Penalized estimators for estimating regression parameters have been considered by many authors for many decades. Penalized regression with rectangular norm is one of the mainly used since it does variable selection and estimating parameters, simultaneously. In this paper, we propose some new estimators by employing uncertain prior information on parameters. Superiority of the proposed shrinkage estimators over the least absoluate and shrinkage operator (LASSO) estimator is demonstrated via a Monte Carlo study. The prediction rate of the proposed estimators compared to the LASSO estimator is also studied in the US State Facts and Figures dataset.

Introducing some efficient model selection criteria for mixed models is a substantial challenge; Its source is indeed fitting the model and computing the maximum likelihood estimates of the parameters. Data cloning is a new method to fit mixed models efficiently in a likelihood-based approach. This method has been popular recently and avoids the main problems of other likelihood-based methods in mixed models. A disadvantage of data cloning is its inability of computing the maximum of likelihood function of the model. This value is a key quantity in proposing and calculating information criteria. Therefore, it seems that we can not, directly, define an appropriate information criterion by data cloning approach. In this paper, this believe is broken and a criterion based on data cloning is introduced. The performance of the proposed model selection criterion is also evaluated by a simulation study.

One way of dealing with the problem of collinearity in linear models, is to make use of the Liu estimator. In this paper, a new estimator by generalizing the modified Liu estimator of Li and Yang (2012) has been proposed. This estimator is constructed based on a prior information of vector parameters in linear regression and the generalized estimator of Akdeniz and Kachiranlar (1995). Using the mean square error matrix criterion, we have obtained the superiority conditions Of this newly defined estimator over the generalized Liu estimator. For comparison sake, a numerical example as well as a Monte Carlo simulation study are considered.

Often‎, ‎in high dimensional problems‎, ‎where the number of variables is large the number of observations‎, ‎penalized estimators based on shrinkage methods have better efficiency than the OLS estimator from the prediction error viewpoint‎. In these estimators‎, ‎the tuning or shrinkage parameter plays a deterministic role in variable selection‎. ‎The bridge estimator is an estimator which simplifies to ridge or LASSO estimators varying the tuning parameter‎. ‎In these paper‎, ‎the shrinkage bridge estimator is derived under a linear constraint on regression coefficients and its consistency is proved‎. ‎Furthermore‎, ‎its efficiency is evaluated in a simulation study and a real example‎.

Geostatistical spatial count data in finite populations can be seen in many applications, such as urban management and medicine. The traditional model for analyzing these data is the spatial logit-binomial model. In the most applied situations, these data have overdispersion alongside the spatial variability. The binomial model is not the appropriate candidate to account for the overdispersion. The proper alternative is a beta-binomial model that has sufficient flexibility to account for the extra variability due to the possible overdispersion of counts. In this paper, we describe a Bayesian spatial beta-binomial for geostatistical count data by using a combination of the integrated nested Laplace approximation and the stochastic partial differential equations methods. We apply the methodology for analyzing the number of people injured/killed in car crashes in Mashhad, Iran. We further evaluate the performance of the model using a simulation study.

Financial and economic indicators, such as housing prices, often show spatial correlation and heterogeneity. While spatial econometric models effectively address spatial dependency, they face challenges in capturing heterogeneity. Geographically weighted regression is naturally used to model this heterogeneity, but it can become too complex when data show homogeneity across subregions. In this paper, spatially homogeneous subareas are identified through spatial clustering, and Bayesian spatial econometric models are then fitted to each subregion. The integrated nested Laplace approximation method is applied to overcome the computational complexity of posterior inference and the difficulties of MCMC algorithms. The proposed methodology is assessed through a simulation study and applied to analyze housing prices in Mashhad City.