Multivariate Behrens-Fisher problem using means of auxiliary variables

2022 ◽  
pp. 1-8
Author(s):  
Jianqi Yu ◽  
Kalimuthu Krishnamoorthy ◽  
Bin Wang
Keyword(s):  
Auxiliary Variables

scholarly journals Prediction of Soil Organic Carbon based on Landsat 8 Monthly NDVI Data for the Jianghan Plain in Hubei Province, China

2019 ◽  
Vol 11 (14) ◽  
pp. 1683 ◽  
Author(s):  
Yangchengsi Zhang ◽  
Long Guo ◽  
Yiyun Chen ◽  
Tiezhu Shi ◽  
Mei Luo ◽  
...  
Keyword(s):  
Time Series ◽  
Organic Carbon ◽  
Time Series Data ◽  
Soil Mapping ◽  
Digital Soil Mapping ◽  
Series Data ◽  
Landsat 8 ◽  
Auxiliary Variables ◽  
Jianghan Plain ◽  
Ndvi Time Series

High-precision maps of soil organic carbon (SOC) are beneficial for managing soil fertility and understanding the global carbon cycle. Digital soil mapping plays an important role in efficiently obtaining the spatial distribution of SOC, which contributes to precision agriculture. However, traditional soil-forming factors (i.e., terrain or climatic factors) have weak variability in low-relief areas, such as plains, and cannot reflect the spatial variation of soil attributes. Meanwhile, vegetation cover hinders the acquisition of the direct information of farmland soil. Thus, useful environmental variables should be utilized for SOC prediction and the digital mapping of such areas. SOC has an important effect on crop growth status, and remote sensing data can record the apparent spectral characteristics of crops. The normalized difference vegetation index (NDVI) is an important index reflecting crop growth and biomass. This study used NDVI time series data rather than traditional soil-forming factors to map SOC. Honghu City, located in the middle of the Jianghan Plain, was selected as the study region, and the NDVI time series data extracted from Landsat 8 were used as the auxiliary variables. SOC maps were estimated through stepwise linear regression (SLR), partial least squares regression (PLSR), support vector machine (SVM), and artificial neural network (ANN). Ordinary kriging (OK) was used as the reference model, while root mean square error of prediction (RMSEP) and coefficient of determination of prediction (R2P) were used to evaluate the model performance. Results showed that SOC had a significant positive correlation in July and August (0.17, 0.29) and a significant negative correlation in January, April, and December (−0.23, −0.27, and −0.23) with NDVI time series data. The best model for SOC prediction was generated by ANN, with the lowest RMSEP of 3.718 and highest R2P of 0.391, followed by SVM (RMSEP = 3.753, R2P = 0.361) and PLSR (RMSEP = 4.087, R2P = 0.283). The SLR model was the worst model, with the lowest R2P of 0.281 and highest RMSEP of 3.930. ANN and SVM were better than OK (RMSEP = 3.727, R2P = 0.372), whereas PLSR and SLR were worse than OK. Moreover, the prediction results using single-data NDVI or short time series NDVI showed low accuracy. The effect of the terrain factor on SOC prediction represented unsatisfactory results. All these results indicated that the NDVI time series data can be used for SOC mapping in plain areas and that the ANN model can maximally extract additional associated information between NDVI time series data and SOC. This study presented an effective method to overcome the selection of auxiliary variables for digital soil mapping in plain areas when the soil was covered with vegetation. This finding indicated that the time series characteristics of NDVI were conducive for predicting SOC in plains.

scholarly journals HIGHER-ORDER CURVATURE TERMS IN BORN–INFELD TYPE BRANE THEORIES

2011 ◽  
Vol 20 (01) ◽  
pp. 59-75 ◽  
Author(s):  
EFRAIN ROJAS
Keyword(s):  
Ricci Tensor ◽  
General Structure ◽  
Extrinsic Curvature ◽  
Higher Order ◽  
Square Root ◽  
Auxiliary Variables ◽  
Field Equations ◽  
Alternative Description ◽  
Brane Models ◽  
Combined Matrix

The field equations associated to Born–Infeld type brane theories are studied by using auxiliary variables. This approach hinges on the fact, that the expressions defining the physical and geometrical quantities describing the worldvolume are varied independently. The general structure of the Born–Infeld type theories for branes contains the square root of a determinant of a combined matrix between the induced metric on the worldvolume swept out by the brane and a symmetric/antisymmetric tensor depending on gauge, matter or extrinsic curvature terms taking place on the worldvolume. The higher-order curvature terms appearing in the determinant form come to play in competition with other effective brane models. Additionally, we suggest a Born–Infeld–Einstein type action for branes where the higher-order curvature content is provided by the worldvolume Ricci tensor. This action provides an alternative description of the dynamics of braneworld scenarios.

Identification of Causal Effects Within Principal Strata Using Auxiliary Variables

2021 ◽  
Vol 36 (4) ◽  
Author(s):  
Zhichao Jiang ◽  
Peng Ding
Keyword(s):  
Causal Effects ◽  
Auxiliary Variables
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