## 1 Introduction  
Food security is one of the major challenges that humanity is facing. The Food and Agriculture Organization (FAO) reported that there were about 815 million people worldwide suffering from food shortages in 2016 [1]. To support food security, monitoring and estimating of crop yields in large areas is of great significance [2]. Moreover, accurate and real-time estimation of major crop yields is helpful for decision makers to formulate informed food trade policies [3; 4; 5]. Crop yield estimation are often based on official statistics derived from crop yield survey performed at some administrative level that are made available several days or months after crop harvesting [6; 7; 8]. Therefore, developing a simple and convenient yield estimation model that can estimate crop yield timely in different spatial scales is urgently required. In recent years, remote sensing has been widely used in agricultural monitoring because of its extensive coverage and regular revisit, which makes regional crop identification [9; 10] and yield estimation [6; 11] possible at acceptable accuracy. The crop yield estimation models based on remote sensing data mainly include three types, i.e., empirical models, crop growth models, and radiation use efficiency (RUE) models. The empirical or statistical models are based on the relationship between remote sensing indexes and crop yields in selected spatial units. The most frequently used remote sensing indexes include the Normalized Difference Vegetation Index (NDVI) [12; 13; 14], the Enhanced Vegetation Index (EVI) [15; 16], the Leaf Area Index [17], and the Soil Adjusted Vegetation Index (SAVI) [4]. Most available studies have shown that there is a strong linear relationship between these remote sensing indexes and crop yields [18; 19; 20]. Although empirical models are simple and easy to use, these models usually consider only a few key indexes and neglect other influence factors, which would affect the accuracy of crop yield estimation. The crop growth models use indexes derived from remote sensing to simulate crop growth and yield [21; 22; 23]. The crop growth process and yield can be well simulated based on accurate model inputs, including climate, soil and agricultural management measures [24; 25]. However, due to the spatial heterogeneity of field conditions, agricultural management, crop planting dates at regional scale, and the complexity of the land uses, the application of crop growth models was generally limited to small areas [26]. At present, crop growth models are usually driven by field measured data and are difficult to extend to large areas where there is a lack of spatial field measured data [27; 28; 29]. The RUE models estimate crop yield based on gross primary productivity (GPP) or net primary productivity (NPP) derived from remote sensing data [30]. Compared with the crop growth model, the RUE models need less parameters and has certain crop physiological basis. Main parameters for calculating crop yields include RUE, absorbed photosynthetically active radiation (APAR), and harvest index (HI) [31; 32; 33]. However, some parameters, especially HI, are difficult to obtain and usually estimated by field experiment or experience. The estimated parameters may neglect the effects of some important environmental factors, which will bring uncertainty to crop yield estimation. Therefore, there are still some problems in regional crop yields estimation using the existing methods. In recent years, machine learning methods, including random forest (RF), support vector machine (SVM), and artificial neural network (ANN), have been gradually used in crop identification based on remote sensing data [34; 35; 36]. More recently, these machine learning methods have been applied to crop yield estimation. The ANN has been successfully applied to yield estimation of various crops, such as maize [11], wheat [37], potato [38], melon [39] and grassland dry matter yield [40].