scholarly journals Linear regression with many controls of limited explanatory power

2021 ◽  
Vol 12 (2) ◽  
pp. 405-442 ◽  
Author(s):  
Chenchuan (Mark) Li ◽  
Ulrich K. Müller
Keyword(s):  
Monte Carlo ◽  
Linear Regression ◽  
Linear Regression Model ◽  
Asymptotic Efficiency ◽  
Explanatory Power ◽  
Monte Carlo Study ◽  
Inference Procedure ◽  
Quadratic Mean ◽  
Additional Information ◽  
Control Coefficients

We consider inference about a scalar coefficient in a linear regression model. One previously considered approach to dealing with many controls imposes sparsity, that is, it is assumed known that nearly all control coefficients are (very nearly) zero. We instead impose a bound on the quadratic mean of the controls' effect on the dependent variable, which also has an interpretation as an R 2‐type bound on the explanatory power of the controls. We develop a simple inference procedure that exploits this additional information in general heteroskedastic models. We study its asymptotic efficiency properties and compare it to a sparsity‐based approach in a Monte Carlo study. The method is illustrated in three empirical applications.

scholarly journals Estimating Root Zone Moisture from Surface Soil Using Limited Data

2017 ◽  
Vol 24 (4) ◽  
pp. 501-516
Author(s):  
Wen-Zhi Zeng ◽  
Guo-Qing Lei ◽  
Hong-Ya Zhang ◽  
Ming-Hai Hong ◽  
Chi Xu ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Soil Moisture ◽  
Linear Regression ◽  
Monte Carlo Simulations ◽  
Linear Regression Model ◽  
Surface Soil ◽  
Root Zone ◽  
Surface Moisture ◽  
Moisture Estimation ◽  
Hydrus 1D

Abstract For estimation of root-zone moisture content from EO-1/Hyperion imagery, surface soil moisture was first predicted by hyperspectral reflectance data using partial least square regression (PLSR) analysis. The textures of more than 300 soil samples extracted from a 900 m × 900 m field site located within the Hetao Irrigation District in China were used to parameterize the HYDRUS-1D numerical model. The study area was spatially discretized into 18,000 compartments (30 m × 30 m × 0.02 m), and Monte Carlo simulations were applied to generate 2000 different soil-particle size distributions for each compartment. Soil hydraulic properties for each realization were determined by application of artificial neural network analysis and used to parameterize HYDRUS-1D to simulate averaged soil-moisture contents within the root zone (0-40 cm) and surface (approximately 0-4 cm). Then the link between surface moisture and root zone was established by use of linear regression analysis, resulting in R and RMSE of 0.38 and 0.03, respectively. Kriging and co-kriging with observed surface moisture, and co-kriging with surface moisture obtained from Hyperion imagery were also used to estimate root-zone moisture. Results indicated that PLSR is a powerful tool for soil moisture estimation from hyperspectral data. Furthermore, co-kriging with observed surface moisture had the highest R (0.41) and linear regression model, and HYDRUS Monte Carlo simulations had a lowest RMSE (0.03) among the four methods. In regions that have similar climatic and soil conditions to our study area, a linear regression model with HYDRUS Monte Carlo simulations is a practical method for root-zone moisture estimation before sowing and it can be easily coupled with remote sensing technology.

scholarly journals Feasible Generalized Stein-Rule Restricted Ridge Regression Estimators

2017 ◽  
Vol 13 (1) ◽  
pp. 77-97
Author(s):  
Nimet Özbay ◽  
Issam Dawoud ◽  
Selahattin Kaçıranlar
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Ridge Regression ◽  
Simulation Experiment ◽  
Regression Estimators ◽  
Coefficient Vector ◽  
General Linear Regression Model

Abstract Several versions of the Stein-rule estimators of the coefficient vector in a linear regression model are proposed in the literature. In the present paper, we propose new feasible generalized Stein-rule restricted ridge regression estimators to examine multicollinearity and autocorrelation problems simultaneously for the general linear regression model, when certain additional exact restrictions are placed on these coefficients. Moreover, a Monte Carlo simulation experiment is performed to investigate the performance of the proposed estimator over the others.

scholarly journals Variation Comparison of OLS and GLS Estimators using Monte Carlo Simulation of Linear Regression Model with Autoregressive Scheme

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Sajid Ali Khan ◽  
Sayyad Khurshid ◽  
Tooba Akhtar ◽  
Kashmala Khurshid
Keyword(s):  
Monte Carlo ◽  
Linear Regression ◽  
Regression Model ◽  
Sample Size ◽  
Least Squares ◽  
Linear Regression Model ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
Small Samples ◽  
Sample Sizes

In this research we discusses to Ordinary Least Squares and Generalized Least Squares techniques and estimate with First Order Autoregressive scheme from different correlation levels by using simple linear regression model. A comparison has been made between these two methods on the basis of variances results. For the purpose of comparison, we use simulation of Monte Carlo study and the experiment is repeated 5000 times. We use sample sizes 50, 100, 200, 300 and 500, and observe the influence of different sample sizes on the estimators. By comparing variances of OLS and GLS at different values of sample sizes and correlation levels with , we found that variance of ( ) at sample size 500, OLS and GLS gives similar results but at sample size 50 variance of GLS ( ) has minimum values as compared to OLS. So it is clear that variance of GLS ( ) is best. Similarly variance of ( ) from OLS and GLS at sample size 500 and correlation -0.05 with , GLS give minimum value as compared to all other sample sizes and correlations. By comparing overall results of Ordinary Least Squares (OLS) and Generalized Least Squares (GLS), we conclude that in large samples both are gives similar results but small samples GLS is best fitted as compared to OLS.

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