Journal of Statistical Research of Iran
Volume:10 Issue: 2, 2015

Imputation is one of the most common methods to reduce item non_response effects. Imputation results in a complete data set، and then it is possible to use naϊve estimators. After using most of common imputation methods، mean and total (imputation estimators) are still unbiased. However their variances (imputation variances) are underestimated by naϊve variance estimators. Sampling mechanism and response variable values are variation sources which have been hidden in naϊve variance estimators. While missing mechanism and imputation processes are other sources which are created after imputation. The naϊve estimator does not account for these new variation sources. In this paper، a recent method of unified approach to linearization imputation variance estimation is explained. In this method، imputation estimator is linearized with respect to nuisance parameters estimators. Then linear estimator is asymptotically equal to imputation estimator. Variance estimators are also asymptotically equal. The unified approach can cover all deterministic and stochastic imputation methods، except nearest neighbors method. By a simulation study، imputation variance estimators of multiple imputation، model-assisted، bootstrap and unified approach are compared when regression imputation has been implemented. Performance of the imputation variance estimators are compared with respect to relative efficiency and coverage probability. Findings of the study show that unified approach and model_assisted are close in values of efficiencies and give more stable results through either increasing sample size or non-response rate.

This paper proposes a simple goodness-of-fit test based on the sample covariance. It is shown that this test is preferable for alternatives of increasing and unimodal failure rate. Critical values for various sample sizes are determined by means of Monte Carlo simulations.We compare the test based on the sample covariance with tests based on Hoeffding's maximum correlation. The usefulness of the proposed test is shown for a real example.An empirical power study shows that the new test has the same level or upper level of performance than the best exponentiality tests in the statistical literature.

Latent Gaussian models are flexible models that are applied in several statistical applications. When posterior marginals or full conditional distributions in hierarchical Bayesian inference from these models are not available in closed form, Markov chain Monte Carlo methods are implemented. The component dependence of the latent field usually causes increase in computational time and divergence of algorithms. In this paper, an integrated nested Laplace approximation is used to solve these problems, in which the Laplace approximation and the numerical integration methods are combined in an efficient way so that hard simulations are replaced by fast computation and accurate approximation. Finally the relationship between house price data, floor size, age, number of rooms, building frame, type of proprietorship and facilities such as electricity, landline, water, gas, central heating and cooling system, kitchen goods, bath and toilet are modeled by using spatial latent Gaussian models. The fitted model can be used for predicting the house price in Tehran city.

Consider a Bayesian optimal design with many support points which poses the problem of collecting data with a few number of observations at each design point. Under such a scenario the asymptotic property of using Fisher information matrix for approximating the covariance matrix of posterior ML estimators might be doubtful. We suggest to use Bhattcharyya matrix in deriving the information matrix, led to modified Bayesian D-optimal criterion. This criterion is used to obtain optimal design for logistic model. It is shown that the resulting optimal design is more efficient than design given by Chaloner and Larentz (1989) using ordinary Bayesian D-optimal criterion.

The Weibull distribution is a very applicable model for the lifetime data. For inference about two Weibull distributions using records, the shape parameters of the distributions are usually considered equal. However, there is not an appropriate method for comparing the shape parameters in the literature. Therefore, comparing the shape parameters of two Weibull distributions is very important. In this paper, we propose a method for constructing confidence interval and testing hypotheses about the ratio and difference of shape parameters using the concept of the generalized p-value and the generalized confidence interval. Simulation studies showed that our method is satisfactory. In the end, a real example is proposed to illustrate this method.

This paper presents the statistical inference on the parameters of the Burr type III distribution, when the data are Type-II hybrid censored. The maximum likelihood estimators are developed for the unknown parameters using the EM algorithm method. We provided the observed Fisher information matrix using the missing information principle which is useful for constructing the asymptotic confidence intervals. The Bayesian estimates of the unknown parameters under the assumption of independent gamma priors are obtained using two approximations, namely Lindley's approximation and the Markov Chain Monte Carlo technique. Monte Carlo simulations are performed to observe the behavior of the proposed methods and a real dataset representing is used to illustrate the derived results.