مجله علوم آماری
سال سوم شماره 1 (پیاپی 5، بهار و تابستان 1388)

Unified hybrid censoring scheme is a mixture of generalized Type-I and Type-II hybrid censoring schemes. In this paper, we mainly consider the analysis of unified hybrid censored data when the lifetime distribution of the individual item is a two-parameter generalized exponential distribution. It is observed that the maximum likelihood estimators can not be obtained in a closed form. We obtain the maximum likelihood estimates of the parameters by using Newton-Raphson algorithm. The Fisher information matrix has been obtained and it can be used for constructing asymptotic confidence intervals. We also obtain the Bayes estimates of the unknown parameters under the assumption of independent gamma priors using the importance sampling procedure. Simulations are performed to compare the performances of the different schemes and one data set is analyzed for illustrative purposes.

One of the tools for determining nonlinear effects and interactions between the explanatory variables in a logistic regression model is using of evolutionary product unit neural networks. To estimate the model parameters constructed by this method, a combination of evolutionary algorithms and classical optimization tools is used. In this paper, we change the structure of neural networks in the form that all model parameters can be estimated by using an evolutionary algorithm. We compare the two methods of estimation. The results show that the estimated parameters by evolutionary algorithms cause a model that its Akaike information criterion is better than conventional logistic model Akaike information criterion, but using the combination method gives the best model.

This paper is concerned with the study of the effect of outliers in GARCH models. Four common outliers are considered: additive outliers, innovation outliers, level change and temporary change. Each of the outlier is embedded to a GARCH model and then the effectness of outliers in this model is studied. The residuals of the models have been investigated for both cases, the usual GARCH model and the GARCH model in the present of outliers.

Gomez et al. (2007) introduced the skew t-normal distribution, showing that it is a good alternative to model heavy tailed data with strong symmetrical nature, specially because it has a larger range of skewness than the skew-normal distribution. Gomez et al. (2007) and Lin et al. (2009) described some properties of this distribution. In this paper, we consider some further properties of skew student-t-normal distribution. Also, we present four theorems for constructing of this distribution. Next we illustrate a numerical example to model the Vanadium pollution data in the Shadegan Wetland by using skew student-t-normal distribution.

Model selection aims to find the best model. Selection in the presence of censored data arises in a variety of problems. In this paper we emphasize that the Kullback-Leibler divergence under complete data has a better advantage. Some procedures are provided to construct a tracking interval for the expected difference of Kullback-Leibler risks based on Type II right censored data. Simulation study shows that this procedure works properly for optimum model selection.

Recently, dynamic panel data models are comprehensively used in social and economic studies. In fitting these models, a lagged response is incorrectly considered as an explanatory variable. This ad-hoc assumption produces unreliable results when using conventional estimation approaches. A principle issue in the analysis of panel data is to take into account the variability of experimental individual effects. These effects are usually assumed fixed in many studies, because of computational complexity. In this paper, we assume random individual effects to handle such variability and then compare the results with fixed effects. Furthermore, we obtain the model parameter estimates by implementing the maximum likelihood and Gibbs sampling methods. We also fit these models on a data set which contains assets and liabilities of banks in Iran.

Modeling of extreme responses in presence nonlinear, temporal, spatial and interaction effects can be accomplished with mixed models. In addition, smoothing spline through mixed model and Bayesian approach together provide convenient framework for inference of extreme values. In this article, by representing as a mixed model, smoothing spline is used to assess nonlinear covariate effect on extreme values. For this reason, we assume that extreme responses given covariates and random effects are independent with generalized extreme value distribution. Then by using MCMC techniques in Bayesian framework, location parameter of distribution is estimated as a smooth function of covariates. Finally, the proposed model is employed to model the extreme values of ozone data.