Estimation of the slope parameter in a linear regression model under a bounded loss function

2021 ◽  
pp. 1-15
Author(s):  
Z. Mahdizadeh ◽  
M. Naghizadeh Qomi ◽  
Shahjahan Khan
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Loss Function ◽  
Linear Regression Model ◽  
Slope Parameter

scholarly journals Risk Comparison of Improved Estimators in a Linear Regression Model with MultivariatetErrors under Balanced Loss Function

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Guikai Hu ◽  
Qingguo Li ◽  
Shenghua Yu
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Loss Function ◽  
Linear Regression Model ◽  
Mean Squared Error ◽  
Ordinary Least Squares ◽  
Balanced Loss Function ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Improved Estimators

Under a balanced loss function, we derive the explicit formulae of the risk of the Stein-rule (SR) estimator, the positive-part Stein-rule (PSR) estimator, the feasible minimum mean squared error (FMMSE) estimator, and the adjusted feasible minimum mean squared error (AFMMSE) estimator in a linear regression model with multivariateterrors. The results show that the PSR estimator dominates the SR estimator under the balanced loss and multivariateterrors. Also, our numerical results show that these estimators dominate the ordinary least squares (OLS) estimator when the weight of precision of estimation is larger than about half, and vice versa. Furthermore, the AFMMSE estimator dominates the PSR estimator in certain occasions.

scholarly journals The Impact of Interviewer Effects on Regression Coefficients

2018 ◽  
Vol 7 (2) ◽  
pp. 250-274 ◽  
Author(s):  
Micha Fischer ◽  
Brady T West ◽  
Michael R Elliott ◽  
Frauke Kreuter
Keyword(s):  
Measurement Error ◽  
Linear Regression ◽  
Regression Model ◽  
Survey Data ◽  
Linear Regression Model ◽  
Regression Coefficients ◽  
Slope Parameter ◽  
Interviewer Effects ◽  
Response Propensity ◽  
The Impact

Abstract This article examines the influence of interviewers on the estimation of regression coefficients from survey data. First, we present theoretical considerations with a focus on measurement errors and nonresponse errors due to interviewers. Then, we show via simulation which of several nonresponse and measurement error scenarios has the biggest impact on the estimate of a slope parameter from a simple linear regression model. When response propensity depends on the dependent variable in a linear regression model, bias in the estimated slope parameter is introduced. We find no evidence that interviewer effects on the response propensity have a large impact on the estimated regression parameters. We do find, however, that interviewer effects on the predictor variable of interest explain a large portion of the bias in the estimated regression parameter. Simulation studies suggest that standard measurement error adjustments using the reliability ratio (i.e., the ratio of the measurement-error-free variance to the observed variance with measurement error) can correct most of the bias introduced by these interviewer effects in a variety of complex settings, suggesting that more routine adjustment for such effects should be considered in regression analysis using survey data.

Physico-Chemical Analysis of Groundwater and Effect of Climatic Change in Angul-Talcher Area

2018 ◽  
Vol 6 (12) ◽  
pp. 26
Author(s):  
Aliva Bera ◽  
D.P. Satapathy
Keyword(s):  
Water Resources ◽  
Linear Regression ◽  
Regression Model ◽  
Climatic Change ◽  
Linear Regression Model ◽  
Ann Model ◽  
Quality Of Water ◽  
Physico Chemical ◽  
Simulation Based

In this paper, the linear regression model using ANN and the linear regression model using MS Excel were developed to estimate the physico-chemical concentrations in groundwater using pH, EC, TDS, TH, HCO3 as input parameters and Ca, Mg and K as output parameters. A comparison was made which indicated that ANN model had the better ability to estimate the physic-chemical concentrations in groundwater. An analytical survey along with simulation based tests for finding the climatic change and its effect on agriculture and water bodies in Angul-Talcher area is done. The various seasonal parameters such as pH, BOD, COD, TDS,TSS along with heavy elements like Pb, Cd, Zn, Cu, Fe, Mn concentration in water resources has been analyzed. For past 30 years rainfall data has been analyzed and water quality index values has been studied to find normal and abnormal quality of water resources and matlab based simulation has been done for performance analysis. All results has been analyzed and it is found that the condition is stable. 

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