Journal of Statistical Sciences

The Choice of an Admissible Set of k Non-nested Models

Abdolreza Sayyareh

Suppose we have a random sample of size n of a population with true density h(.). In general, h(.) is unknown and we use the model f as an approximation of this density function. We do inference based on f. Clearly, f must be close to the true density h, to reach a valid inference about the population. The suggestion of an absolute model based on a few obsevations, as an approximation or estimation of the true density, h, results a great risk in the model selection. For this reason, we choose k non-nested models and investigate the model which is closer to the true density. In this paper, we investigate this main question in the model selection that how is it possible to gain a collection of appropriate models for the estimation of the true density function h, based on Kullback-Leibler risk.

Incorporating Various Distributional Properties Using Weight Distributions

Afshin Fallah

This paper considers the weight distributions in order to incorporating the topics related to construction of skew-symetric (skew-normal) and bimodal distributions. It discusses that many of skew-normal distributions disscussed in recent years researches can be studid in more general form along with some other interesting aspects in context of weigth distributions. Two cosiderable case of the recent years reaserches have been disscussed. It is shown that the introduced distributions in these reseaches along with all of their interesting properties can be obtain from weigth distribution perspective as only special cases.

Minimax Generalized Bayes Estimator of Normal Mean Vector with Unknown Covariance Matrix

Ahmad Parsian

In this paper, a class of generalized Bayes Minimax estimators of the mean vector of a normal distribution with unknown positive definite covariance matrix is obtained under the sum of squared error loss function. It is shown that this class is an extension of the class obtained by Lin and Tasi (1973).

Improved Kullback-Leibler Upper Bound Baised on Convex Combination of k Rival Models

Abdolreza Sayyareh

In this paper we have established for the Kullback-Leibler divergence that the relative error is supperadditive. It shows that a mixture of k rival models gives a better upper bound for Kullback-Leibler divergence to model selection. In fact, it is shown that the mixed model introduce a model which is better than of the all rival models in the mixture or a model which is better than the worst rival model in the mixture.

Bayesian Time Dependent Evaluation of Biomarkers as Surrogate Endpoint

Soghrat Faghihzadeh

Sometimes it is impossible to directly measure the effect of intervention (medicine or therapeutic methods) in medical researches. That is because of high costs, long time, the aggressiveness of therapeutic methods, lack of clinical responses, and etc. In such cases, the effect of intervention on surrogate variables is measured. Many statistical studies have been accomplished for measuring the validity of surrogates and introducing a criterion for testing. The first criterion was established based on hypothesis testing. Other criterions were introduced over time. Then by using the classic methods, the Likelihood Ratio Factor was introduced. After that, the Bayesian Likelihood Ratio Factor developed and published. This article aims to introduce the Bayesian Likelihood Ratio Factor based on time dependent data. The illness under study is lung disease in victims of chemical weapons. The surrogate therapy method uses the forced expiratory volume at fist second.

Improved Estimator of Coefficent of Determination in Multivariate Normal Distribution

Ahad Malekzadeh

Coefficient of determination is an important criterion in different applications. The problem of point estimation of this parameter has been considered by many researchers. In this paper, the class of linear estimators of R^2 was considered. Then, two new estimators were proposed, which have lower risks than other usual estimator, such as the sample coefficient of determination and its adjusted form. Also on the basis of some simulations, we show that the Jacknife estimator is an efficient estimator with lower risk, when the number of observations is small.

Introduce a Necessary Method for Rrecognize Non-Isomorphic Designs

Hooshang Talebi

Two designs, with N runs and k factors all with two levels are said to be isomorphic or equivalent if one is obtained from another by permuting rows, columns or/and changing the levels of one or more factors. When N and k increase the matter of isomorphic recognition of two designs will be complicated. Therefore it is essential to apply needed conditions which are able to recognize and separate non-isomorphic designs. It should be done in the least possible time. Majority of needed existed conditions in the literature review can’t meet the two objectives, maximum separation in minimum span, at the same time. In this paper, a new method has been used to present non-equivalent. This new method has been designed abased on choice and comparisons of one or some rows of design matrix. This new method hopefully has higher ability to recognize non-equivalence. Besides, the new method has lower calculation and therefore is able to determine non-equivalence of two designs.