Mvlue In -Class For Srswr 6.6 Estimation In &Not--Class 6.7 Some Results Due To Godambe Exercises 7. Theory Of Successive Sampling 7.1 Introduction 7.2 Preliminary Results 7.3 Successive Sampling On H ( ) Occasions 7.4 A General Discussion On Unistage Successive Sampling With Varying Probabilities 7.5 A General Discussion On Multistage Successive Sampling.