A Comparison of the Stein-Rule and Positive-Part Stein-Rule Estimators in a Misspecified Linear Regression Model

1993 ◽  
Vol 9 (4) ◽  
pp. 668-679 ◽  
Author(s):  
Kazuhiro Ohtani
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Numerical Computation ◽  
Linear Regression Model ◽  
Exact Formula ◽  
Sufficient Condition ◽  
Omitted Variables ◽  
Specification Error ◽  
Positive Part ◽  
Predictive Risk

In this paper, we examine the performance of the predictive risk of the Steinrule (SR) and positive-part Stein-rule (PSR) estimators when relevant regressors are omitted in the specified model. The exact formula of the predictive risk of the PSR estimator is derived, and the sufficient condition for the PSR estimator to dominate the SR estimator under a specification error is given. It is shown by numerical computation that the PSR estimator seems to be the best choice among the OLS, SR, and PSR estimators even when there are omitted variables.

scholarly journals PMSE PERFORMANCE OF THE BIASED ESTIMATORS IN A LINEAR REGRESSION MODEL WHEN RELEVANT REGRESSORS ARE OMITTED

2002 ◽  
Vol 18 (5) ◽  
pp. 1086-1098 ◽  
Author(s):  
Akio Namba
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Mean Squared Error ◽  
Ordinary Least Squares ◽  
Positive Part ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Explicit Formulae ◽  
Biased Estimators

In this paper, we consider a linear regression model when relevant regressors are omitted. We derive the explicit formulae for the predictive mean squared errors (PMSEs) of the Stein-rule (SR) estimator, the positive-part Stein-rule (PSR) estimator, the minimum mean squared error (MMSE) estimator, and the adjusted minimum mean squared error (AMMSE) estimator. It is shown analytically that the PSR estimator dominates the SR estimator in terms of PMSE even when there are omitted relevant regressors. Also, our numerical results show that the PSR estimator and the AMMSE estimator have much smaller PMSEs than the ordinary least squares estimator even when the relevant regressors are omitted.

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. 

Prediction of Surface Roughness and Optimization of Cutting Parameters in CNC Turning of Rotational Features

2020 ◽  
Vol 38 (8A) ◽  
pp. 1143-1153
Author(s):  
Yousif K. Shounia ◽  
Tahseen F. Abbas ◽  
Raed R. Shwaish
Keyword(s):  
Surface Roughness ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Feed Rate ◽  
Cutting Parameters ◽  
Spindle Speed ◽  
Depth Of Cut ◽  
Non Linear ◽  
Optimization Of Cutting Parameters

This research presents a model for prediction surface roughness in terms of process parameters in turning aluminum alloy 1200. The geometry to be machined has four rotational features: straight, taper, convex and concave, while a design of experiments was created through the Taguchi L25 orthogonal array experiments in minitab17 three factors with five Levels depth of cut (0.04, 0.06, 0.08, 0.10 and 0.12) mm, spindle speed (1200, 1400, 1600, 1800 and 2000) r.p.m and feed rate (60, 70, 80, 90 and 100) mm/min. A multiple non-linear regression model has been used which is a set of statistical extrapolation processes to estimate the relationships input variables and output which the surface roughness which prediction outside the range of the data. According to the non-linear regression model, the optimum surface roughness can be obtained at 1800 rpm of spindle speed, feed-rate of 80 mm/min and depth of cut 0.04 mm then the best surface roughness comes out to be 0.04 μm at tapper feature at depth of cut 0.01 mm and same spindle speed and feed rate pervious which gives the error of 3.23% at evolution equation.

An Enhanced Multiple Linear Regression Model for Seasonal Rainfall Prediction

2020 ◽  
Vol 10 (4) ◽  
pp. 473-483
Author(s):  
Pundra Chandra Shaker Reddy ◽  
Alladi Sureshbabu
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Multiple Linear Regression ◽  
Linear Regression Model ◽  
Weather Prediction ◽  
Big Data Analytics ◽  
Multiple Linear Regression Model ◽  
Seasonal Rainfall ◽  
Climate Data ◽  
Rainfall Forecasting

Aims & Background: India is a country which has exemplary climate circumstances comprising of different seasons and topographical conditions like high temperatures, cold atmosphere, and drought, heavy rainfall seasonal wise. These utmost varieties in climate make us exact weather prediction is a challenging task. Majority people of the country depend on agriculture. Farmers require climate information to decide the planting. Weather prediction turns into an orientation in farming sector to deciding the start of the planting season and furthermore quality and amount of their harvesting. One of the variables are influencing agriculture is rainfall. Objectives & Methods: The main goal of this project is early and proper rainfall forecasting, that helpful to people who live in regions which are inclined natural calamities such as floods and it helps agriculturists for decision making in their crop and water management using big data analytics which produces high in terms of profit and production for farmers. In this project, we proposed an advanced automated framework called Enhanced Multiple Linear Regression Model (EMLRM) with MapReduce algorithm and Hadoop file system. We used climate data from IMD (Indian Metrological Department, Hyderabad) in 1901 to 2002 period. Results: Our experimental outcomes demonstrate that the proposed model forecasting the rainfall with better accuracy compared with other existing models. Conclusion: The results of the analysis will help the farmers to adopt effective modeling approach by anticipating long-term seasonal rainfall.

Sign in / Sign up

Export Citation Format

Share Document