Journal of Statistical Sciences

Estimating Value-at-Risk and Average Value-at-Risk Measures Using Composite quantile Regression

Ali Aghamohammadi

Value-at-Risk and Average Value-at-Risk are tow important risk measures based on statistical methoeds that used to measure the market's risk with quantity structure. Recently, linear regression models such as least squares and quantile methods are introduced to estimate these risk measures. In this paper, these two risk measures are estimated by using omposite quantile regression. To evaluate the performance of the proposed model with the other models, a simulation study was conducted and at the end, applications to real data set from Iran's stock market are illustarted.

The Improve of Two Stage Least Square Method in Regression Model with Endogenous Variables

Mousa Golalizadeh

The presence of endogenous variables in the statistical models leads to inconsistent and bias estimators for the parameters. In this case, several approaches have been proposed which are able to tackle the biase and inconsistency problems only in large sample situations. One of these methods is biased on instrumental variables which causes removing endogenous variables. The method of two-stage least squares is another approach in this case that it has more accurate than ordinary least squares. This paper aims to enhance the accuracy of three methods of estimation based upon least square methodology called, two-stage iterative least squares, two-stage Jackknife least squares and also two-stage calibration least squares. In order to evaluate the performance of each method, a simulation study is conducted. Also, using data collected in 1390 related to the cost and revenue in Iran, those methods to estimate parameters are compared.

D-Optimal Design for Paired Comparison Model in Quadratic Regression with Random Effects

Habib Jafari

The optimal criteria are used to find the optimal design in the studied model. These kinds of models are included the paired comparison models. In these models, the optimal criteria (D-optimality) determine the optimal paired comparison. In this paper, in addition to introducing the quadratic regression model with random effects, the paired comparison models were presented and the optimal design has been calculated for them.

Approximate Bayesian Analysis of Spatio-Temporal Data Using a Gaussian Markov Random Field

Fatemeh Hosseini

Hierarchical spatio-temporal models are used for modeling space-time responses and temporally and spatially correlations of the data is considered via Gaussian latent random field with Matérn covariance function. The most important interest in these models is estimation of the model parameters and the latent variables, and is predict of the response variables at new locations and times. In this paper, to analyze these models, the Bayesian approach is presented. Because of the complexity of the posterior distributions and the full conditional distributions of these models and the use of Monte Carlo samples in a Bayesian analysis, the computation time is too long. For solving this problem, Gaussian latent random field with Matern covariance function are represented as a Gaussian Markov Random Field (GMRF) through the Stochastic Partial Differential Equations (SPDE) approach. Approximatin Baysian method and Integrated Nested Laplace Approximation (INLA) are used to obtain an approximation of the posterior distributions and to inference about the model. Finally, the presented methods are applied to a case study on rainfall data observed in the weather stations of Semnan in 2013.

Optimal Circular Neighbour-Balanced Designs

Fateme Delshad Chermahini

Neighbour effects, that is the response on a given plot is affected by the treatments in neighbouring plot and the effect by the treatment applied to that plot. As a result, the estimate of treatment differences may deviate because of this interference from neighbouring plots. Neighbour-balanced designs ensure that the treatment comparisons will be as little affected by neighbour effects as possible. Circular neighbour-balanced design are divided into two groups. In the previouse researchs, method of cyclic shifts to construct CNB1 has been used, the authors used this method to construct CNB2. Some series of CNB2 are found by omputer programming using in MATLAB software and method of cyclic shifts. Then, some of these designs witch are universally optimal under models with one sided neighbour effect (M1) are identified.

The Effect of Weight Function on the Estimation of Regression Parameters under Weighted Sampling

Mohammad Reaz Alavi

In weighted sampling as a generalization of random sampling, every observation, y, is recorded with probably proportional to a non-negative function of y. In this paper, the normal regression model is investigated under the weighted sampling for a common weight function. Parameters of the model are estimated for known and unknown weight parameters. Using simulation, efficiency of estimators is studied when they have not closed forms. As an application, the data of number of visited patients by specialist doctors in Social Security Organization of Ahvaz in Iran (SSOAI) are analyzed.

An Approximate Tolerance Interval for the Size-Biased Poisson-Lindley Random Variable

Azadeh Kiapour

In this paper, an approximate tolerance interval is presented for the discrete size-biased Poisson-Lindley distribution. This approximate tolerance interval, is constructed based on large sample Wald confidence interval for the parameter of the size-biased Poisson-Lindley distribution. Then, coverage probabilities and expected widths of the proposed tolerance interval is considered. The results show that the coverage probabilities have a better performance for the small values of the parameter and are close to the nominal confidence level, and are conservative for the large values of the parameter. Finally, an applicable example is provided for illustrating approximate tolerance interval.

Statistical Inference in Fractional Brownian Motion

Meysam Moghimbeigi

Statistical analysis of fractional Brownian motion process is one of the most important issues in the field of stochastic processes. The most important issue in the study of this process is statistical inference about the Hurst parametersof the fractional Brownian motion. One of the methods for estimation of aforementioned parameter is maximum likelihood approach. Due to the computational complexity of this approach to give a closed estimate, it is attempting to derive the parameter estimated through the numerical method approach. Also, the theoretical result of the paper is evaluated in a simulation study for different scenarios.

A New Proof for Winitzki's Approximation of Normal Cumulative Distribution Function

Shahram Mansouri

Among all statistical distributions, standard normal distribution has been the most important and practical distribution in which calculation of area under probability density function and cumulative distribution function are required. Unfortunately, the cumulative distribution function of this is, in general, expressed as a definite integral with no closed form or analytical solution. Consequently, it has to be approximated. In this paper, attempts have been made for Winitzki's approximation to be proved by a new approach. Then, the approximation is improved with some modifications and shown that the maximum error resulted from this is less than 0.0000584. Finally, an inverse function for computation of normal distribution quantiles has been derived.

Estimation After Selection in the Proportional Hazard and Proportional Reversed Hazard Rate Models

Nader Nematollahi

In some applied problems we need to choose a population from the given populations and estimate the parameter of the selected population. Suppose k random samples are chosen from k populations with proportional hazard rate model or proportional reversed hazard rate model. According to a specified selection rule, it is desired to estimate the parameter of the best (worst) selected population. In this paper, under the entropy loss function we obtain the uniformly minimum risk unbiased (UMRU) estimator of the parameters of the selected population, and derived sufficient conditions for minimaxity of a given estimator. Then we find the class of admissible and inadmissible linear estimators of the parameters of the selected population and determine the class of dominators of a given estimator. We show that the UMRU estimator is inadmissible and compare the obtained estimators by plotting their risk functions.