Sampling Theory for Forest Inventory: A Teach-Yourself Course

Sampling Theory for Forest Inventory: A Teach-Yourself Course

by Pieter Vries


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Product Details

ISBN-13: 9783540170662
Publisher: Springer Berlin Heidelberg
Publication date: 12/01/1986
Pages: 400
Product dimensions: 6.69(w) x 9.61(h) x 0.03(d)

Table of Contents

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.- Single-Stage Cluster Sampling.- Primary Units of Equal Size.- Equal Within-Cluster Variances.- 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.

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