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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.

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‎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.

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In this paper, the worst allocation of deductibles  and limits in layer policies are discussed from the viewpoint  of the insurer. It is shown that if n independent and identically distributed exponential risks are covered by the layer policies and  the policy limits are equal, then the worst allocation of deductibles from the viewpoint of the insurer is (d‎, ‎0‎, ‎..., ‎0)‎.

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The advent of new technology in recent years has facilitated the production of high dimension data. In these data we need evaluating more than one assumption.  Multiple testing can be used for the collection of assumptions that are simultaneously tested and controlled the rate of family wise error that is the most critical issue in such tests. In this report, the authors apply Sidak and Stepwise strategies for controlling family wise error rate in detecting outlier profiles and comparing to each other. Considering our simulation results, the performance of such methods are compared using the parametric bootstrap snd by applying on real data in dataset illustrate the implementation of the proposed methods.

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This article aims to joint modeling of longitudinal CD4 cells count and time to death in HIV patients based on the AFT model. The modeling of the longitudinal count response, a GLME model under the family of PSD, was used. In contrast, for the TTE data, the parametric AFT model under the Weibull distribution was investigated. These two responses are linked through random effects correlated with the normal distribution. The longitudinal and survival data are then assumed independent, given the latent linking process and any available covariates. Considering excess zeros for two responses and right censoring, presented a joint model that has not yet been investigated by other researchers. The parameters were also estimated using MCMC methods.

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One of the most frequently encountered longitudinal studies issues is data with losing the appointments or getting censoring. In such cases, all of the subjects do not have the same set of observation times. The missingness in the analysis of longitudinal discrete and continuous mixed data is also common, and missing may occur in one or both responses. Failure to pay attention to the cause of the missing (the mechanism of the missingness) leads to unbiased estimates and inferences. Therefore, in this paper, we investigate the mechanism of nonignorable missing in set-inflated continuous and zero-inflation power series, as well as the continuous and k-inflated ordinal mixed responses. A full likelihood-based approach is used to obtain the maximum likelihood estimates of the parameters of the models. In order to assess the performance of the models, some simulation studies are performed. Two applications of our models are illustrated for the American's Changing Lives  survey, and the Peabody Individual Achievement Test  data set.

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Paying attention to the copula function in order to model the structure of data dependence has become very common in recent decades. Three methods of estimation, moment method, mixture method, and copula moment, are considered to estimate the dependence parameter of copula function in the presence of outlier data. Although the moment method is an old method, sometimes this method leads to inaccurate estimation. Thus, two other moment-based methods are intended to improve that old method. The simulation study results showed that when we use copula moment and mixture moment for estimating the dependence parameter of copula function in the presence of outlier data, the obtained MSEs are smaller. Also, the copula moment method is the best estimate based on MSE. Finally, the obtained numerical results are used in a practical example.

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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.

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High interpretability and ease of understanding decision trees have made
them one of the most widely used machine learning algorithms. The key to building
efficient and effective decision trees is to use the suitable splitting method. This
paper proposes a new splitting approach to produce a tree based on the T-entropy criterion
for the splitting method. The method presented on three data sets is examined
by 11 evaluation criteria. The results show that the introduced method in making
the decision tree has a more accurate performance than the well-known methods of
Gini index, Shannon, Tisalis, and Renny entropies and can be used as an alternative
method in producing the decision tree.

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Although the multiple dependent state sampling (MDS) plan is preferred over the conditional plans due to the small size required, it is impossible to use it in a situation where the quality of manufactured products depends on more than one quality characteristic. In this study, to improve the performance of the mentioned method, S^T_{pk}-based MDS plan is proposed, which is applicable to inspect products with independent and multivariate normally distributed characteristics. The principal component analysis technique is used to develop an application of the proposed plan in the presence of dependent variables. Moreover, optimal values of plan parameters are obtained based on a nonlinear optimization problem. Findings indicate that compared to S^T_{pk}-based variable single sampling and repetitive group sampling plans, the proposed method is the best in terms of required sample size and OC curve. Finally, an industrial example is given to explain how to use the proposed plan.

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In the 1980s, Genichi Taguchi, a Japanese quality advisor, claimed that most of the variability affiliated with the response could be attributed to the company of unmanageable (noise) factors. In some practical cases, his modeling proposition evidence leads the quality improvement to many runs in a crossed array. Hence, several researchers have em-braced noteworthy attitudes of response surface methodology along with the robust parameter design action as alternatives to Taguchi's plan. These alternatives model the response's mean and variance corresponding to the combination of control and noise factors in a combined array to accomplish a robust process or production. Indeed, using response surface methods to the robust parameter design minimises the impression of noise factors on assembling processes or productions. This paper intends to develop further modeling of the predicted response and variance in the presence of noise factors based on unbiased and robust estimators. Another goal is to design the experiments according to the optimal designs to improve these estimators' accuracy and precision simultaneously.

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This paper proposes a different attitude for analyzing three-way contingency tables using conditional independence. We show that different  types of independence explored in log-linear models can be achieved without using these models and only by using conditional independence. Some numerical examples are presented to illustrate the proposed methods.

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Production of high-quality products necessitates identifying the most influential factors, among many factors, for controlling and reducing quality variation. In such a setting, the factorial designs are utilized to determine the active factors with maximal information and model an appropriate relation between the factors and the variable of interest. In this regard, robust parameter designs dividing the factors to control- and noise factors are efficient methods for offline quality control for stabilizing the quality variation in the presence of the noise factors. Interestingly, this could be achieved through exploiting active control by noise interactions. One needs to experiment with numerous treatments to detect the active interaction effects. Search designs are suggested to save treatments, and a superior one is recommended among the appropriate ones. To determine the superior design, one needs a design criterion; however, the existing criteria could be more beneficial for robust parameter designs. In this paper, we proposed a criterion to rank the search designs and determine the superior one.

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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.