Journal of Statistical Sciences

Estimation of Semiparametric Survival Models with Time Varying Effects for Recurrent Event Data by Using Kernel Method

Hossein Baghishani

In some semiparametric survival models with time dependent coefficients, a closed-form solution for coefficients estimates does not exist. Therefore, they have to be estimated by using approximate numerical methods. Due to the complicated forms of such estimators, it is too hard to extract their sampling distributions. In such cases, one usually uses the asymptotic theory to evaluate properties of the estimators. In this paper, first the model is introduced and a method is proposed, by using the Taylor expansion and kernel methods, to estimate the model. Then, the consistency and asymptotic normality of the estimators are established. The performance of the model and estimating procedure are evaluated by a heavy simulation study as well. Finally, the proposed model is applied on a real data set on heart disease patients in one of the Mashhad hospitals.

New Results on Stochastic Comparison of (n-1) -out-of-n Systems

Ghobad Barmalzan

Suppose there are two groups of random variables, one with independent and non-identical distributed and another with independent and identical distributed. In this paper, for the case when the size of groups are not equal, and all of the underlying random variables have exponential distribution, the necessary and sufficient conditions are obtained for establishing the mean residual life, hazard rate and dispersive orders between the second order statistics of two groups. Moreover, when random variables follow the Weibull distribution, the hazard rate, dispersive and likelihood ratio order between the second order statistics from two groups are investigated.

On Hypergeometric Generalized Negative Binomial Distribution in Promotion Time Cure Model

Ahmad Reza Baghestani

On Hypergeometric Generalized Negative Binomial Distribution in Promotion Time Cure Model In analysis of survival data if exposes a high percentage of censoring due to termination of the study, whereas the study has lasted long enough, it is preferred to utilize cure models. These models, which are based on the latent variable distribution, has obtained much attention in the last decade. In this paper the Hypergeometric Generalized Negative Binomial distribution of the latent variable is used to model the long time survival data. The new model parameters are estimated in Bayesian approach. This model is applied for a Primary Biliary Cirrhosis clinical trial data and a simulated data set. With respect to DIC, Hypergeometric Generalized Negative Binomial model is a suitable fit to the data.

Goodness of Fit Tests of Exponentiality Based on New Entropy Estimators

Ehsan Zamanzade

In this paper, two new entropy estimators are proposed. Then, entropy-based tests of exponentiality based on our entropy estimators are introduced. Simulation results show that the proposed estimators and related goodness of fit tests have good performances in comparison with their leading competitors.

Bayesian Regression Model with Finite Mixture Bivariate Poisson Response Variable

Afshin Fallah

In this paper the regression analysis with finite mixture bivariate poisson response variable is investigated from the Bayesian point of view. It is shown that the posterior distribution can not be written in a closed form due to the complexity of the likelihood function of bivariate Poisson distribution. Hence, the full conditional posterior distributions of the parameters are computed and the Gibbs algorithm is used to sampling from posterior distributions. A simulation study is performed in order to assess the proposed Bayesian model and its efficiency in estimation of the parameters is compared with their frequentist counterparts. Also, a real example presented to illustrate and assess the proposed Bayesian model. The results indicate to the more efficiency of the estimators resulted from Bayesian approach than estimators of frequentist approach at least for small sample sizes.

Spatial Analysis of Structured Additive Regression and Modeling of Crime Data in Tehran City Using Integrated Nested Laplace Approximation

Kobra Gholizadeh

In Bayesian analysis of structured additive regression models which are a flexible class of statistical models, the posterior distributions are not available in a closed form, so Markov chain Monte Carlo algorithm due to complexity and large number of hyperparameters takes long time. Integrated nested Laplace approximation method can avoid the hard simulations using the Gaussian and Laplace approximations. In this paper, consideration of spatial correlation of the data in structured additive regression model and its estimation by the integrated nested Laplace approximation are studied. Then a crime data set in Tehran city are modeled and evaluated. Next, a simulation study is performed to compare the computational time and precision of the models provided by the integrated nested Laplace approximation and Markov chain Monte Carlo algorithm

Inverse Multiquadratic Functions as Nonlinear Effects in Logistic Regression Models

Arezou Mojiri

Logistic regression models in classification problems by assuming the linear effects of covariates is a modeling for class membership posterior probabilities. The main problem that includes nonlinear combinations of covariates is maximum likelihood estimation (MLE) of the model parameters. In recent investigations, an approach of solving this problem is combination of neural networks, evolutionary algorithms and MLE methods. In this paper, another type of radial basis functions, namely inverse multiquadratic functions and hybrid method, are considered for estimating the parameters of these models. The experimental results of comparing the proposed models show that the inverse multiquadratic functions compared to the Gaussian functions have better precision in classification problems.