Sampling Theory for Forest Inventory : A Teach-Yourself Course - Vries, Pieter G.de.; SpringerLink (Online service) (Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1986)
1 Simple Random Sampling without Replacement -- 1.1 Introduction -- 1.2 Expected Value. Estimators for Population Mean and Total -- 1.3 Population and Sample Variance -- 1.4 Variances of Estimated Population Mean and Total -- 1.5 Confidence Interval and Confidence Statement -- 1.6 Estimation of Proportions -- 1.7 Required Sample Size -- 1.8 Some General Remarks on Sample Plots -- 1.9 Numerical Examples -- 2 Stratified Random Sampling -- 2.1 Introduction -- 2.2 Unbiased Estimators for Population Mean and Total. Variances -- 2.3 Some Special Cases -- 2.4 Optimization of the Sampling Scheme -- 2.5 Confidence Intervals. Behrens-Fisher Problem -- 2.6 Gain in Precision Relative to Simple Random Sampling -- 2.7 Numerical Examples -- 3 Ratio Estimators in Simple Random Sampling -- 3.1 Introduction. Population Ratio. Ratio Estimators for Total and Mean -- 3.2 Variances -- 3.3 Confidence Interval. Precision versus SRS. Required Sample Size -- 3.4 Bias of the Ratio Estimator -- 3.5 Ratio Estimator per Species Group in Mixed Forest -- 3.6 Numerical Example -- 3.7 Combining Results of Different Samples to Obtain New Information -- 4 Ratio Estimators in Stratified Random Sampling -- 4.1 Introduction -- 4.2 The Separate Ratio Estimator -- 4.3 The Combined Ratio Estimator -- 4.4 Illustrations -- 4.5 Numerical Example -- 5 Regression Estimator -- 5.1 Introduction -- 5.2 Unbiased Estimator of Population Regression Line from Sample Data -- 5.3 Linear Regression Estimator and its Variance -- 5.4 Regression Estimator in Stratified Random Sampling -- 5.5 Numerical Example -- 6 Two-Phase Sampling or Double Sampling -- 6.1 Introduction -- 6.2 The Ratio Estimator in Double Sampling -- 6.2.1 Ratio Estimator in Double Sampling - Dependent Phases -- 6.2.2 Ratio Estimator in Double Sampling - Independent Phases -- 6.3 The Regression Estimator in Double Sampling -- 6.3.1 Regression Estimator in Double Sampling - Independent Phases -- 6.3.2 Regression Estimator in Double Sampling - Dependent Phases. -- 6.3.3 Numerical Example - Dependent Phases -- 6.4 Optimization in Double Sampling with Ratio and Regression Estimators -- 6.5 Double Sampling for Stratification -- 6.5.1 Introduction -- 6.5.2 Unbiased Estimator for Population Mean. Variance Expression -- 6.5.3 Variance Estimator -- 6.5.4 Optimization of the Sampling Scheme -- 6.5.5 Numerical Example -- 6.6 Correction for Misinterpretation in Estimating Stratum Proportions from Aerial Photographs -- 6.6.1 Derivation of Formulas -- 6.6.2 Numerical Example -- 6.7 Volume Estimation with Correction for Misinterpretation -- 6.7.1 Derivation of Formulas -- 6.7.2 Numerical Example -- 7 Continuous Forest Inventory with Partial Replacement of Sample Plots -- 7.1 Introduction -- 7.2 Definition of Symbols -- 7.3 Most Precise Unbiased Linear Estimator for Population Mean on the Second Occasion -- 7.4 Optimization of Sampling for Current Estimate -- 7.5 Estimation of Change (Growth or Drain) -- 7.6 A Compromise Sampling Scheme -- 7.7 Numerical Example -- 8 Single- and More-Stage Cluster Sampling -- 8.1 Introduction -- 8.2 Estimators in Two-Stage Sampling -- 8.2.1 Definition of Symbols -- 8.2.2 Unbiased Estimators for Population Total and Mean per SU -- 8.2.3 Unbiased Estimators in Special Cases -- 8.2.3.1 Single-Stage Cluster Sampling -- 8.2.3.2 Primary Units of Equal Size -- 8.2.3.3 Equal Within-Cluster Variances -- 8.2.3.4 Relation to Stratified Random Sampling -- 8.2.4 Ratio Estimator for Population Total and Mean per SU -- 8.3 Optimization of the Two-Stage Sampling Scheme -- 8.4 Three- and More-Stage Sampling -- 8.5 Numerical Example of Two-Stage Sampling -- 9 Single-Stage Cluster Sampling as a Research Tool -- 9.1. Introduction -- 9.2. Intracluster Correlation Coefficient -- 9.3. Variance and Intracluster Correlation -- 9.4. Measures of Heterogeneity -- 9.4.1. The Intracluster Correlation Coefficient -- 9.4.2. The C-Index -- 9.4.3. The Index of Dispersion -- 9.4.4. Numerical Example -- 9.5. Intracluster Correlation Coefficient in Terms of Anova Quantities -- 9.6. About the Optimum Sample Plot Size -- 10 Area Estimation with Systematic Dot Grids -- 10.1. Random Sampling with n Points -- 10.2. Systematic Sampling with n Points -- 10.3. Numerical Example -- 11 Sampling with Circular Plots -- 11.1. Sampling from a Fixed Grid of Squares -- 11.2. Sampling from a Population of Fixed Circles -- 11.3. Sampling with Floating Circular Plots -- 11.4. Comparison of Variances -- 12 Point Sampling -- 12.1. General Estimator -- 12.2. Specific Estimators -- 12.3. Variances -- 12.4. Sampling Near the Stand Margin -- 12.5. Required Sample Size. Choice of K. Questionable Trees -- 12.6. Numerical Example -- 12.7. A More General View at PPS-Sampling, wtr -- 13 Line Intersect Sampling -- 13.1. Introduction -- 13.2. BUFFON's Needle Problem and Related Cases -- 13.3. Total-Estimator Based on One-line Data -- 13.4. Variance in Case of One-Line Data -- 13.5. Sampling with More Than One Line -- 13.6. Required Number and Length of Transects -- 13.7. Estimating Properties of Residual Logs in Exploited Areas -- 13.8. Estimators Based on Circular Elements -- 13.8.1. Generalization of STRAND's Estimator -- 13.8.2. Density Estimation of Mobile Animal Populations -- 13.8.3. Biomass Estimation in Arid Regions -- 13.9. Bias in Oriented Needle Populations -- 13.10. Generalization of LIS Theory -- 13.10.1. KENDALL Projection and Expected Number of Intersections -- 13.10.2. General LIS Estimator and its Variance -- 13.10.3. Applications -- 13.11. Line Intersect Subsampling -- 14 List Sampling -- 14.1. Introduction -- 14.2. Estimation of Population Total. Variance -- 14.3. Optimum Measure of Size. Comparison with Simple Random Sampling. -- 14.4. Numerical Example -- 14.5. Two-Stage List Sampling -- 15 3-P Sampling -- 15.1. Introduction -- 15.2. The Principle of 3-P Sampling -- 15.3. Variance and Expected Value of Sample Size and its Inverse -- 15.4. Considerations about the Sample Size -- 15.5. GROSENBAUGH's 3-P Estimators -- 15.6. Summary and Conclusions -- 15.7. Numerical Example -- 15.8. List of Equivalent Symbols -- 1. A Family of Sampling Schemes -- 2. Permutations, Variations, Combinations -- 3. Stochastic Variables -- 3.1. Stochastic Variables in General. Normal and Standard Norm. Variable -- 3.2. The Chi-Suare Distribution -- 3.3. STUDENT's t-Distribution -- 3.4. FISHER's F-Distribution -- 4. Stochastic Vectors and Some of their Applications -- App1.2. Distribution of the Pooled Variance in Stratified R. S. -- App1.3. Analysis of Variance in Stratified Random Sampling -- App1.4. Analysis of Variance in 2-Stage Sampling -- Appl.5. Proof of STEIN's Method for Estimating Required Sample size -- 5. Covariance, Correlation, Regression -- 6. The LAGRANGE Multiplier Method of Optimization -- 7. Expected Value and Variance in Multivariate Distributions -- 8. Hypergeometric, Multinomial and Binomial Distributions -- 9. The Most Precise Unbiased Linear Estimator of a Parameter X, based on a Number of Independent Unbiased Estimates of Different Precision -- 10. Variance Formulas for Sums, Differences, Products and Ratios -- 11. The Random Forest (POISSON FOREST) -- 12. Derivation of the Identity used in List Sampling -- 13. Expanding a Function in a TAYLOR Series -- 14. About Double Sums -- 15. Exercises -- References.
Keywords: Agriculture; Forestry; Plant science; Botany; Agriculture; Forestry; Plant Sciences