فهرست مطالب mohammad arashi

The multilinear normal distribution is a widely used tool in the tensor analysis of magnetic resonance imaging (MRI). Diffusion tensor MRI provides a statistical estimate of a symmetric 2nd-order diffusion tensor for each voxel within an imaging volume. In this article, tensor elliptical (TE) distribution is introduced as an extension to the multilinear normal (MLN) distribution. Some properties, including the characteristic function and distribution of affine transformations are given. An integral representation connecting densities of TE and MLN distributions is exhibited that is used in deriving the expectation of any measurable function of a TE variate.

Matrix-variate beta distributions are applied in different fields of hypothesis testing, multivariate correlation analysis, zero regression, canonical correlation analysis and etc. A methodology is proposed to generate matrix-variate beta generator distributions by combining the matrix-variate beta kernel with an unknown function of the trace operator. Several statistical characteristics, extensions and developments are presented. Special members are then used in a univariate and multivariate Bayesian analysis setting. These models are fitted to simulated and real datasets, and their fitting and performance are compared to well-established competitors.

Partial linear model is very flexible when the relation between the covariates and responses, either parametric and nonparametric. However, estimation of the regression coefficients is challenging since one must also estimate the nonparametric component simultaneously. As a remedy, the differencing approach, to eliminate the nonparametric component and estimate the regression coefficients, can be used. Here, suppose the regression vector-parameter is subjected to lie in a sub-space hypothesis. In situations where the use of difference-based least absolute and shrinkage selection operator (D-LASSO) is desired for, we propose a restricted D-LASSO estimator. To improve its performance, LASSO-type shrinkage estimators are also developed. The relative dominance picture of suggested estimators is investigated. In particular, the suitability of estimating the nonparametric component based on the Speckman approach is explored. A real data example is given to compare the proposed estimators. From the numerical analysis, it is obtained that the partial difference-based shrinkage estimators perform better than the difference-based regression model in average prediction error sense.

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.

In this paper, a new method called adaptive bandwidth in the kernel function has been used for two-dimensional upscaling of reservoir data. Bandwidth in the kernel can be considered as a variability parameter in porous media. Given that the variability of the reservoir characteristics depends on the complexity of the system, either in terms of geological structure or the specific feature distribution, variations must be considered differently for upscaling from a fine model to a coarse one. The upscaling algorithm, introduced in this paper, is based on the kernel function bandwidth, written in combination with the A* search algorithm and the first-depth search algorithm. In this algorithm, each cell in its x and y neighborhoods as well as the optimal bandwidth, obtained in two directions will be able to be merged with its adjacent cells. The upscaling process is performed on artificial data with 30×30 grid dimensions and SPE-10 model as real data. Four modes are used to start the point of upscaling and the process is performed according to the desired pattern, and in each case, the upscaling error and the number of final upscaled blocks are obtained. Based on the number of coarsen cells as well as the upscaling error, the first pattern is selected as the optimal pattern for synthetic data and the second pattern is selected as the optimal simulator model for real data. In this model, the number of cells was 236 and 3600, and the upscaling errors for synthetic and real data were 0.4183 and 12.2, respectively. The results of the upscaling in the real data were compared with the normalization method and showed that the upscaling error of the normalization method was 15 times the upscaling error of the kernel bandwidth algorithm.

This paper considers the problem of simultaneous variable selection and estimation in a semiparametric mixed-effects model for longitudinal data with normal errors. We approximate the nonparametric function by regression spline and simultaneously estimate and select the variables under the optimization of the penalized objective function. Under some regularity conditions, the asymptotic behaviour of the resulting estimators is established in a high-dimensional framework where the number of parametric covariates increases as the sample size increases. For practical implementation, we use an EM algorithm to selects the significant variables and estimates the nonzero coefficient functions. Simulation studies are carried out to assess the performance of our proposed method, and a real data set is analyzed to illustrate the proposed procedure.

In the present article, we develop the well-known preliminary test and Stein-type estimators for the probability density function under association. In this respect, we derive the asymptotic characteristics of the proposed estimators under a set of local alternatives. Some numerical studies are provided for supporting the findings. The result of this article improves the kernel estimate of the marginal probability density function of a strictly stationary sequence of associated random variables. For practical sake, the behavior of the proposed estimators is also analyzed using a real data set.

In this paper we are used as two different approaches; wavelet transformation and adaptive bandwidth in kernel method in upscaling process of geomechanical parameters of the reservoir. Geomechanics in oil field have been investigated compressive strength parameters, Young's Moduli, Bulk Moduli and shear Moduli to determine the quality of reservoir and rock as well as the effect of rock resistance and stress on the behavior of formations as a result of oil activities. The geomechanical parameters of the reservoir rock are calculated using petrophysical logs such as acoustic and porosity log. Identifying uniform zones and classifying rock quality requires looking at geomechanical parameters along a well. Upscaling can be used to ease the use of this classifier. In the wavelet theory, after the analyze or the desired signal to the desired level, the upscaled signal will be obtained from the composition of the approximation section of the same level and the remaining samples of the coefficient of detail. This is the same as multiresolution upscaling. In upscaling using the bandwidth of the kernel function, the threshold or bandwidth is defined which is in fact a function of the geomechanical parameter variability. Adaptive bandwidth method can provide a good model upscaling of cells. In areas of high variability, by choosing optimal bandwidth, the cells remain fine, and vice versa, in areas with smooth changes, the number of cells will be merged more together. Comparison of the results of the two methods is observed. Under identical conditions, the upscaling error of the upscaled-optimized model with the kernel bandwidth method is about 1.4 wavelet transforms, and it is also possible that according to the probable error rate, depending on the threshold and appropriate bandwidth can be used to determine the number of upscaled block of the simulated model according to the computational time.

In this paper, we introduce a two-step procedure, in the context of high dimensional additive models, to identify nonzero linear and nonlinear components. We first develop a sure independence screening procedure based on the distance correlation between predictors and marginal distribution function of the response variable to reduce the dimensionality of the feature space to a moderate scale. Then a double penalization based procedure is applied to identify nonzero and linear components, simultaneously. We conduct extensive simulation experiments and a real data analysis to evaluate the numerical performance of the proposed method.

One way of dealing with the problem of collinearity in linear models, is to make use of the Liu estimator. In this paper, a new estimator by generalizing the modified Liu estimator of Li and Yang (2012) has been proposed. This estimator is constructed based on a prior information of vector parameters in linear regression and the generalized estimator of Akdeniz and Kachiranlar (1995). Using the mean square error matrix criterion, we have obtained the superiority conditions Of this newly defined estimator over the generalized Liu estimator. For comparison sake, a numerical example as well as a Monte Carlo simulation study are considered.

Penalized estimators for estimating regression parameters have been considered by many authors for many decades. Penalized regression with rectangular norm is one of the mainly used since it does variable selection and estimating parameters, simultaneously. In this paper, we propose some new estimators by employing uncertain prior information on parameters. Superiority of the proposed shrinkage estimators over the least absoluate and shrinkage operator (LASSO) estimator is demonstrated via a Monte Carlo study. The prediction rate of the proposed estimators compared to the LASSO estimator is also studied in the US State Facts and Figures dataset.

In mathematical modeling, determining most influential parameters on outputs is of major importance. Thus, sensitivity analysis of parameters plays an important role in model validation. We give detailed procedure of constructing a new derivative estimator for general performance measure in Gaussian systems. We will take advantage of using score function and measure-value derivative estimators in our approach. It is shown that the proposed estimator performs better than other estimators for a dense class of test functions in the sense of having smaller variance.

In this paper we consider Selberg-type square matrices integrals with focus on Kummer beta types I & II integrals. For generality of the results for real normed division algebras, the generalized matrix variate Kummer-beta types I & II are defined under the abstract algebra. Then Selberg-type integrals are calculated under orthogonal transformations.

In this paper we consider of location parameter estimation in the multivariate normal distribution with unknown covariance. Two restrictions on the mean vector parameter are imposed. First we assume that all elements of mean vector are nonnegative، at the second hand assumed only a subset of elements are nonnegative. We propose a class of shrinkage estimators which dominate the minimax estimator of mean vector under the quadratic loss function.

In this paper, we obtain the generalized least square, restricted generalized least square and shrinkage estimators for the regression vector parameter assuming that the errors have multivariate t distribution. Also we calculate their quadratic risks and propose the dominance order of the underlying estimators.