This paper introduces a novel Semiparametric Bayesian approach for bivariate meta-regression. The method extends traditional binomial models to trinomial distributions, accounting for positive, neutral, and negative treatment effects. Using a conditional Dirichlet process, we develop a model to compare treatment and control groups across multiple clinical centers. This approach addresses the challenges posed by confounding factors in such studies. The primary objective is to assess treatment efficacy by modeling response outcomes as trinomial distributions. We employ Gibbs sampling and the Metropolis-Hastings algorithm for posterior computation. These methods generate estimates of treatment effects while incorporating auxiliary variables that may influence outcomes. Simulations across various scenarios demonstrate the model’s effectiveness. We also establish credible intervals to evaluate hypotheses related to treatment effects. Furthermore, we apply the methodology to real-world data on economic activity in Iran from 2009 to 2021. This application highlights the practical utility of our approach in meta-analytic contexts. Our research contributes to the growing body of literature on Bayesian methods in meta-analysis. It provides valuable insights for improving clinical study evaluations.

This paper considers an extension of the linear mixed model, called Semiparametric mixed effects model, for longitudinal data, when multicollinearity is present. To overcome this problem, a new mixed ridge estimator is proposed while the nonparametric function in the Semiparametric model is approximated by the kernel method. The proposed approache integrates ridge method into the Semiparametric mixed effects modeling framework in order to account for both the correlation induced by repeatedly measuring an outcome on each individual over time, as well as the potentially high degree of correlation among possible predictor variables. The asymptotic normality of the exhibited estimator is established. To improve efficiency, the estimation of the covariance function is accomplished using an iterative algorithm. Performance of the proposed estimator is compared through a simulation study and analysis of CD4 data.

so many natural phenomena of determining relationship and the effect of input variables on response variable in statistical studies may be different from the suggested model that the researcher selects for his study due to the occupant exists in the structure of data. It may be so influential on different distributions considered for response variables. The optimal properties of estimators evaluated and studied for two statistical variables considered for response variable and input variables in the suggested model. It has been simulated for study and real data has been also investigated. The results confirmed the superiority of a model which is close to the structure of the data.

Introduction Statistical shape analysis is one of the fields of multivariate statistics, where the main focus is on the geometric structures of objects. This analysis method is widely used in many scientific fields, such as medicine and morphology. One of the tools for diagnosing diseases or determining animal species is the images and the shapes extracted from them. Introducing methods of classifying shapes can be a solution to determine the class of each observation. Usually, in regression modelling, explanatory and dependent variables are quantitative. However, one may want to measure the relationship between an explanatory variable (with continuous values) and a dependent variable with qualitative values. One option is to use the multinomial logistic regression model. Therefore, a Semiparametric multinomial logistic regression model to classify shape data is introduced in this paper. Material and Methods The power-divergence criterion is a measure for hypothesis testing in multinomial data. This criterion is used to define the kernel function of explanatory variables. The model is a multinomial logistic regression model based on kernel function as a function of explanatory variables and an intercept. Since the shapes’,geometric structure and size play a key role in the classification of shapes, the kernel function is determined based on the shape distances. The smoothing parameter was estimated using the least square cross-validation method. Also, the estimation of model parameters was done using the neural network method. Results and Discussion The shape space is a manifold, but most of the methods presented in the literature for classifying shapes were done in the shape tangent space or used linear transformations. Since mapping from the manifold to linear space decreases data information, applying tangent space and linear spaces will reduce classification accuracy. Therefore, the shape space is used to classify the shape data. The performance of the model in a simulation study and two real data sets were investigated in the paper. The two real data sets used in this paper are taken from the shape package in R software. The first data set is related to schizophrenia patients and people as control, and the second one is associated with the skull of three species of apes of two sexes. The classification of these data showed an accuracy of 82% and 84%, respectively. Also, a comparison was made with the previous methods based on a real data set, which showed the proper performance of our approach compared to the other two techniques. Conclusion Since in the nonparametric kernel function, suitable distances of the shape space were used, the introduced method performs better than those based on Euclidean spaces. Also, the ability to use other shape distances, such as partial, full Procrustes and Riemannian distances, makes the model more flexible in classifying different types of shape data. On the other hand, sizeand-shape distance can be used in the kernel function to classify data whose size plays a key role in their geometric structure. Furthermore, since few statistical distributions have been introduced in the shape space, nonparametric methods can be helpful in the analysis of shape data. However, using nonparametric methods in the shape space is time-consuming from the point of view of computer calculations.

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.

Semiparametric linear mixed measurement error models are extensions of linear mixed measurement error models to include a nonparametric function of some covariate. They have been found to be useful in both cross-sectional and longitudinal studies. In this paper first we propose a penalized corrected likelihood approach to estimate the parametric component in Semiparametric linear mixed measurement error model and then using the case deletion and subject deletion analysis we survey the influence diagnostics in such models. Finally, the performance of our influence diagnostics methods are illustrated through a simulated example and a real data set.

Lam (2007) introduces a generalization of renewal processes named Geometric processes, where inter-arrival times are independent and identically distributed up to a multiplicative scale parameter, in a geometric fashion. We here envision a more general scaling, not necessarily geometric. The corresponding counting process is named Extended Geometric Process (EGP). Semiparametric estimates are provided and studied for an EGP, which includes consistency results and convergence rates. In a reliability context, arrivals of an EGP may stand for successive failure times of a system submitted to imperfect repairs. In this context, we study: 1) the mean number of failures on some finite horizon time; 2) a replacement policy assessed through a cost function on an infinite horizon time.