scholarly journals Two Kinds of Weighted Biased Estimators in Stochastic Restricted Regression Model

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Chaolin Liu ◽  
Haina Jiang ◽  
Xinhui Shi ◽  
Donglin Liu
Keyword(s):  
Monte Carlo ◽  
Regression Model ◽  
Prior Information ◽  
Monte Carlo Study ◽  
Real Data ◽  
Variance Matrix ◽  
Unbiased Estimators ◽  
Biased Estimators ◽  
Theoretical Results ◽  
Almost Unbiased

We consider two kinds of weighted mixed almost unbiased estimators in a linear stochastic restricted regression model when the prior information and the sample information are not equally important. The superiorities of the two new estimators are discussed according to quadratic bias and variance matrix criteria. Under such criteria, we perform a real data example and a Monte Carlo study to illustrate theoretical results.

scholarly journals Stochastic Restricted Biased Estimators in Misspecified Regression Model with Incomplete Prior Information

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Manickavasagar Kayanan ◽  
Pushpakanthie Wijekoon
Keyword(s):  
Regression Model ◽  
Prior Information ◽  
Ridge Estimator ◽  
Monte Carlo Simulation Study ◽  
Error Matrix ◽  
Liu Estimator ◽  
Explanatory Variables ◽  
Biased Estimators ◽  
Incomplete Prior Information ◽  
Almost Unbiased

The analysis of misspecification was extended to the recently introduced stochastic restricted biased estimators when multicollinearity exists among the explanatory variables. The Stochastic Restricted Ridge Estimator (SRRE), Stochastic Restricted Almost Unbiased Ridge Estimator (SRAURE), Stochastic Restricted Liu Estimator (SRLE), Stochastic Restricted Almost Unbiased Liu Estimator (SRAULE), Stochastic Restricted Principal Component Regression Estimator (SRPCRE), Stochastic Restricted r-k (SRrk) class estimator, and Stochastic Restricted r-d (SRrd) class estimator were examined in the misspecified regression model due to missing relevant explanatory variables when incomplete prior information of the regression coefficients is available. Further, the superiority conditions between estimators and their respective predictors were obtained in the mean square error matrix (MSEM) sense. Finally, a numerical example and a Monte Carlo simulation study were used to illustrate the theoretical findings.

scholarly journals On the Weighted Mixed Almost Unbiased Ridge Estimator in Stochastic Restricted Linear Regression

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Chaolin Liu ◽  
Hu Yang ◽  
Jibo Wu
Keyword(s):  
Linear Regression ◽  
Monte Carlo Study ◽  
Real Data ◽  
Ridge Estimator ◽  
Error Matrix ◽  
Mixed Estimator ◽  
Optimal Values ◽  
The Mean ◽  
Theoretical Results ◽  
Almost Unbiased

We introduce the weighted mixed almost unbiased ridge estimator (WMAURE) based on the weighted mixed estimator (WME) (Trenkler and Toutenburg 1990) and the almost unbiased ridge estimator (AURE) (Akdeniz and Erol 2003) in linear regression model. We discuss superiorities of the new estimator under the quadratic bias (QB) and the mean square error matrix (MSEM) criteria. Additionally, we give a method about how to obtain the optimal values of parameterskandw. Finally, theoretical results are illustrated by a real data example and a Monte Carlo study.

scholarly journals Preliminary test almost unbiased ridge estimator in a linear regression model with multivariate Student-t errors

2020 ◽  
Vol 15 (1) ◽  
pp. 27-43
Author(s):  
Jianwen Xu ◽  
Hu Yang
Keyword(s):  
Regression Model ◽  
Sufficient Conditions ◽  
Preliminary Test ◽  
Multiple Regression Model ◽  
Regression Coefficients ◽  
Lagrangian Multiplier ◽  
Ridge Estimator ◽  
Lm Tests ◽  
Theoretical Results ◽  
Almost Unbiased

In this paper, the preliminary test almost unbiased ridge estimators of the regression coefficients based on the conflicting Wald (W), Likelihood ratio (LR) and Lagrangian multiplier (LM) tests in a multiple regression model with multivariate Student-t errors are introduced when it is suspected that the regression coefficients may be restricted to a subspace. The bias and quadratic risks of the proposed estimators are derived and compared. Sufficient conditions on the departure parameter ∆ and the ridge parameter k are derived for the proposed estimators to be superior to the almost unbiased ridge estimator, restricted almost unbiased ridge estimator and preliminary test estimator. Furthermore, some graphical results are provided to illustrate theoretical results.

scholarly journals An Unbiased Two-Parameter Estimation with Prior Information in Linear Regression Model

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jibo Wu
Keyword(s):  
Parameter Estimation ◽  
Linear Regression ◽  
Prior Information ◽  
Ordinary Least Squares ◽  
Parameter Estimator ◽  
Ordinary Least Squares Estimator ◽  
Theoretical Results ◽  
Two Parameter ◽  
Almost Unbiased ◽  
Better Than

We introduce an unbiased two-parameter estimator based on prior information and two-parameter estimator proposed by Özkale and Kaçıranlar, 2007. Then we discuss its properties and our results show that the new estimator is better than the two-parameter estimator, the ordinary least squares estimator, and explain the almost unbiased two-parameter estimator which is proposed by Wu and Yang, 2013. Finally, we give a simulation study to show the theoretical results.

scholarly journals POWER OF THE TESTS DENGAN NON-SAMPLE PRIOR INFORMATION PADA PENGUJIAN HIPOTESIS SATU ARAH

2016 ◽  
Vol 8 (2) ◽  
pp. 89
Author(s):  
Budi Pratikno ◽  
Lina Sulistia ◽  
Yuliatri Wirawidya Haryono
Keyword(s):  
Regression Model ◽  
Prior Information ◽  
Real Data ◽  
Preliminary Test ◽  
Graphical Analysis ◽  
Minimum Size ◽  
Power Of The Test ◽  
Simple Regression Model ◽  
Alternative Choice ◽  
Simple Regression

The research discussed power of the tests with  non-sample prior information (NSPI) in testing intercept on one-side-hypothesis. The testing is condcuted on a simple regression model (SRM) and multivariate simple regression model (MSRM), and the power of the tests are unrestricted test (UT), restricted test (RT), and preliminary-test test (PTT). The method for choosing the best  tests is a maximum power and minimum size. A simulation study and graphical analysis are given using generate and real data. The result showed that the power of the test of the PTT  are an alternative choice  among the tests on both SRM and MSRM.

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