ADVANCES IN MATHEMATICAL MODELING
Year:2014 | Volume:4 | Issue:1|Papers Count:6

The 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 requires much less computing power than existing methods.

The bi-level programming problem (BLPP), have received much interest from researchers because of their application in several areas such as economic, traffic, transportation and so on. There are several known algorithms to solve BLPP as an NP-hard problem. Almost all proposed algorithms in references have been used the Karush-Kuhn–Tucker to convert the BLPP into the single level problem which the obtained problem is complicated. In this paper, we attempt to develop two effective approaches, one based on enumeration method and the other based on duality characteristic for solving the linear BLPP. In these approaches, the BLPP is solved without using the Karush-Kuhn–Tucker conditions. The presented approaches achieve an efficient and feasible solution in an appropriate time, which has been evaluated by comparing to references and test problems.

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 parameters and prediction of the latent variables. In this paper, first, a prediction method is presented. Then a Bayesian approach and MCMC algorithms are proposed. Since these models are complicated and Monte Carlo sampling is used in the Bayesian inference of these models, computation time is long. In order to resolve this problem, the Approximate Bayesian methods are considered. Finally, the proposed methods are applied to a case study on rainfall data observed in the weather stations of Semnan in 1391.

Process capability analysis is an effective means to measure the performance and potential capabilities of a process. Process capability analysis has the following benefits: continuously monitoring the process quality through process capability indices (PCIs) in order to assure the products manufactured are conforming to the specifications; supplying information on product design and process quality improvement for engineers and designer; and providing the basis for reducing the cost of product failures. In the manufacturing industry, process capability indices are utilized to assess whether product quality meets the required level. For instance, Montgomery proposed the process capability index CL (or CPL) for evaluating the lifetime performance of electronic components, where L is the lower specification limit, since the lifetime of electronic components exhibits the larger-the-better quality characteristic of time orientation. In lifetime testing experiments, the experimenter may not always be in a position to observe the lifetimes of all the products on test. This may be because of time limitation or other restrictions (such as lack of funds, lack of material resources, mechanical or experimental difficulties, etc.) on data collection. Therefore, censored samples may arise in practice. And, in an industrial experiment, products may break accidently. Therefore, in this paper, we consider the case of the progressive type II right censoring. 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 CL based on the progressive type II right censored sample. An admissible estimator of CL is given for Pareto distribution with respect to the weighted squared-error loss function. The MLE and Bayes estimator of CL 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. 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, 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.