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When probability samples are not available, the model-based framework may be the only option for constructing inferences in the form of prediction intervals for population means. Further, for machine learning and some non-parametric and nonlinear regression prediction techniques, resampling methods such as the bootstrap may be the only option for obtaining the standard errors necessary for constructing those prediction intervals. All bootstrap approaches entail repeatedly sampling from the original sample, estimating the parameter of interest for each replication, and estimating the standard error of the estimate of the parameter as the standard deviation of the bootstrap estimates over replications. The objective of the study was to develop a procedure for terminating resampling such that the resulting number of replications assures, at least in probability, that the estimate of the standard error stabilizes to the standard error corresponding to one million replications. The analyses used a variety of datasets: five forest inventory datasets with either volume or aboveground biomass as the dependent variable and metrics from either airborne laser scanning or Landsat as independent variables, three from Europe, one from Southwest Asia, and one from Africa; and two forest/non-forest versus Landsat datasets, one from Minnesota and one from Wisconsin, both in the USA. The primary contribution of the study was development and demonstration of a procedure that specifies criteria for terminating resampling that assure in probability that the bootstrap estimate of the standard error stabilizes to the estimate obtained with one million replications. • Proposes and demonstrates criteria for terminating bootstrap resampling. • Assures in probability that the bootstrap standard error stabilizes. • Minimizes the uncertainty of a bootstrap standard error-based prediction interval. • Results are demonstrated for seven international forest inventory datasets. [ABSTRACT FROM AUTHOR]

Abstract: National forest inventories report estimates of parameters related to forest area and growing stock volume for geographic areas ranging in size from municipalities to entire countries. Landsat imagery has been shown to be a source of auxiliary information that can be used with stratified estimation to increase the precision of estimates, although the increase is greater for estimates of forest area than for estimates of growing stock volume. The objective of the study was to assess the utility of lidar-based stratifications for increasing the precision of mean proportion forest area and mean growing stock volume per unit area. Stratifications based on nonlinear logistic regression model predictions of volume obtained from lidar data reduced variances of mean growing stock volume estimates by factors as great as 3.2 and variances of mean proportion forest area estimates by factors as great as 1.5. [Copyright &y& Elsevier]

Nearest neighbors techniques have been shown to be useful for predicting multiple forest attributes from forest inventory and Landsat satellite image data. However, in regions lacking good digital land cover information, nearest neighbors selected to predict continuous variables such as tree volume must be selected without regard to relevant categorical variables such as forest/non-forest. The result is that non-zero volume predictions may be obtained for pixels predicted to be non-forest, and volume predictions for pixels predicted to be forest may be erroneously small due to non-forest nearest neighbors. For users who wish to circumvent this discrepancy, a two-step algorithm is proposed in which the class of a relevant categorical variable such as land cover is predicted in the first step, and continuous variables such as volume are predicted in the second step subject to the constraint that all nearest neighbors must come from the predicted class of the categorical variable. Nearest neighbors, multinomial logistic regression, and discriminant analysis techniques were investigated for use in the first step. The results were generally similar for the three techniques, although the multinomial logistic regression technique was slightly superior. The k-Nearest Neighbors technique was used in the second step because many continuous forest inventory variables do not satisfy the distributional assumptions necessary for parametric multivariate techniques. The results for six 15-km×15-km areas of interest in northern Minnesota, USA, indicate that areal estimates of tree volume, basal area, and density obtained from pixel predictions are comparable to plot-based estimates and estimates by conifer and deciduous classes are also comparable to plot-based estimates. When a mixed conifer/deciduous class was included, predictions for the mixed and deciduous class were confused. [Copyright &y& Elsevier]

For tropical countries that do not have extensive ground sampling programs such as national forest inventories, the gain-loss approach for greenhouse gas inventories is often used. With the gain-loss approach, emissions and removals are estimated as the product of activity data defined as the areas of human-caused emissions and removals and emissions factors defined as the per unit area responses of carbon stocks for those activities. Remotely sensed imagery and remote sensing-based land use and land use change maps have emerged as crucial information sources for facilitating the statistically rigorous estimation of activity data. Similarly, remote sensing-based biomass maps have been used as sources of auxiliary data for enhancing estimates of emissions and removals factors and as sources of biomass data for remote and inaccessible regions. The current status of statistically rigorous methods for combining ground and remotely sensed data that comply with the good practice guidelines for greenhouse gas inventories of the Intergovernmental Panel on Climate Change is reviewed. [ABSTRACT FROM AUTHOR]

Accurate spatial estimation of forest carbon stocks and their spatial uncertainties at local, regional, national, and global scales is a critical step in global carbon cycle modeling and management. This study aimed at enhancing the methods that are currently used in this area by combining plot data from the forest inventory and analysis program of the U.S. Forest Service and free landsat thematic mapper image data. Three mapping methods including linear regression, sequential Gaussian co-simulation, and block co-simulation algorithm were compared with respect to the accuracy of forest carbon stock estimates obtained for a study area in Southern Illinois, USA. The results indicated that although the linear regression resulted in smaller prediction errors than the sequential Gaussian co-simulation and the block co-simulation approaches, it also produced both negative and unreasonably large estimates, which is a serious drawback. Moreover, the sequential Gaussian co-simulation and the block co-simulation produced not only accurate carbon predictions, but also uncertainties for the local estimates. In addition, the block co-simulation approach scaled up both forest carbon stocks and the input uncertainties from finer to coarser spatial resolutions as is required for mapping forest carbon at national and global scales. Thus, the co-simulation and block co-simulation algorithms resolved an important current methodological challenge. [ABSTRACT FROM AUTHOR]