| With the booming development of civil land observation satellite industry,satellite remote sensing technology plays a huge role in national defense construction,economic construction,social development and other fields.Its specific applications include the monitoring of renewable resources such as crops and forests,land use,urbanization and desertification assessment,etc.Compared with traditional monitoring methods,the biggest advantage of remote sensing satellite is that it can monitor target objects in a fine range and provide dynamic monitoring information of target objects in a small range.In recent years,governments at all levels have shown increasing interest in estimating targets for small areas.Local governments hope to understand the economic and social development of their regions through relevant statistical data.But large sample surveys are often aimed at meeting central demand,so little or no sample size may fall into counties and cities.Such a population that cannot obtain reliable estimators by direct estimation method due to the limitation of the number of samples is called "small area",which can be geographical counties,cities and districts,or people meeting a specific nature,etc.The research on "small domain" target estimation is called " small area estimation".The existing small-field estimation methods mainly include sampling-based design and statistical model.Among them,the basic idea of sampling design method is to optimize the sampling scheme and expand the sample size of interested "small area ";However,due to budget constraints in real life,the increase of sample size in one region usually means the decrease of sample size in other regions,so statistical model-based methods are more feasible.Small domain estimation model is proposed to solve the problem of small domain estimation.Its core idea is to "borrow strength" from other small areas or related administrative data,so as to increase the effective sample size.However,the development of small domain estimation model is often limited by the lack of corresponding small domain level auxiliary information,and the appearance of remote sensing data resources provides a new solution to this dilemma.High-precision,multi-scale,small-scale monitoring information has become an excellent source of auxiliary information,which greatly stimulates the application of small area estimation model.The analysis of satellite remote sensing data using small area estimation model has a long history in statistics.The classical Nested-error regression model started from the analysis of crop growth in Iowa,USA.There are two types of classical small area estimation models:(1)FayHarriot model,also known as area-level model;(2)Nested-error regression model,also known as unit-level model.For small area estimation models,people are often interested in(a)the prediction of mixed effects and(b)the uncertainty assessment of related predictions.In recent years,although many research literatures have studied(a)-(b)of small area estimation model,and many prediction and uncertainty evaluation methods have been proposed from different perspectives,there is no comprehensive comparison result of these prediction and uncertainty assessment methods from a unified perspective in(Q1)so far.In addition,(Q2)Most of the existing literature mainly focuses on the premise that the underlying model has been correctly assumed,and less attention is paid to the prediction and evaluation of the model in the case of model misspecification.And(Q3)most of the existing researches on the prediction of small region estimation model are "in-bag" prediction,that is,the prediction of the small area means of the sampling regions.There are a few literatures to discuss the prediction of unsampled areas.In this thesis,model misspecification means that the assumed model is inconsistent with the potential real model,and there is model misspecification.Firstly,for(Q1),this thesis summarizes the main methods of model uncertainty assessment(MSPE)based on two types of classical small-area estimation models,and compares the estimation accuracy,computational efficiency,and robustness of all methods with a unified standard.In the past few decades,many scholars have studied mixed effect predictors and MSPE estimators from different perspectives.However,it is worth noting that the past research work was concerned with the performance of a specific MSPE estimator,and no scholars have comprehensively combed and compared the existing MSPE estimators from a unified perspective,especially the new MSPE estimation method proposed in recent years.In addition,the program is packaged into R software package ‘sae MSPE’ for the calculation of small domain estimation model MSPE.Secondly,it is found that all estimation methods are robust to the model misspecification of the mean function.This thesis further explains the robustness from a theoretical perspective.In the research of MSPE estimation methods,most of the classical estimators are derived based on the premise that the model is correctly specified.When this condition is not satisfied,the second-order unbiased property of estimators will not hold any more.However,the simulation results show that the estimation accuracy of all estimators is still excellent even if there is a certain degree of deviation between the assumed model and the real model.In view of this,this chapter deduces the expressions of each estimator when there is model misspecification,and analyzes the reasons why the estimation accuracy of each estimator is not affected by the model misspecification based on the derived formulas.Then,for(Q2),we derive the second-order unbiased MSPE estimator for OBP predictor of the nested-error regression model called "OBOR",and apply the model to the prediction of temporal and spatial characteristics of carbon emissions by using VIIRS nighttime light data.Finally,the performance of the nested-error regression model is demonstrated by both OBOR and heat map.The research on MSPE estimation of EBLUP of small area estimation model has been relatively mature,while OBP is a new robust predictor appearing in recent years,and its literature on MSPE estimation is very limited.Based on this,inspired by the work of Liu et al.(2021),this thesis divides MSPE into two parts.Firstly,the dominant term and high-order term of each part are found.Secondly,the unbiased estimator of the design is derived for the dominant term,and the order of the high-order term is proved to be.Thus,the second-order unbiased estimation of MSPE can be obtained naturally.Finally,for(Q3),an MCMMP method is proposed to deal with the out-of-bag prediction problem of small area estimation models.MCMMP method is an improved version of CMMP(Jiang et al.(2018)),which inherits the idea of "match before prediction" of CMMP.Firstly,‘K-means’ is used to classify based on the covariate features of small areas,and then other sampling regions other than and non-sampling regions are used for parameter estimation.Finally,the random effect of the sampling region in the same category as the unsampled region is taken as the random effect of the unsampled region.In this thesis,MCMMP method was applied to estimate wheat planting area in Yanzhou District,Jining City,Shandong Province.In agricultural sampling work,the design of sampling quantity mostly serves the national or provincial level.For areas with small population or underdeveloped economy,it is easy to have no samples selected.Agriculture is often the main industry in these areas,so ignoring the area of crops in these areas will have a significant impact on the realization of agricultural precision monitoring in China.Considering the characteristics of wide range and large regional difference of crop planting,small area estimation model is a very suitable choice for area estimation.The empirical results show that MCMMP has smaller relative error than the existing methods. |
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