Sampling Theory For the Ecological and Natural Resource Sciences

We present a rigorous but understandable introduction to the field of sampling theory for ecologists and natural resource scientists. Sampling theory concerns itself with development of procedures for random selection of a subset of units, a sample, from a larger finite population, and with how to b...

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Bibliographic Details
Main Authors Hankin, David, Mohr, Michael S, Newman, Kenneth B
Format eBook
LanguageEnglish
Published Oxford Oxford University Press 26.09.2019
Oxford University Press, Incorporated
Edition1
Subjects
Biomathematics and Statistics
Ecology and Conservation
Sampling (Statistics)
Social sciences
Social sciences-Statistical methods
estimation
random
sampling theory
design-based
finite population
sampling
Online AccessGet full text
ISBN9780198815792
0198815794
9780198815808
0198815808
DOI10.1093/oso/9780198815792.001.0001

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Table of Contents:
  • A.2.6 Union and intersection
  • 7.1.6 Sample size determination -- Ratio estimation -- Regression estimation -- 7.1.7 Relative efficiency -- Ratio estimator -- Regression estimator -- 7.2 Ratio estimation of a proportion -- 7.3 Ratio estimation with stratified sampling -- 7.3.1 Combined estimator -- 7.3.2 Separate estimator -- 7.3.3 Choosing between combined and separate estimators -- 7.4 A model-based perspective -- 7.4.1 Estimation of model parameters -- Mean model -- Linear models -- 7.4.2 Prediction of population parameters -- Mean model -- Ratio model -- Regression model -- 7.4.3 Prediction error -- Mean model -- Ratio model -- Regression model -- 7.4.4 Prediction variance estimators -- 7.5 Monte Carlo performance evaluation -- 7.6 Mark-recapture estimation -- 7.7 Chapter comments -- Problems -- CHAPTER 8: Unequal probability sampling -- 8.1 Unbiased ratio estimator -- 8.2 Sampling with replacement -- 8.2.1 Hansen-Hurwitz estimator -- 8.2.2 Unbiasedness -- 8.2.3 Sampling variance and variance estimation -- 8.3 Sampling without replacement -- 8.3.1 Horvitz-Thompson estimator -- 8.3.2 Unbiasedness -- 8.3.3 Sampling variance and variance estimation -- 8.3.4 Alternative selection methods -- Chao's method -- Sunter's method -- 8.3.5 Strategy performance comparisons -- 8.3.6 Survey cost comparisons -- 8.4 Sampling distribution -- 8.5 Systematic sampling -- 8.6 Generality of Horvitz-Thompson estimation -- 8.7 Generalized Horvitz-Thompson estimation -- 8.7.1 Variance, covariance, and correlation estimators -- 8.7.2 Mean-per-unit, ratio, and regression estimators -- 8.7.3 Performance of generalized Horvitz-Thompson estimators -- 8.8 Poisson sampling -- 8.9 Nonresponse and oversampling -- 8.9.1 Hansen-Hurwitz estimator -- 8.9.2 Horvitz-Thompson estimator -- 8.10 Chapter comments -- Problems -- CHAPTER 9: Multi-stage sampling -- 9.1 Two-stage sampling: Clusters of equal size
  • Cover -- Sampling Theory: For the Ecological and Natural Resource Sciences -- Copyright -- Dedication -- Preface -- Contents -- CHAPTER 1: Introduction -- 1.1 The design-based paradigm -- 1.2 Text content and orientation -- 1.3 What distinguishes this text? -- 1.4 Recommendations for instructors -- 1.5 Sampling theory: A brief history -- CHAPTER 2: Basic concepts -- 2.1 Terminology -- 2.2 Components of a sampling strategy -- 2.3 Selection methods -- 2.4 Properties of estimators -- 2.5 Sampling distribution of an estimator -- 2.6 Judgment sampling versus random sampling -- CHAPTER 3: Equal probability sampling -- 3.1 Without replacement sampling -- 3.1.1 Estimation of the population mean, proportion,and total -- 3.1.2 Sampling variance -- 3.1.3 Estimation of sampling variance -- 3.1.4 Bernoulli sampling -- 3.2 With replacement sampling -- 3.2.1 Estimation of the population mean, proportion, and total -- 3.2.2 Sampling variance and variance estimation -- 3.2.3 Rao-Blackwell theorem -- 3.3 Relative performance of alternative sampling strategies -- 3.3.1 Measures of relative performance -- 3.3.2 An example: SRS/mean-per-unit estimation versus SWR -- 3.4 Sample size to achieve desired level of precision -- 3.4.1 Approximate normality of sampling distributions -- 3.4.2 Confidence interval construction -- 3.4.3 Sample size determination -- 3.5 Nonresponse and oversampling -- 3.6 Sampling in R -- 3.6.1 SRS and SWR -- 3.6.2 Sample Spaces -- 3.7 Chapter comments -- Problems -- CHAPTER 4: Systematic sampling -- 4.1 Linear systematic sampling -- 4.1.1 N /k is integer-valued -- Relative efficiency -- 4.1.2 N/k is not integer-valued -- Unbiased estimation -- 4.2 Selection methods that guarantee fixed n -- 4.2.1 Circular systematic sampling -- 4.2.2 Fractiona linterval random start -- 4.3 Estimation of sampling variance -- 4.3.1 Biased estimation -- SRS proxy
  • 9.1.1 Estimation of the population mean -- 9.1.2 Expectation -- 9.1.3 Sampling variance and its estimation -- Estimation of first- and second-stage contributions -- 9.1.4 Optimal allocation -- 9.1.5 Net relative efficiency -- Estimation of finite population variance -- 9.2 Two-stage sampling: Clusters of unequal size -- 9.2.1 Single-stage cluster sampling -- Estimation of the population mean and total -- Sample space illustration -- 9.2.2 Two-stage estimation of the population mean and total -- 9.2.3 Sampling variance and its estimation -- General expressions -- SRS within clusters -- Sample space illustration: Horvitz-Thompson estimation -- More than two stages -- 9.2.4 Optimal allocation -- 9.3 Chapter comments -- 9.3.1 Generality of the multi-stage framework -- 9.3.2 Taking advantage of ecological understanding -- 9.3.3 Implications for large-scale natural resource surveys -- Problems -- CHAPTER 10: Multi-phase sampling -- 10.1 Two-phase estimation of the population mean and total -- 10.1.1 Estimators -- 10.1.2 Sampling variance and its estimation -- 10.1.3 Sample space illustration -- 10.1.4 Optimal allocation -- Two-phase ratio estimation -- Two-phase regression estimation -- 10.1.5 Net relative efficiency -- Graphical analysis -- 10.2 Two-phase ratio estimation of a proportion -- 10.3 Two-phase sampling with stratification -- 10.3.1 Estimation of the population mean and total -- 10.3.2 Sampling variance and its estimation -- 10.3.3 Optimal allocation -- 10.3.4 Net relative efficiency -- 10.4 Chapter comments -- Problems -- CHAPTER 11: Adaptive sampling -- 11.1 Adaptive cluster sampling -- 11.1.1 Basic scheme -- 11.1.2 Definitions -- 11.1.3 Inclusion probabilities and expected sample size -- 11.1.4 Estimators and relative efficiency -- Adaptive mean-per-unit estimation -- Adaptive Horvitz-Thompson estimation
  • 11.2 Other adaptive sampling designs -- 11.2.1 Single-stage strip and systematic designs -- 11.2.2 Two-stage complete allocation cluster sampling -- Murthy's estimator for Ti -- Two-stage estimators -- 11.3 Chapter comments -- Problems -- CHAPTER 12: Spatially balanced sampling -- 12.1 Introduction -- 12.2 Finite populations -- 12.2.1 Generalized random tessellation stratified sampling -- Procedure -- Application: coastal salmonid monitoring -- 12.2.2 Balanced acceptance sampling -- Spatial balance and Voronoi polygons -- van der Corput sequence -- Halton sequence -- Procedure -- Procedure with Halton frame -- Halton boxes. -- Halton frame. -- Sample selection. -- 12.2.3 Estimation -- Neighborhood variance estimator -- 12.3 Infinite populations -- 12.3.1 Generalized random tessellation stratified sampling -- 12.3.2 Balanced acceptance sampling -- 12.3.3 Estimation -- 12.4 Chapter comments -- CHAPTER 13: Sampling through time -- 13.1 Sampling on two occasions -- 13.1.1 Design 1: Full retention of units across occasions -- 13.1.2 Design 2: Independent SRS on each occasion -- 13.1.3 Comparison of full retention and independent SRS designs -- 13.1.4 Design 3: Partial retention/partial replacement -- Sampling variance -- 13.2 Monitoring design -- 13.2.1 Membership design -- 13.2.2 Revisit design -- Shorthand notation -- 13.3 Estimation of status and trend -- 13.3.1 Design-based estimation -- 13.3.2 Estimators for some specific designs -- 13.4 Sample size determination -- 13.5 Dual frame sampling -- 13.6 Chapter comments -- APPENDIX A: Mathematical foundations -- A.1 Counting techniques -- A.1.1 Permutations -- A.1.2 k-Permutations -- A.1.3 Combinations -- A.1.4 Partitions -- A.2 Basic principles of probability theory -- A.2.1 Random experiment -- A.2.2 Sample space -- A.2.3 Outcome probability -- A.2.4 Event -- A.2.5 Event relations
  • Estimation in presence of linear trend -- 4.3.2 Unbiased estimation -- m samples selected independently -- m samples selected without replacement -- 4.4 Unpredictable trend in sampling variance with n -- 4.5 Warning: Pathological settings -- 4.6 Nonresponse and oversampling -- 4.7 Chapter comments -- Problems -- CHAPTER 5: Stratified sampling -- 5.1 Estimation of the population mean -- 5.1.1 Expected value -- 5.1.2 Sampling variance -- 5.1.3 Numerical examples -- 5.2 Estimation of the population proportion -- 5.3 Estimation of the population total -- 5.4 Estimation of sampling variance -- 5.5 Allocation of the sample across strata -- 5.5.1 Optimal allocation: Graphical analysis -- 5.5.2 Optimal allocation: Analytical analysis -- Use of Lagrange multipliers -- 5.5.3 Comments on optimal allocation -- 5.6 Sample size determination -- 5.7 Relative efficiency -- 5.7.1 Proportional allocation -- 5.7.2 Estimation of finite population variance -- 5.8 Effective degrees of freedom -- 5.9 Post-stratification -- 5.9.1 Unconditional sampling variance -- 5.9.2 Conditional sampling variance -- 5.10 Chapter comments -- Problems -- CHAPTER 6: Single-stage cluster sampling: Clusters of equal size -- 6.1 Estimation of the population mean -- 6.2 Sampling variance -- 6.2.1 ANOVA/mean squares approach -- 6.2.2 Intracluster correlation approach -- 6.3 Estimation of the population total and proportion -- 6.4 Estimation of sampling variance -- 6.5 Estimation of finite population variance -- 6.6 Sample size determination -- 6. 7 Relative efficiency -- 6.8 Chapter comments -- Problems -- CHAPTER 7: Ratio and regression estimation -- 7.1 Estimation of the mean and total -- 7.1.1 Graphical representation -- 7.1.2 Sample space illustration -- 7.1.3 Bias -- 7.1.4 Sampling variance -- Ratio estimator -- Regression estimator -- 7.1.5 Estimation of sampling variance