نشریه اندیشه آماری
سال بیست و پنجم شماره 1 (پیاپی 49، بهار و تابستان 1399)

In this study, the interval estimations are proposed for the functions of the parameter in exponential lifetimes, when interval censoring is used. Optimal monitoring time and simulation studies are examined as well as the applicability of the topics.

In spatial generalized linear mixed models, spatial correlation is assumed by adding normal latent variables to the model. In these models because of the non-Gaussian spatial response and the presence of latent variables the likelihood function cannot usually be given in a closed form, thus the maximum likelihood approach is very challenging. The main purpose of this paper is to introduce two new algorithms for the maximum likelihood estimations of parameters and to compare them in terms of speed and accuracy with existing algorithms. The presented algorithms are applied to a simulation study and their performance are compared.

Spatial count data is usually found in most sciences such as environmental science, meteorology, geology and medicine. Spatial generalized linear models based on poisson (poisson-lognormal spatial model) and binomial (binomial-logitnormal spatial model) distributions are often used to analyze discrete count data in which spatial correlation is observed. The likelihood function of these models is complex as analytic and so computation.  The Bayesian approach using Monte Carlo Markov chain algorithms can be a solution to fit these models, although there are usually problems with low sample acceptance rates and long runtime to implement the algorithms. An appropriate solution is to use the Hamilton (hybrid) Monte Carlo algorithm  in The Bayesian approach. In this paper, the new Hamilton (hybrid) Monte Carlo method for Bayesian analysis of spatial count models on air pollution data in Tehran is studied. Also, the two common Monte Carlo algorithms such as the Markov chain (Gibbs and Metropolis-Hastings) and Langevin-Hastings are used to apply  the complete Bayesian approach on the data modeling.  Finally, an appropriate approach to data analysis and forecasting in all points of the city is introduced with the diagnostic criteria.

Many populations encountered in survival analysis are often not homogeneous. Individuals are flexible in their susceptibility to causes of death, response to treatment and influence of various risk factors. Ignoring this heterogeneity can result in misleading conclusions. To deal with these problems, the proportional hazard frailty model was introduced. In this paper, the frailty model is explained as the product of the frailty random variable and baseline hazard rate. We examine the fit of the frailty model to the right censored data from in the presence of explanatory variables (observable variables) and use it as a practical example to fit the frailty model to the data by considering the Weibull basis distribution and exponential in the likelihood functions. It is used to estimate the model parameters and compare the fit of the models with different criteria.

Evidence-based management and development planning relies on official statistics. There are some obstacles that make it impossible to do single mode survey. These obstacles are sampling frame, time, the budget and accuracy of measurment of each mode. Always we can not use single mode survey becase of these factors. So we need to use other data collection method to overcome these obstacles. This method is called the mixed mode survey, which is a combination of several modes. In this article we show that mixed mode surveys can produce more accurate official statistics than single mode surveys.

Varying coefficient Models are among the most important tools for discovering the dynamic patterns when a fixed pattern does not fit adequately well on the data, due to existing diverse temporal or local patterns. These models are natural extensions of classical parametric models that have achieved great popularity in data analysis with good interpretability.The high flexibility and interpretability of these models have led to use in many real applications. In this paper, after presenting a brief review of varying coefficient models, we use the parameter estimation method using the kernel function and cubic spline then confidence band and hypothesis testing are investigated. Finally, using the real data of Iranchr(chr('39')39chr('39'))s inflation rate from 1989 to 2017, we show the application and capabilities of the varying coefficient model in interpreting the results. The main challenge in this application is that the panel or longitudinal models or even time series models with heterogeneous variances such as ARCH and GARCH models and their derived models did not fit adequately well on this dataset which justify the use of varying coefficient model.

The proportional hazard Cox regression models play a key role in analyzing censored survival data. We use penalized methods in high dimensional scenarios to achieve more efficient models. This article reviews the penalized Cox regression for some frequently used penalty functions. Analysis of medical data namely ”mgus2” confirms the penalized Cox regression performs better than the cox regression model. Among all penalty functions, LASSO provides the best fit.

By evolving science, knowledge and technology, new and precise methods for measuring, collecting and recording information have been innovated, which have resulted in the appearance and development of high-dimensional data. The high-dimensional data set, i.e., a data set in which the number of explanatory variables is much larger than the number of observations, cannot be easily analyzed by traditional and classical methods, same as the ordinary least-squares method, and its interpretability will be very complex. Although, in classical regression analysis, the ordinary least-squares estimation is the best estimation method if the essential assumptions are met, but it is not applicable for high-dimensional data and in this cconditions, we need to apply the modern methods. In this research, it is firstly mentioned to the drawbacks of classical methods in analysis of high-dimensional data and then, it is proceeded to introduce and explain about the modern and common approaches of the regression analysis for high-dimensional data same as principal component analysis and penalized methods. Finally, a simulation study is performed to apply and compare the mentioned methods in high-dimensional data.

Classroom evaluation is a key part of the teaching and learning process. The purpose of this study is to investigate the factor validity and reliability of the "Student Perceptions Questionnaire of Assessment and Evaluation of Activities" by Yuji. In this regard, the questionnaire of studentschr(chr('39')39chr('39')) perception of measuring and evaluating activities was performed on 400 students who were selected by cluster sampling method from Mazandaran University students. Cranbachchr(chr('39')39chr('39'))s alpha coefficient was used to evaluate the reliability of the questionnaire and confirmatory factor analysis was used to determine the validity of the factor. The results of the present study showed that this questionnaire has an acceptable internal consistency and Cranbachchr(chr('39')39chr('39'))s alpha coefficient in its subtests was between 0.71 and 0.78. Also, the results of confirmatory factor analysis confirm that the structure of the questionnaire has an acceptable fit with the data and all indicators of good fit confirm the model. Therefore, the questionnaire can be a good tool for assessing studentschr(chr('39')39chr('39')) perceptions of assessment and evaluation of activities and assignments.

Nonrespose is a source of error in the survey results and national statistical organizations are always looking for ways to control and reduce it. Predicting nonrespons sampling units in the survey before conducting the survey is one of the solutions that can help a lot in reducing and treating the survey nonresponse. Recent advances in technology and the facilitation of complex calculations have made it possible to apply statistical learning methods, such as regression and classification trees or support vector machines, to many issues, including predicting the nonresponse of sampling units in statistics. In this article, while reviewing the above methods, the nonresponse sampling units are predicted using them in an establishment survey and it is shown that a combination of the above methods is more accurate in predicting the correct nonresponse than any of these methods.

‎Whenever approximate and initial information about the unknown parameter of a distribution is available, the shrinkage estimation method can be used to estimate it. In this paper, first the $ E $-Bayesian estimation of the parameter of inverse Rayleigh distribution under the general entropy loss function is obtained. Then, the shrinkage estimate of the inverse Rayleigh distribution parameter is investigated using the guess value. Also, using Monte Carlo simulations and a real data set, the proposed shrinkage estimation is compared with the UMVU and $ E $-Bayesian estimators based on the relative efficiency criterion.

Economic theories seek a scientific explanation or prediction of economic phenomena using a set of axiom, defined expressions, and theorems. Mathematically explicit economic models are one of these theories. Due to the unknown structure of each model, the existence of measurement error in economic committees and failure of Ceteris Paribus; the Synthetic of any economic theory requires probabilistic and statistical modeling. Therefore, understanding the current method of modeling and the importance of its proper use in economics requires economists to have an accurate knowledge of statistical modeling. The present study seeks to correct the view that although the purpose of providing statistical models is to experimentally test the claims of theories, statistical methods do not play a secondary role in economic theories, but the appropriate method of economic modeling depends on the correct use of statistical methods and probability models in the situation. of make a theory.