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 On the Stochastic Restrictedr-kClass Estimator and Stochastic Restrictedr-dClass Estimator in Linear Regression Model

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Jibo Wu
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Mean Squared Error ◽  
Multiple Linear Regression Model ◽  
Error Matrix ◽  
Squared Error ◽  
The Mean ◽  
Linear Restrictions ◽  
Theoretical Results

The stochastic restrictedr-kclass estimator and stochastic restrictedr-dclass estimator are proposed for the vector of parameters in a multiple linear regression model with stochastic linear restrictions. The mean squared error matrix of the proposed estimators is derived and compared, and some properties of the proposed estimators are also discussed. Finally, a numerical example is given to show some of the theoretical results.

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 Two Classes of Almost Unbiased Type Principal Component Estimators in Linear Regression Model

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Yalian Li ◽  
Hu Yang
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Mean Squared Error ◽  
Principal Component ◽  
Monte Carlo Simulation Study ◽  
Error Matrix ◽  
Squared Error ◽  
The Mean ◽  
Almost Unbiased

This paper is concerned with the parameter estimator in linear regression model. To overcome the multicollinearity problem, two new classes of estimators called the almost unbiased ridge-type principal component estimator (AURPCE) and the almost unbiased Liu-type principal component estimator (AULPCE) are proposed, respectively. The mean squared error matrix of the proposed estimators is derived and compared, and some properties of the proposed estimators are also discussed. Finally, a Monte Carlo simulation study is given to illustrate the performance of the proposed estimators.

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 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 Performance of Principal Component Liu-Type Estimator under the Mean Square Error Criterion

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Jibo Wu
Keyword(s):  
Principal Component Regression ◽  
Principal Component ◽  
Ordinary Least Squares ◽  
Mean Square ◽  
Ridge Estimator ◽  
Error Criterion ◽  
Ordinary Least Squares Estimator ◽  
The Mean ◽  
Mean Square Error Criterion ◽  
Theoretical Results

Wu (2013) proposed an estimator, principal component Liu-type estimator, to overcome multicollinearity. This estimator is a general estimator which includes ordinary least squares estimator, principal component regression estimator, ridge estimator, Liu estimator, Liu-type estimator,r-kclass estimator, andr-dclass estimator. In this paper, firstly we use a new method to propose the principal component Liu-type estimator; then we study the superior of the new estimator by using the scalar mean squares error criterion. Finally, we give a numerical example to show the 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 Performance of Some Stochastic Restricted Ridge Estimator in Linear Regression Model

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Jibo Wu ◽  
Chaolin Liu
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Simulation Study ◽  
Linear Regression Model ◽  
Ridge Regression ◽  
Ridge Estimator ◽  
Numerical Example ◽  
Regression Estimators ◽  
Mixed Estimator

This paper considers several estimators for estimating the stochastic restricted ridge regression estimators. A simulation study has been conducted to compare the performance of the estimators. The result from the simulation study shows that stochastic restricted ridge regression estimators outperform mixed estimator. A numerical example has been also given to illustrate the performance of the estimators.

scholarly journals P170 The validity and utility of the SLE-key® rule-out serological test when applied in a selected cohort of patients with SLE and other connective tissue diseases

Rheumatology ◽  
2021 ◽  
Vol 60 (Supplement_1) ◽  
Author(s):  
Sheilla Achieng ◽  
John A Reynolds ◽  
Ian N Bruce ◽  
Marwan Bukhari
Keyword(s):  
Linear Regression ◽  
Connective Tissue ◽  
Connective Tissue Disease ◽  
Negative Correlation ◽  
Connective Tissue Diseases ◽  
Inflammatory Myositis ◽  
The Mean ◽  
Negative Rule ◽  
Spearman’S Correlation ◽  
Rule Out

Abstract Background/Aims  We aimed to establish the validity of the SLE-key® rule-out test and analyse its utility in distinguishing systemic lupus erythematosus (SLE) from other autoimmune rheumatic connective tissue diseases. Methods  We used data from the Lupus Extended Autoimmune Phenotype (LEAP) study, which included a representative cross-sectional sample of patients with a variety of rheumatic connective tissue diseases, including SLE, mixed connective tissue disease (MCTD), inflammatory myositis, systemic sclerosis, primary Sjögren’s syndrome and undifferentiated connective tissue disease (UCTD). The modified 1997 ACR criteria were used to classify patients with SLE. Banked serum samples were sent to Immune-Array’s CLIA- certified laboratory Veracis (Richmond, VA) for testing. Patients were assigned test scores between 0 and 1 where a score of 0 was considered a negative rule-out test (i.e. SLE cannot be excluded) whilst a score of 1 was assigned for a positive rule-out test (i.e. SLE excluded). Performance measures were used to assess the test’s validity and measures of association determined using linear regression and Spearman’s correlation. Results  Our study included a total of 155 patients of whom 66 had SLE. The mean age in the SLE group was 44.2 years (SD 13.04). 146 patients (94.1%) were female. 84 (54.2%) patients from the entire cohort had ACR SLE scores of ≤ 3 whilst 71 (45.8%) had ACR SLE scores ≥ 4. The mean ACR SLE total score for the SLE patients was 4.85 (SD 1.67), ranging from 2 to 8, with mean disease duration of 12.9 years. The Sensitivity of the SLE-Key® Rule-Out test in diagnosing SLE from other connective tissue diseases was 54.5%, specificity was 44.9%, PPV 42.4% and NPV 57.1 %. 45% of the SLE patients had a positive rule-out test. SLE could not be ruled out in 73% of the MCTD patients whilst 51% of the UCTD patients had a positive Rule-Out test and >85% of the inflammatory myositis patients had a negative rule-out test. ROC analysis generated an AUC of 0.525 illustrating weak class separation capacity. Linear regression established a negative correlation between the SLE-key Rule-Out score and ACR SLE total scores. Spearman’s correlation was run to determine the relationship between ACR SLE total scores and SLE-key rule-out score and showed very weak negative correlation (rs = -0.0815, n = 155, p = 0.313). Conclusion  Our findings demonstrate that when applied in clinical practice in a rheumatology CTD clinic setting, the SLE-key® rule-out test does not accurately distinguish SLE from other CTDs. The development of a robust test that could achieve this would be pivotal. It is however important to highlight that the test was designed to distinguish healthy subjects from SLE patients and not for the purpose of differentiating SLE from other connective tissue diseases. Disclosure  S. Achieng: None. J.A. Reynolds: None. I.N. Bruce: Other; I.N.B is a National Institute for Health Research (NIHR) Senior Investigator and is funded by the NIHR Manchester Biomedical Research Centre. M. Bukhari: None.

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