In this paper, we investigate the connection between the hierarchical models and the power prior distribution in quantile regression (QReg). Under specific quantile, we develop an expression for the power parameter ( ) to calibrate the power prior distribution for quantile regression to a corresponding hierarchical model. In addition, we estimate the relation between the  and the quantile level via hierarchical model. Our proposed methodology is illustrated with real data example.

     Recently Tobit  Quantile Regression(TQR) has emerged as an important tool in statistical analysis . in order to improve the parameter estimation in (TQR) we proposed Bayesian hierarchical model with double adaptive elastic net technique  and Bayesian hierarchical model with adaptive ridge regression technique .

 in double adaptive elastic net technique we assume  different penalization parameters  for penalization different regression coefficients in both parameters λ₁and  λ₂  , also in adaptive ridge regression technique we assume different  penalization parameters for penalization different regression coefficients i

Abstract:

      In this research we discussed the parameter estimation and variable selection in Tobit quantile regression model in present of multicollinearity problem. We used elastic net technique as an important technique for dealing with both multicollinearity and variable selection. Depending on the data we proposed Bayesian Tobit hierarchical model with four level prior distributions . We assumed both tuning parameter are random variable and estimated them with the other unknown parameter in the model .Simulation study was used for explain the efficiency of the proposed method and then we compared our approach with (Alhamzwi 2014 & standard QR) .The result illustrated that our approach

Regression models are among the most important tools in scientific research and data analysis. Among these models, fuzzy regression models stand out as a modern form that addresses issues of uncertain data that do not conform to the assumptions of traditional models. In this study, we present fuzzy regression models with a focus on fuzzy linear quantitative models, in addition to fuzzy support vector machine (SVM) models. Generally, linear models are considered less effective compared to non-linear models, and to address this issue, hybrid models combining both types have been introduced. The concept of hybrid models has been generalized to fuzzy models in this paper, where we introduce a hybrid model that combines both linear and non-linea

In this paper, Bayes estimators of the parameter of Maxwell distribution have been derived along with maximum likelihood estimator. The non-informative priors; Jeffreys and the extension of Jeffreys prior information has been considered under two different loss functions, the squared error loss function and the modified squared error loss function for comparison purpose. A simulation study has been developed in order to gain an insight into the performance on small, moderate and large samples. The performance of these estimators has been explored numerically under different conditions. The efficiency for the estimators was compared according to the mean square error MSE. The results of comparison by MSE show that the efficiency of Bayes est

In this paper we used frequentist and Bayesian approaches for the linear regression model to predict future observations for unemployment rates in Iraq. Parameters are estimated using the ordinary least squares method and for the Bayesian approach using the Markov Chain Monte Carlo (MCMC) method. Calculations are done using the R program. The analysis showed that the linear regression model using the Bayesian approach is better and can be used as an alternative to the frequentist approach. Two criteria, the root mean square error (RMSE) and the median absolute deviation (MAD) were used to compare the performance of the estimates. The results obtained showed that the unemployment rates will continue to increase in the next two decade

In this paper, we present a comparison of double informative priors which are assumed for the parameter of inverted exponential distribution.To estimate the parameter of inverted exponential distribution by using Bayes estimation ,will be  used two different kind of information in the Bayes estimation; two different priors have been selected for the parameter of inverted exponential distribution. Also assumed Chi-squared - Gamma distribution, Chi-squared - Erlang distribution, and- Gamma- Erlang distribution as double priors. The results are the derivations of these estimators under the squared error loss function with three different double priors.

Additionally Maximum likelihood estimation method

Spatial Autoregressive Model (SAR) is one of the modeling frameworks that indicates a spatial dependence in the response variable. SAR model has a weakness, which is represented by the unknown variance of the residuals. Therefore, an alternative model has used titled Spatial Autoregressive Quantile Regression (SARQR) model That which is obtained by combining SAR and Quantile Regression (QR) models, is a regression method with the approach of dividing the data into particular quantiles that are likely to have different estimate values. This alternative model addresses the variance issues in SAR models. Additionally, the SARQR model not only resolves the issue of spatial variance but also serves as a solution for dealing with non-normal data

In this paper, Bayes estimators of the parameter of Maxwell distribution have been derived along with maximum likelihood estimator. The non-informative priors; Jeffreys and the extension of Jeffreys prior information has been considered under two different loss functions, the squared error loss function and the modified squared error loss function for comparison purpose. A simulation study has been developed in order to gain an insight into the performance on small, moderate and large samples. The performance of these estimators has been explored numerically under different conditions. The efficiency for the estimators was compared according to the mean square error MSE. The results of comparison by MSE show that the efficiency of B