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The difference-based partially linear model is an appropriate regression model when both linear and nonlinear predictors are present in the data. However, when we want to optimize the weights using the difference-based method, the problem of variable selection can be difficult since low-variance predictors present a challenge. Therefore, this study aims to establish a novel methodology based on marginal theory to tackle such mixed relationships successfully, emphasizing variable selection in low dimensions. We suggest using a marginalized LASSO estimator with a penalty term that is not as severe and related to the difference order. As part of our numerical analysis of small sample performance, we undertake comprehensive simulation experiments to numerically demonstrate the strength of our proposed technique in estimation and prediction compared to the LASSO under a low-dimensional setup. This is done so that we can numerically demonstrate the strength of our proposed method in estimation and prediction. The bootstrapped method is utilized to evaluate how well our proposed prediction method performs when examining the King House dataset. [ABSTRACT FROM AUTHOR]

The construction of earthen embankment terraces in the Douro Region raises a set of problems related to hydrological processes. The main objective of this study is the evaluation of the spatial variation of electrical resistivity in agriculture terraces at Douro valley (Portugal). To achieve this objective, two variables are analysed, the soil electrical resistivity and the flow direction algorithm. In a field survey we recorded 13 electrical resistivity profiles. The contributing area was calculated with the algorithms D∞ (Deterministic Infinity Flow) and MFD (Multiple Flow Direction) and the results are the base of the internal runoff modelling, both supported by the digital elevation model with a spatial resolution of 1m2. A correlation between the spatial variation of the soil electrical resistivity represented by the standard deviation of the electrical resistivity for each profile and the average value of the contributing area coincident with each profile was established. The electrical resistivity standard deviation seems to be moderately well correlated according to the D∞ algorithm at about 1m of depth, and it has a good correlation at 1,5m to 2m of depth with the MFD algorithm. Taken together, the results show a significant positive statistical correlation between the electrical resistivity standard deviation and the contributing areas (MFD and D∞) depending on the soil depth.