Abstract:

Objective: 1) To quantify the effects of the“outdated”models on the population parameter estimates. 2) To correct bias due to“outdated”model by model-assisted inference. 3) To quantify the correction effects of the errors-in-variable (EIV) model on the inferential bias. Method: Correcting for the effect of outdated models on estimates (the population mean, and the variance of the population mean) using EIV model under three inference frameworks: design-based inference, model-based inference, and model-assisted inference. Result: 1) Compare the estimates based on model-based inference with the estimates of two-stage sampling. The model-based estimates of the mean, $ \hat{\mu } $, including the regular model and the EIV model, were similar to each other and to the two-stage sampling estimate of the mean, 6.774 m³·hm^?2. The design-based and the model-based estimates of $ \mathrm{\widehat{Var}}\left(\hat{\mu}\right) $ have great disparity, with two-stage sampling of 0.965 and model-based averaging 0.117, meaning that the average precision for model-based was improved by 87.93%. 2) The adverse effects of temporally external independent variables are exacerbated over time with respect to a model and propagate to the population parameter estimation. 3) In the model-assisted inference, the estimates of mean $ \hat{\mu } $, including the regular and the EIV models, range from 6.5 to 6.8, with a small fluctuation range and the same trend, and the differences between the mean estimates of the two are small, but the latter has higher inference accuracy, with an accuracy improvement range of 5.71%?22.50%, with an average of 13.34%. Conclusion: 1) Remotely sensed data as auxiliary information can effectively improve the estimation accuracy. 2) When remote sensing data are“out of date”, the model is invaild, the mean estimate bias increases, and the variance estimate is underestimated. 3) Model-assisted inference solves the problem of inference bias caused by“outdated”model, maintains the approximate unbiasedness of the estimates, and the accuracy is positively correlated with the sample size of the probability sample. 4) EIV model reduces the variance estimates, but the adverse effects of the“outdated”model cannot be eliminated by using the EIV model alone.

Key words: statistical inference, forest inventory, sampling design, remotely sensed auxiliary data, “outdated”model