Mahdi Roozbeh

• Ph.D.
• Professor (Associate) at Semnan University

Outliers are a common problem in applied statistics, together with multicollinearity. In this paper, robust Liu estimators are introduced into a partially linear model to combat the presence of multicollinearity and outlier challenges when the error terms are not independent and some linear constraints are assumed to hold in the parameter space. Th...

Determining the predictor variables that have a non-linear effect as well as those that have a linear effect on the response variable is crucial in additive semi-parametric models. This issue has been extensively investigated by many researchers in the area of semi-parametric linear additive models, and various separation methods are proposed by th...

Regression analysis frequently encounters two issues: multicollinearity among the explanatory variables, and the existence of outliers in the data set. Multicollinearity in the semiparametric regression model causes the variance of the ordinary least-squares estimator to become inflated. Furthermore, the existence of multicollinearity may lead to w...

The analysis of the high-dimensional dataset when the number of explanatory variables is greater than the observations using classical regression approaches is not applicable and the results may be misleading. In this research, we proposed to analyze such data by introducing modern and up-to-date techniques such as support vector regression, symmet...

By evolving science, knowledge, and technology, new and precise methods for measuring, collecting, and recording information have been innovated, which have been resulted in the appearance and developing of high-dimensional data, in which the number of explanatory variables is much larger than the number of observations. Analysis and modeling the h...

In many applications, indexing of high-dimensional data has become increasingly important. High-dimensional data is characterized by multiple dimensions. There can be thousands, if not millions, of dimensions in applications. Classic methods cannot analyse this kind of data set. So, we need the appropriate alternative methods to analyse them. In hi...

Background and purpose: Machine learning is a class of modern and strong tools that can solve many important problems that nowadays Humans may be faced with. Support Vector Regression (SVR) is a way to build a regression model which is an incredible member of the machine learning family. SVR has been proven to be an effective tool in real-value fun...

Nowadays, high-dimensional data appear in many practical applications such as biosciences. In the regression analysis literature, the well-known ordinary least-squares estimation may be misleading when the full ranking of the design matrix is missed. As a popular issue, outliers may corrupt normal distribution of the residuals. Thus, since not bein...

As known, outliers and multicollinearity in the data set are among the important difficulties in regression models, which badly affect the least-squares estimators. Under multicollinearity and outliers’ existence in the data set, the prediction performance of the least-squares regression method is decreased dramatically. Here, proposing an approxim...

The ridge regression estimator is a commonly used procedure to deal with multicollinear data. This paper proposes an estimation procedure for high-dimensional multicollinear data that can be alternatively used. This usage gives a continuous estimate, including the ridge estimator as a particular case. We study its asymptotic performance for the gro...

The ridge regression estimator is a commonly used procedure to deal with multicollinear data. This paper proposes an estimation procedure for high-dimensional multicollinear data that can be alternatively used. This usage gives a continuous estimate, including the ridge estimator as a particular case. We study its asymptotic performance for the gro...

Modern statistical studies often encounter regression models with high dimensions in which the number of features p is greater than the sample size n. Although the theory of linear models is well–established for the traditional assumption p < n, making valid statistical inference in high dimensional cases is a considerable challenge. With recent ad...

With the advancement of technology, analysis of large-scale data of gene expression is feasible and has become very popular in the era of machine learning. This paper develops an improved ridge approach for the genome regression modeling. When multicollinearity exists in the data set with outliers, we consider a robust ridge estimator, namely the r...

In classical linear regression analysis problems, the ordinary least-squares (OLS) estimation is the popular method to obtain the regression weights, given the essential assumptions are satisfied. However, often, in real-life studies, the response data and its associated explanatory variables do not meet the required conditions, in particular under...

Background and purpose: By evolving science, knowledge, and technology, we deal with high-dimensional data in which the number of predictors may considerably exceed the sample size. The main problems with high-dimensional data are the estimation of the coefficients and interpretation. For high-dimension problems, classical methods are not reliable...

In classical regression analysis, the ordinary least-squares estimation is the best estimation if the essential assumptions are satisfied. However, if the data does not satisfy some of these assumptions, then results can be misleading. Especially, outliers violate the assumption of normally distributed residuals in the least-squares regression. Rob...

This paper applies a ridge estimation approach in an existing partial logistic regression model with exact predictors, intuitionistic fuzzy responses, intuitionistic fuzzy coefficients and intuitionistic fuzzy smooth function to improve an existing intuitionistic fuzzy partial logistic regression model in the presence of multicollinearity. For this...

In fitting a regression model to survey data, using additional information or prior knowledge, stochastic uncertainty occurs in specifying linear programming due to economic and financial studies. These stochastic constraints, definitely cause some changes in the classic estimators and their efficiencies. In this paper, stochastic shrinkage estimat...

Some linear stochastic constraints may occur during real data set modeling, based on either additional information or prior knowledge. These stochastic constraints often cause some changes in the behaviors of estimators. In this research, shrinkage ridge estimators as well as their positive parts are proposed in the semi-parametric model when some...

When multicollinearity exists in the context of robust regression, ridge rank regression estimator can be used as an alternative to the rank estimator. Performance of the ridge rank regression estimator is highly dependent on the ridge parameter, here the tuning parameter. On the other hand, suppose we are provided with some non-sample uncertain pr...

Introduction: Estimation of age has an important role in legal medicine, endocrine diseases and clinical dentistry. Correspondingly, evaluation of dental development stages is more valuable than tooth erosion. In this research, the modeling of calendar age has been done using new and rich statistical methods. Considerably, it can be considering as...

In this paper, a generalized difference-based estimator is introduced for the vector parameter \(\beta \) in partially linear model when the errors are correlated. A generalized difference-based almost unbiased ridge estimator is defined for the vector parameter \(\beta \). Under the linear stochastic constraint \(r=R\beta +e\), a new generalized d...

Due to advances in technologies, modern statistical studies often encounter linear models with high-dimension, where the number of explanatory variables is larger than the sample size. Estimation in these high-dimensional problems with deterministic covariates or designs is very different from those in the case of random covariates, due to the iden...

It is shown that the prediction performance of the LASSO method is improved for high dimensional data sets by subtracting structural noises through a sparse additive partially linear model. A mild combination of the partial residual estimation method and the back-fitting algorithm by further implying the LASSO method to the predictors of the linear...

In this paper, a generalized difference-based estimator is introduced for the vector parameter β in the partially linear model when the errors are correlated. A generalized difference-based Liu estimator is defined for the vector parameter β. Under the linear stochastic constraint r=Rβ+e, a new generalized difference-based weighted mixed Liu estima...

Modern statistical analysis often encounters linear models with the number of explanatory variables much larger than the sample size. Estimation in these high-dimensional problems needs some regularization methods to be employed due to rank deficiency of the design matrix. In this paper, the ridge estimators are considered and their restricted regr...

There are some classes of biased estimators for solving the multicollinearity among the predictor variables in statistical literature. In this research, we propose a modified estimator based on the QR decomposition in the semiparametric regression models, to combat the multicollinearity problem of design matrix which makes the data to be less disto...

In order to down-weight or ignore unusual data and multicollinearity effects, some alternative robust estimators are introduced. Firstly, a ridge least trimmed squares approach is discussed. Then, based on a penalization scheme, a nonlinear integer programming problem is suggested. Because of complexity and difficulty, the proposed optimization pro...

Multicollinearity among the predictor variables is a serious problem in regression analysis. There are some classes of biased estimators for solving the problem in statistical literature. In these biased classes, estimation of the shrinkage parameter plays an important role in data analyzing. Using eigenvalue analysis, efforts have been made to dev...

As known, the ordinary least-squares estimator (OLSE) is unbiased and also, has the minimum variance among all the linear unbiased estimators. However, under multicollinearity the estimator is generally unstable and poor in the sense that variance of the regression coefficients may be inflated and absolute values of the estimates may be too large....

In this paper, a generalized difference-based estimator is introduced for the vector parameter β in partially linear model when the errors are correlated. A generalized difference-based almost unbiased two parameter estimator is defined for the vector parameter β. Under the linear stochastic constraint r = Rβ + e, we introduce a new generalized dif...

In classical regression analysis, the ordinary least–squares estimation is the best strategy when the essential assumptions such as normality and independency to the error terms as well as ignorable multicollinearity in the covariates are met. However, if one of these assumptions is violated, then the results may be misleading. Especially, outliers...

In classical regression analysis, the ordinary least-squares estimation is the best method if the essential assumptions are met to obtain regression weights. However, if the data do not satisfy some of these assumptions, then results can be misleading. Especially, outliers violate the assumption of normally distributed residuals in the least-square...

Under some non-stochastic linear restrictions based on either additional information or prior knowledge in a semiparametric regression model, a family of feasible generalized robust estimators for the regression parameter is proposed. The least trimmed squares (LTS) method was proposed by Rousseeuw as a highly robust regression estimator, is a stat...

Multicollinearity among the explanatory variables is a serious problem in regression analysis. There are some classes of biased estimators for solving this problem in statistical literature. In these biased classes, estimation of the shrinkage parameter plays an important role in data analyzing. Using eigenvalue analysis, efforts have been made to...

In this paper, ridge and non-ridge type estimators and their robust forms are defined in the semiparametric regression model when the errors are dependent and some non-stochastic linear restrictions are imposed under a multicollinearity setting. In the context of ridge regression, the estimation of shrinkage parameter plays an important role in ana...

Two common problems in applied statistics are multicollinearity between variables and the presence of outliers in the data. In a partially linear regression model, a family of robust ridge estimators for the regression parameters and the nonlinear part is introduced by adding an penalty to the well-known least trimmed squares estimator. The partial...

In this paper shrinkage ridge estimator and its positive part are defined for the regression coefficient vector in a partial linear model. The differencing approach is used to enjoy the ease of parameter estimation after removing the non-parametric part of the model. The exact risk expressions in addition to biases are derived for the estimators un...

In the context of ridge regression, the estimation of ridge (shrinkage) parameter plays an important role in analyzing data. Many efforts have been put to develop skills and methods of computing shrinkage estimators for different full-parametric ridge regression approaches, using eigenvalues. However, the estimation of shrinkage parameter is neglec...

This article considers the problem of point/set estimation in a specific seemingly unrelated regression model, namely system regression model. Feasible type of shrinkage estimator and its positive part are defined for the effective regression coefficient vector, when the covariance matrix of the error term is assumed to be unknown. Their asymptotic...

Fuzzy least-squares regression can be very sensitive to unusual data (e.g., outliers). In this paper, we describe how to fit an alternative robust-regression estimator in fuzzy environment, which attempts to identify and ignore unusual data. The proposed approach concerns classical robust regression and estimation methods that are insensitive to ou...

In this paper, ridge and non-ridge type shrinkage estimators and their positive parts are defined in the semiparametric regression model when the errors are dependent and some non-stochastic linear restrictions are imposed under a multicollinearity setting. The exact risk expressions in addition to biases are derived for the estimators under study...

In the context of ridge regression, the estimation of shrinkage parameter plays an important role in analyzing data. Many efforts have been put to develop the computation of risk function in different full-parametric ridge regression approaches using eigenvalues and then bringing an efficient estimator of shrinkage parameter based on them. In this...

Under a semiparametric regression model, a family of robust estimates for the regression parameter is proposed. The least trimmed squares (LTS) method is a statistical technique for fitting a regression model to a set of points. Given a set of n observations and the integer trimming parameter , the LTS estimator involves computing the hyperplane th...

This paper is concerned with the ridge estimation of the parameter vector in partial linear regression model , with correlated errors, that is, when , with a positive definite matrix and , under the linear constraint , for a given matrix and a given vector . The partial residual estimation method is used to estimate and the function . Under appropr...

In this paper, a generalized difference-based estimator is introduced for the vector parameter β in the semiparametric regression model when the errors are correlated. A generalized difference-based Liu estimator is defined for the vector parameter β in the semiparametric regression model. Under the linear nonstochastic constraint Rβ=R, the general...

This article considers estimation in the seemingly unrelated semiparametric models, when the explanatory variables are affected by multicollinearity. It is also suspected that some additional linear constraints may hold on the whole parameter space. In sequel we propose difference-based ridge type estimators combining the restricted least squares m...

In a partial linear model, some non-stochastic linear restrictions are imposed under a multicollinearity setting. Semiparametric ridge and non-ridge type estimators, in a restricted manifold are defined. For practical use, it is assumed that the covariance matrix of the error term is unknown and thus feasible estimators are replaced and their asymp...

In this paper, an exact sufficient condition for the dominance of the Stein-type shrinkage estimator over the usual unbiased estimator in a partial linear model is exhibited. Comparison result is then done under the balanced loss function. It is assumed that the vector of disturbances is typically distributed according to the law belonging to the s...

This article is concerned with the problem of multicollinearity in the linear part of a seemingly unrelated semiparametric (SUS) model. It is also suspected that some additional non stochastic linear constraints hold on the whole parameter space. In the sequel, we propose semiparametric ridge and non ridge type estimators combining the restricted l...

In this article, a generalized restricted difference-based ridge estimator is defined for the vector parameter in a partial linear model when the errors are dependent. It is suspected that some additional linear constraints may hold on to the whole parameter space. The estimator is a generalization of the well-known restricted least-squares estimat...

In this article, we introduce a semiparametric ridge regression estimator for the vector-parameter in a partial linear model. It is also assumed that some additional artificial linear restrictions are imposed to the whole parameter space and the errors are dependent. This estimator is a generalization of the well-known restricted least-squares esti...

In this paper, the geometric distribution is considered. The means, variances, and covariances of its order statistics are derived. The Fisher information in any set of order statistics in any distribution can be represented as a sum of Fisher information in at most two order statistics. It is shown that, for the geometric distribution, it can be f...