Abstract:

Objective: 1) Evaluate the effects of linear and nonlinear model forms of the model, as well as residual assumptions on inferential uncertainty. 2) Compare two methods of estimating variance of the population mean-bootstrap and analytical method. 3) Assess the effects of multiple factors on inferential uncertainty, and construct empirical rules of statistical inference based on remote sensing models to guide practice. Method: 160 sample plots were selected from the population using a two-stage sampling design. The variable of interest was denoted by forest volume as an example. Under the model-based inference, based on the measured sample plots of firewood volume in African savannahs and Landsat 8 remote sensing auxiliary data, the population parameters were estimated under different modeling assumptions, which aimed to quantitatively analyze the effects of analytical parameter model assumptions on estimating uncertainty and using diagnostic methods such as confidence ellipses to ensure the validity of the analysis. Result: 1) Under the different model assumptions, the population mean estimates $ {\hat{\mu }}_{\mathrm{m}\mathrm{b}} $ ranged from 7.159 to 7.331 m³·hm^?2. Analytical variance of the population mean estimates $ {\widehat{\mathrm{V}\mathrm{a}\mathrm{r}}(\hat{\mu }}_{\mathrm{m}\mathrm{b}}) $ ranged from 0.147 to 0.221. The sampling precision ranged from 93.59% to 96.64%. Empirical variance of the population mean estimates $ {\widehat{\mathrm{V}\mathrm{a}\mathrm{r}}(\hat{\mu }}_{\mathrm{b}\mathrm{o}\mathrm{o}\mathrm{t}}) $ ranged from 0.143 to 0.237. Model assumptions will affect inferential the estimation of model parameters, which will ultimately affect inferential precision $ {\widehat{\mathrm{V}\mathrm{a}\mathrm{r}}(\hat{\mu }}_{\mathrm{m}\mathrm{b}} )$. The bootstrap method is an effective method for testing the unbiasedness of the analytical estimate of population parameters; 2) Under design-based inference, the estimated mean $ {\hat{\mu }}_{\mathrm{d}\mathrm{b}} $ was 6.774 m³·hm^?2 with a variance $ {\widehat{\mathrm{V}\mathrm{a}\mathrm{r}}(\hat{\mu }}_{\mathrm{d}\mathrm{b}}) $ of 0.965, the sampling precision is 85.50%. Under established conditions, compared with design-based inference, model-based inference effectively increased the inferential precision by 77.10%-84.77% and improved the sampling precision between 9.46%-13.03%. Conclusion: Model-based inference has higher inferential precision and sampling precision in small sample inference, which is conducive to achieving the goal of high-precision, small-sample size and short-period forest inventory, but the uncertainty in the modeling process will affect inferential precision, among which the residual variability has the greatest influence on the inferential uncertainty. Ignoring spatial autocorrelation to infer population parameters under homogeneous variance assumptions will underestimation of $ {\widehat{\mathrm{V}\mathrm{a}\mathrm{r}}(\hat{\mu }}_{\mathrm{m}\mathrm{b}} )$. Therefore, it is important to account for the spatial autocorrelation apart from taking the heteroscedasticity into the estimation of model parameters using appropriate variance and correlation functions.

Key words: remote sensing-assisted forest inventory, model-based inference, regression model, variance estimation