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

Author(s):  
Jianwen Xu ◽  
Hu Yang

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.

2016 ◽  
Vol 15 (1) ◽  
Author(s):  
Antonio Boada

This paper, a practical application, proven through actual data, how the Bayesian Dynamic Linear Model Order 1 can be applied directly to the random waste from a multiple regression model Classic Static, thus creating an interesting addition is exposed for predictive statistical models. This Bayesian component generates a retro factor that feeds on waste (difference between predictions and actual historical values), adjusted according to the most recent historical information, all of them automatically and without the need to continually adjusts the Multiple Regression coefficients, generating an increase in the strength and stability of such models for prediction automated tools companies. This article provides a case of how Bayesian statistics can be an excellent complement to the techniques of classical frequentist statistics.RESUMEN Mediante este artículo, se expone una aplicación práctica, comprobada a través de datos reales, de cómo el Modelo Lineal Dinámico Bayesiano de Orden 1, puede ser aplicado directamente sobre los residuos aleatorios provenientes de un Modelo Clásico de Regresión Múltiple Estático, generando así un complemento interesante para los modelos estadísticos predictivos. Este componente bayesiano, genera un factor que se retro alimenta de los residuos (diferencia entre las predicciones y los valores históricos reales), ajustándose según la información histórica más reciente, todo ellos de forma automatizada y sin necesidad de ajustar continuamente los coeficientes de Regresión Múltiple, lo que genera un incremento en la robustez y estabilidad de dichos modelos para herramientas automatizadas de predicción en empresas. Este artículo establece un caso de cómo la estadística bayesiana puede ser un excelente complemento para las técnicas de las estadística clásica frecuentista.RESUMO Através deste artigo, uma aplicação prática, comprovada através de dados reais, como o modelo linear dinâmico Bayesian Ordem 1 pode ser aplicado diretamente sobre os resíduos aleatória de um modelo clássico de regressão múltipla estático, gerando assim um suplemento exposta interessante para os modelos estatísticos preditivos. Este componente Bayesian gera um fator que retro alimenta de resíduos (diferença entre as previsões e os valores históricos reais), ajustado de acordo com as últimas informações históricas, todas elas automaticamente e sem a necessidade de ajustar continuamente os coeficientes de regressão múltipla , gerando um aumento na força e estabilidade de tais modelos para ferramentas de previsão automatizada empresas. Este artigo fornece um exemplo de como as estatísticas Bayesian pode ser um excelente complemento para as técnicas de estatística freqüentista clássicos.


Author(s):  
Muhammad Amin ◽  
Muhammad Qasim ◽  
Ahad Yasin ◽  
Muhammad Amanullah

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Manickavasagar Kayanan ◽  
Pushpakanthie Wijekoon

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.


2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Chaolin Liu ◽  
Haina Jiang ◽  
Xinhui Shi ◽  
Donglin Liu

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.


2005 ◽  
Vol 57 (3-4) ◽  
pp. 143-160
Author(s):  
Z. Hoque ◽  
B. Billah ◽  
S. Khan

In this paper we propose shrinkage preliminary test estimator (SPTE) of the coefficient vector in the multiple linear regression model based on the size corrected Wald ( W), likelihood ratio ( LR) and Lagrangian multiplier ( LM) tests. The correction factors used are those obt,ained from degrees of freedom corrections to the estimate of the error variance and those obtained from the second­order Edgeworth approximations to the exact distributions of the test statistics. The bias and weighted mean squared error (WMSE) fun ctions of the estimators are derived. With respect to WMSE, the relative efficiencies of the SPTEs relative to the maximum likelihood estimator are calculated. This study shows that the amount of conflict can be substantial when the three t ests are based on the same asymptotic chi­square critical value. The conflict among the SPTEs is due to the asymptotic tests not having the correct significance level. The Edgeworth size corrected W, LR and LM tests reduce the conflict remarkably.


2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Chaolin Liu ◽  
Hu Yang ◽  
Jibo Wu

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.


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