---

In this paper the mixed Poisson regression model is discussed and a Poisson Birnbaum-Saunders regression model is introduced consider the over-dispersion. The Birnbaum-Saunders distribution is the mixture of two the generalized inverse Gaussian distributions, therefore it can be considered as an extension of traditional models. Our proposed model has less dimensional parameter space than the Poisson- generalized inverse Gaussian regression model. We also show that the proposed model has a closed form for likelihood function and we obtain its moments. The EM algorithm is used to estimate the parameters and its efficiency is compared with conventional models by a simulation study. An analysis of a real data is provided for more illustration.

---

---

The nonparametric and semiparametric regression models have been improved extensively in the field of cross-sectional study and independent data, but their improvement in the field of longitudinal data is restricted to the recent years or decade. Since the common methods for correlated data have a much lower ability rather than for the independent data, we should use the models which consider the correlation among the data. The mixed and marginal models consider the correlation factor among the data, and so obtain a better fit for that. Furthermore, the semiparametric regression has more flexibility compared to the parametric and nonparametric regression. Consequently, based on the properties of the longitudinal data, the marginal longitudinal semiparametric regression with the penalized spline estimations, is a suitable choice for the analysis of the longitudinal data. In this article, the semiparametric regression with different coefficients which specifies the relationship between a response variable and an explanatory variable based on another explanatory variable is assessed. In addition, Bayesian inference on the nonparametric model for a simulated data and the marginal longitudinal semiparametric model for a real data have been done by standard software; and the results have good performance.

---

The study of regression diagnostic, including identification of the influential observations and outliers, is of particular importance. The sensitivity of least squares estimators to the outliers and influential observations lead to extending the regression diagnostic in order to provide criteria to assess the anomalous observations. Detecting influential observations and outliers in the presence of collinearity is a complicated task, in the sense that collinearity may cover some of the unusual data. One of the considerable methods to identify outliers is the mean shift outliers method. In this article, we extend the mean shift outliers method to the ridge estimates under linear stochastic restrictions, which is used to reduce the effect of collinearity, and to provide the test statistic to identify the outliers in these estimators. Finally, we show the ability of our proposed method using a practical example of real data.

---

Recalling the definition of shape as a point on hyper-sphere, proposed by Kendall, the regression model is studied in this paper. In order to simplify the modeling, the triangulation via two landmarks is proposed. The triangulation not only simplifies the regression modelling of the shapes but also provides straightforward computation procedure to reconstruct geometrical structure of the objects. Novelty of the proposed method in this paper is on using the predictor variable, based upon the shape, which suitably describes the geometrical variability of the response. The comparison and evaluation of the proposed methods with the full Procrustes matching through the mean square error criteria are done. Application of two models for the configurations of rat skulls is investigated.

---

‎In many fields such as econometrics‎, ‎psychology‎, ‎social sciences‎, ‎medical sciences‎, ‎engineering‎, ‎etc.‎, ‎we face with multicollinearity among the explanatory variables and the existence of outliers in data‎. ‎In such situations‎, ‎the ordinary least-squares estimator leads to an inaccurate estimate‎. ‎The robust methods are used to handle the outliers‎. ‎Also‎, ‎to overcome multicollinearity ridge estimators are suggested‎. ‎On the other hand‎, ‎when the error terms are heteroscedastic or correlated‎, ‎the generalized least squares method is used‎. ‎In this paper‎, ‎a fast algorithm for computation of the feasible generalized least trimmed squares ridge estimator in a semiparametric regression model is proposed and then‎, ‎the performance of the proposed estimators is examined through a Monte Carlo simulation study and a real data set.

---

‎The methodology of sufficient dimension reduction has offered an effective means to facilitate regression analysis of high-dimensional data‎. ‎When the response is censored‎, ‎most existing estimators cannot be applied‎, ‎or require some restrictive conditions‎. ‎In this article modification of sliced inverse‎, ‎regression-II have proposed for dimension reduction for non-linear censored regression data‎. ‎The proposed method requires no model specification‎, ‎it retains full regression information‎, ‎and it provides a usually small set of composite variables upon which subsequent model formulation and prediction can be based‎. ‎Finally‎, ‎the performance of the method is compared based on the simulation studies and some real data set include primary biliary cirrhosis data‎. ‎We also compare with the sliced inverse regression-I estimator‎.

---

---

One of the most critical discussions in regression models is the selection of the optimal model, by identifying critical explanatory variables and negligible variables and more easily express the relationship between the response variable and explanatory variables. Given the limitations of selecting variables in classical methods, such as stepwise selection, it is possible to use penalized regression methods. One of the penalized regression models is the Lasso regression model, in which it is assumed that errors follow a normal distribution. In this paper, we introduce the Bayesian Lasso regression model with an asymmetric distribution error and the high dimensional setting. Then, using the simulation studies and real data analysis, the performance of the proposed model's performance is discussed.

---

---

---

The panel data model is used in many areas, such as economics, social sciences, medicine, and epidemiology. In recent decades, inference on regression coefficients has been developed in panel data models. In this paper, methods are introduced to test the equality models of the panel model among the groups in the data set. First, we present a random quantity that we estimate its distribution by two methods of approximation and parametric bootstrap. We also introduce a pivotal quantity for performing this hypothesis test. In a simulation study, we compare our proposed approaches with an available method based on the type I error and test power. We also apply our method to gasoline panel data as a real data set.

---

This paper suggests Liu-type shrinkage estimators in linear regression model in the presence of multicollinearity under subspace information. The performance of the proposed estimators is compared to Liu-type estimator in terms of their relative efficiency via a Monte Carlo simulation study and a real data set. The results reveal that the proposed estimators outperform better than the Liu-type estimator.

---

This article introduces a semiparametric multinomial logistic regression model to classify labeled configurations. In the regression model, the explanatory variable is the kernel function obtained using the power-divergence criterion. Also, the response variable was categorical and showed the class of each configuration. This semiparametric regression model is introduced based on distances defined in the shape space, and for this reason, the correct classification of shapes using this method has been improved compared to previous methods. ‎The performance of this model has been investigated in the comprehensive simulation study‎. ‎Two real datasets were analyzed using this article's method as an application‎. ‎Finally‎, ‎the method presented in this article was compared with the techniques introduced in the literature‎, ‎which shows the proper performance of this method in classifying configurations‎.

---

‎The high-dimensional data analysis using classical regression approaches is not applicable, and the consequences may need to be more accurate.
This study tried to analyze such data by introducing new and powerful approaches such as support vector regression, functional regression, LASSO and ridge regression. On this subject, by investigating two high-dimensional data sets  (riboflavin and simulated data sets) using the suggested approaches, it is progressed to derive the most efficient model based on three criteria (correlation squared, mean squared error and mean absolute error percentage deviation) according to the type of data.

---

‎Modeling and efficient estimation of the trend function is of great importance in the estimation of variogram and prediction of spatial data. In this article, the support vector regression method is used to model the trend function. Then the data is de-trended and the estimation of variogram and prediction is done. On a real data set, the prediction results obtained from the proposed method have been compared with Spline and kriging prediction methods through cross-validation.  The criterion for choosing the appropriate method for prediction is to minimize the root mean square of the error. The prediction results for several positions with known values were left out of the data set (for some reason) and were obtained for new positions. The results show the high accuracy of prediction (for all positions and elimination positions) with the proposed method compared to kriging and spline.

---

‎

The mixed effects model is one of the powerful statistical approaches used to model the relationship between the response variable and some predictors in analyzing data with a hierarchical structure. The estimation of parameters in these models is often done following either the least squares error or maximum likelihood approaches. The estimated parameters obtained either through the least squares error or the maximum likelihood approaches are inefficient, while the error distributions are non-normal.   In such cases, the mixed effects quantile regression can be used. Moreover, when the number of variables studied increases, the penalized mixed effects quantile regression is one of the best methods to gain prediction accuracy and the model's interpretability. In this paper, under the assumption of an asymmetric Laplace distribution for random effects, we proposed a double penalized model in which both the random and fixed effects are independently penalized. Then, the performance of this new method is evaluated in the simulation studies, and a discussion of the results is presented along with a comparison with some competing models. In addition, its application is demonstrated by analyzing a real example.

---

In this paper, we consider the issue of data classification in which the response (dependent) variable is two (or multi) valued and the predictor (independent) variables are ordinary variables. The errors could be nonprecise and random. In this case, the response variable is also a fuzzy random variable. Based on this and logistic regression, we formulate a model and find the estimation of the coefficients using the least squares method. We will describe the results with an example of one independent random variable. Finally, we provide recurrence relations for the estimation of parameters. This relation can be used in machine learning and big data classification.

---

In this article, autoregressive spatial regression and second-order moving average will be presented to model the outputs of a heavy-tailed skewed spatial random field resulting from the developed multivariate generalized Skew-Laplace distribution. The model parameters are estimated by the maximum likelihood method using the Kolbeck-Leibler divergence criterion. Also, the best spatial predictor will be provided. Then, a simulation study is conducted to validate and evaluate the performance of the proposed model. The method is applied to analyze a real data.

---

One of the most widely used statistical topics in research fields is regression problems. In these models, the basic assumption of model errors is their normality, which, in some cases, is different due to asymmetry features or break points in the data. Piecewise regression models have been widely used in various fields, and it is essential to detect the breakpoint. The break points in piecewise regression models are necessary to know when and how the pattern of the data structure changes. One of the major problems is that there is a heavy tail in these data, which has been solved by using some distributions that generalize the normal distribution. In this paper, the piecewise regression model will be investigated based on the scale mixture of the normal distribution. Also, this model will be compared with the standard piecewise regression model derived from normal errors.