The exact distribution and density functions of a pre-test estimator of the error variance in a linear regression model with proxy variables

1998 ◽  
Vol 39 (2) ◽  
pp. 163-177
Author(s):  
Hiroko Kurumai ◽  
Kazuhiro Ohtani
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Error Variance ◽  
Exact Distribution ◽  
Density Functions ◽  
Proxy Variables

OPTIMAL SIMILAR TESTS FOR STRUCTURAL CHANGE FOR THE LINEAR REGRESSION MODEL

2002 ◽  
Vol 18 (4) ◽  
pp. 853-867 ◽  
Author(s):  
G. Forchini
Keyword(s):  
Structural Change ◽  
Linear Regression ◽  
Regression Model ◽  
Simulation Study ◽  
Linear Regression Model ◽  
American Mathematical Society ◽  
Error Variance ◽  
Optimal Test ◽  
Finite Samples ◽  
Power Comparisons

This paper analyzes similar tests for structural change for the normal linear regression model in finite samples. Using the approach of Wald (1943, American Mathematical Society Transactions 54, 426–482), Hillier (1987, Econometric Theory 3, 1–44), Andrews and Ploberger (1994, Econometrica 62, 1382–1414), and Andrews, Lee, and Ploberger (1996, Journal of Econometrics 70, 9–36), we characterize a class of optimal similar tests for the existence of (possibly multiple) changepoints at unknown times. We extend the analysis of Andrews et al. (1996) by deriving weighted optimal similar tests for the case where the error variance is not known. We also show that when the sample size is large, the tests of Andrews et al. constructed by replacing the error variance with an estimate are equivalent to the optimal test derived in this paper. Power comparisons are provided by a small simulation study.

On Small Sample Properties of R2 in a Linear Regression Model with Multivariate t Errors and Proxy Variables

1993 ◽  
Vol 9 (3) ◽  
pp. 504-515 ◽  
Author(s):  
Kazuhiro Ohtani ◽  
Hikaru Hasegawa
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Important Variable ◽  
Small Sample ◽  
Small Samples ◽  
Coefficient Of Determination ◽  
Proxy Variables ◽  
Small Sample Properties ◽  
Multivariate T

In this paper we consider the small sample properties of the coefficient of determination in a linear regression model with multivariate t errors when proxy variables are used instead of unobservable regressors. The results show that if the unobservable variable is an important variable, the adjusted coefficient of determination can be more unreliable in small samples than the unadjusted coefficient of determination from both viewpoints of the bias and the MSE.

scholarly journals Bayesian Estimation of Normal Linear Regression Model with Heteroscedasticity Error Structures

2019 ◽  
pp. 1-13
Author(s):  
Bolanle A. Oseni ◽  
Olusanya E. Olubusoye ◽  
Adedayo A. Adepoju
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Credible Interval ◽  
Error Variance ◽  
Sample Information ◽  
Out Of Sample ◽  
Functional Forms ◽  
Stock Of Knowledge ◽  
Bayesian Estimators

Non-constant error variance in Normal Linear Regression Model (NLRM) is an econometric problem generally referred to as heteroscedasticity. Its presence renders statistical inference invalid. Classical approach to its detection, estimation and remediation are widely discussed in the econometric literature. However, estimation of a NLRM using the Bayesian approach when heteroscedasticity problem is present is a major gap in the existing stock of knowledge on this subject. This approach has grown widely in recent times because it combines out-of-sample information with observed data. The study derived Bayesian estimators of the NLRM in the presence of functional forms of heteroscedasticity. Variance was treated as a linear function and as an exponential function of exogenous variables. The estimators are found to be unbiased and consistent and the precision values tend to zero. The estimates obtained from the estimators approximately 95% draws fall within each of the corresponding credible interval. Therefore, the results obtained for the derived Bayesian estimators for different functional forms of heteroscedasticity considered are similar, thus, providing a credible alternative to the existing classical methods which depend solely on the sample information.

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.

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