فصلنامه مدل سازی پیشرفته ریاضی
سال چهارم شماره 1 (بهار و تابستان 1393)

Purpose of this paper is identifying best covariates of a semi-parametric model in the presence of penalized coefficients. It should be noted that in each model، coefficients of the existing variables is considered as a combination of parameters where some of them affect the response variable linearly and some of them functionally. So، semi-parametric method was considered as an optimum solution. In this paper we concerned with variable selection in finite mixture of generalized semi-parametric models. This task consists of model selection for nonparametric component and variable selection for parametric part. Thus we encounter with separate model selection for each nonparametric component of each sub model. To overcome to this computational burden، we introduce a class of variable selection procedures for finite mixture of generalized semi-parametric models. It is shown that the new method is consistent for variable selection. Simulations show that the performance of proposed method is good and improve pervious works in this area and also requires much less computing power than existing methods.

Spatial generalized linear mixed models are used for modeling geostatistical discrete spatial responses and spatial correlation of the data is considered via latent variables. The most important interest in these models is estimation of the model parameters and the prediction of the latent variables. In this paper، first a prediction method is presented and then، Bayesian approach and MCMC algorithms are intrpretation. Since these models are complex and in the Bayes inference of these models، are used Monte Carlo sampling، computation time is long. The Approximatin Baysian methods are considered for solving this problem. Finally، the proposed methods are applied to a case study on rainfall data observed in the weather stations of Semnan in 1391.

In this paper، under the assumption of Pareto distribution، construct a maximum likelihood estimator، UMVUE and also، assuming the Exponential prior distribution and weighted squared-error loss function، this study construct Bayes and Empirical Bayes estimator of C_L based on the progressive type II right censored sample. An admissible estimator of C_L is given for Pareto distribution with respect to the weighted squared-error loss function. The MLE and Bayes estimator of C_L is then utilize to develop a confidence and credible interval. Moreover، we also propose a likelihood Ratio Tests and a Bayesian Test to assess the lifetime performance index. Finally، we give one example to illustrate the use of testing procedure under given significance level.

Neural networks are among those mathematical models which are used to model non-linear time series with high accuracy. The advantage with these linear times series as opposed to topical ones is that they don’t require restrictive assumptions. The accuracy of neural network based estimators as nonparametric models is of high importance. In that light، we can use bootstrapping to calculate the accuracy of estimators in the time series’ complex nonlinear structures. Though introduced in recent years these methods yield more accurate results in the bias calculation of estimators compared to the other ones. This paper introduces neural network bootstrap، bootstrap autoregressive، moving block bootstrap method and residual bootstrap methods in time series. Then these four algorithms are compared with each other in a simulation study. Finally an example related to Iran’s kerosene price monthly data is worked out.

The mean response time plays an important role in the analyzing and optimizing the queuing system which determines the number and type of giving service. In this paper، new confidence intervals of mean response time for an M/G/1 FCFS queuing system is contrasted based on the nonparametric delta method and five bootstrap methods. These methods include: nonparametric delta method confidence interval based on the influence function، standard bootstrap confidence interval، percentile bootstrap confidence interval، bootstrap-t confidence interval، bias corrected and acceleration bootstrap confidence interval and bootstrap pivotal confidence interval. In a simulation study، these six methods are compared and evaluated the accuracy and performance of the confidence intervals for three different M/G/1 FCFS queuing systems based on the coverage percentage and the average length of confidence intervals.