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    In this paper, we introduce the weighted ridge estimators of fixed and random effects in stochastic restricted linear mixed measurement error models when collinearity is present. The asymptotic properties of the resulting estimates are examined. The necessary and sufficient conditions, for the superiority of the weighted ridge estimators against the weighted estimator in order to select the ridge parameter based on the mean squared error matrix of estimators, are investigated. Finally, theoretical results are augmented with a simulation study and a numerical example.

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Cancer progression among patients can be assessed by creating a set of gene markers using statistical data analysis methods. Still, one of the main problems in the statistical study of this type of data is the large number of genes versus a small number of samples. Therefore, it is essential to use dimensionality reduction techniques to eliminate and find the optimal number of genes to predict the desired classes accurately. On the other hand, choosing an appropriate method can help extract valuable information and improve the machine learning model's efficiency. This article uses an ensemble learning approach, a random support vector machine cluster, to find the optimal feature set. In the current paper and in dealing with real data, it is shown that via randomly projecting the original high-dimensional feature space onto multiple lower-dimensional feature subspaces and combining support vector machine classifiers, not only the essential genes are found in causing prostate cancer, but also the classification precision is increased.

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‎This paper presents a nonparametric multi-class depth-based classification approach for multivariate data. This approach is easy to implement rather than most existing nonparametric methods that have computational complexity. If the assumption of the elliptical symmetry holds, this method is equivalent to the Bayes optimal rule. Some simulated data sets as well as real example have been used to evaluate the performance of these depth-based classifiers.

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Model-based clustering is the most widely used statistical clustering method, in which heterogeneous data are divided into homogeneous groups using inference based on mixture models. The presence of measurement error in the data can reduce the quality of clustering and, for example, cause overfitting and produce spurious clusters. To solve this problem, model-based clustering assuming a normal distribution for measurement errors has been introduced. However, too large or too small (outlier) values ​​of measurement errors cause poor performance of existing clustering methods. To tackle this problem {and build a stable model against the presence of outlier measurement errors in the data}, in this article, a symmetric $alpha$-stable distribution is proposed as a replacement for the normal distribution for measurement errors, and the model parameters are estimated using the EM algorithm and numerical methods. Through simulation and real data analysis, the new model is compared with the MCLUST-based model, considering cases with and without measurement errors, and the performance of the proposed model  for data clustering in the presence of various outlier measurement errors is shown.

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Due to the volume and complexity of emerging data in survival analysis, it is necessary to use statistical learning methods in this field. These methods can estimate the probability of survival and the effect of various factors on the survival of patients. In this article, the performance of the Cox model as a common model in survival analysis is compared with compensation-based methods such as Cox Ridge and Cox Lasso, as well as statistical learning methods such as random survival forests and neural networks. The simulation results show that in linear conditions, the performance of the models mentioned above is similar to the Cox model. In non-linear conditions, methods such as Cox lasso, random survival forest, and neural networks perform better. Then, these models were evaluated in the analysis of the data of patients with atheromatous, and the results showed that when faced with data with a large number of explanatory variables, statistical learning approaches generally perform better than the classical survival model.

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Systemic risk, as one of the challenges of the financial system, has attracted special attention from policymakers, investors, and researchers. Identifying and assessing systemic risk is crucial for enhancing the financial stability of the banking system. In this regard, this article uses the Conditional Value at Risk method to evaluate the systemic risk of simulated data and Iran's banking system. In this method, the conditional mean and conditional variance are modeled using Autoregressive Moving Average and Generalized Autoregressive Conditional Heteroskedasticity models, respectively. The data studied includes the daily stock prices of 17 Iranian banks from April 8, 2019, to May 1, 2023, which contains missing values in some periods. The Kalman filter approach has been used for interpolating the missing values. Additionally, Vine copulas  with a hierarchical tree structure have been employed to describe the nonlinear dependencies and hierarchical risk structure of the returns of the studied banks. The results of these calculations indicate that Bank Tejarat has the highest systemic risk, and the increase in systemic risk, in addition to causing financial crises, has adverse effects on macroeconomic performance. These results can significantly help in predicting and mitigating the effects of financial crises and managing them effectively.

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‎Support vector machine (SVM) as a supervised algorithm was initially invented for the binary case‎, ‎then due to its applications‎, ‎multi-class algorithms were also designed and are still being studied as research‎. ‎Recently‎, ‎models have been presented to improve multi-class methods‎. ‎Most of them examine the cases in which the inputs are non-random‎, ‎while in the real world‎, ‎we are faced with uncertain and imprecise data‎. ‎Therefore‎, ‎this paper examines a model in which the inputs are uncertain and the problem's constraints are also probabilistic‎. ‎Using statistical theorems and mathematical expectations‎, ‎the problem's constraints have been removed from the random state‎. ‎Then‎, ‎the moment estimation method has been used to estimate the mathematical expectation‎. ‎Using Monte Carlo simulation‎, ‎synthetic data has been generated and the bootstrap resampling method has been used to provide samples as input to the model and the accuracy of the model has been examined‎. ‎Finally‎, ‎the proposed model was trained with real data and its accuracy was evaluated with statistical indicators‎. ‎The results from simulation and real examples show the superiority of the proposed model over the model based on deterministic inputs‎.

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Researchers often face the problem of how to address missing data. Multiple imputation by chained equations is one of the most common methods for imputation. In theory, any imputation model can be used to predict the missing values. However, if the predictive models are incorrect, it can lead to biased estimates and invalid inferences. One of the latest solutions for dealing with missing data is machine learning methods and the SuperMICE method. In this paper, We present a set of simulations indicating that this approach produces final parameter estimates with lower bias and better coverage than other commonly used imputation methods. Also, implementing some machine learning methods and an ensemble algorithm, SuperMICE, on the data of the Industrial establishment survey is discussed,  in which the imputation of different variables in the data co-occurs. Also, the evaluation of various methods is discussed, and the method that has better performance than the other methods is introduced.

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This paper investigates repetitive acceptance sampling inspection plans of lots based on type I censoring when the lifetime has a Tsallis q-exponential distribution. A repetitive acceptance sampling inspection plan is introduced, and its components, along with the optimal average sample number and the operating characteristic value of the plan, are calculated under the specified values for the parameter of distribution and consumer's and producer's risks using a nonlinear programming optimization problem. Comparing the results of the proposed repetitive acceptance sampling plan with the optimal single sampling inspection plan demonstrates the efficiency of the repetitive acceptance sampling plan over the single sampling plan. Moreover, repetitive sampling plans with a limited linear combination of risks are introduced and compared with the existing plan. Results of the introduced plan in tables and figures show that this plan has a lower ASN and, therefore, more efficiency than the existing design. A practical example in the textile industry is used to apply the proposed schemes.