Journal of Statistical Sciences

Trend Removal in Spatial Statistics Using Support Vector Regression

Javad Etminan

‎Modeling and efficient estimation of the trend function is of great importance in the estimation of variogram and prediction of spatial data. In this article, the support vector regression method is used to model the trend function. Then the data is de-trended and the estimation of variogram and prediction is done. On a real data set, the prediction results obtained from the proposed method have been compared with Spline and kriging prediction methods through cross-validation.  The criterion for choosing the appropriate method for prediction is to minimize the root mean square of the error. The prediction results for several positions with known values were left out of the data set (for some reason) and were obtained for new positions. The results show the high accuracy of prediction (for all positions and elimination positions) with the proposed method compared to kriging and spline.

Estimation of Linear Mixed Measurement Error Models in the Presence of Multicollinearity

Babak Babadi

In this paper, we introduce the weighted ridge estimators of fixed and random effects in stochastic restricted linear mixed measurement error models when collinearity is present. The asymptotic properties of the resulting estimates are examined. The necessary and sufficient conditions, for the superiority of the weighted ridge estimators against the weighted estimator in order to select the ridge parameter based on the mean squared error matrix of estimators, are investigated. Finally, theoretical results are augmented with a simulation study and a numerical example.

Analysis of Censored Data Using Dirichlet Process Mixture Model with Generalized Inverse Weibull Distribution as Kernel

Bahram Haji Joudaki

In this paper, a new Dirichlet process mixture model with the generalized inverse Weibull distribution as the kernel is proposed. After determining the prior distribution of the parameters in the proposed model, Markov Chain Monte Carlo methods were applied to generate a sample from the posterior distribution of the parameters. The performance of the presented model is illustrated by analyzing real and simulated data sets, in which some data are right-censored. Another potential of the proposed model demonstrated for data clustering. Obtained results indicate the acceptable performance of the introduced model.

On the Mean Residual of Records in the Geometric Random Record Model

Ali Khosravi Tanak

Record values have many applications in reliability theory, such as the shock and minimal repairs models. In this regard, many works have been done based on records in the classical model. In this paper, the records are studied in the geometric random model. The concept of the mean residual of records is defined in the random record model and some of its properties are investigated in the geometric random record model. Then, it is shown that the parent distribution can be characterized by using the sequence of the mean residual of records in a geometric random model. Finally, the application of the characterization results to job search models in labor economics is mentioned.

Multi-class Depth-based Classification for Multivariate Data

Sakineh Dehghan

‎This paper presents a nonparametric multi-class depth-based classification approach for multivariate data. This approach is easy to implement rather than most existing nonparametric methods that have computational complexity. If the assumption of the elliptical symmetry holds, this method is equivalent to the Bayes optimal rule. Some simulated data sets as well as real example have been used to evaluate the performance of these depth-based classifiers.

Application of Periodically Correlated Spatial Processes and Spatial Periodogram in Image Processing

Roya Nasirzadeh

Spatial processes are widely used in data analysis, specifically image processing. In image processing, examining periodic images is one of the most critical challenges. To investigate this issue, we can use periodically correlated spatial processes. To this end, it is necessary to determine whether the images are periodic or not, and if they are, what type of period it is. In the current study, we first introduce and express the properties of periodically correlated spatial processes. Then, we present a spatial periodogram to determine the period of periodically correlated spatial processes. Finally, we will elaborate on its usage to recognize the periodicity of the images.

Identification of Influential Observations for High-Dimensional Regression

Nasrin Noori

The prevalence of high-dimensional datasets has driven increased utilization of the penalized likelihood methods. However, when the number of observations is relatively few compared to the number of covariates, each observation can tremendously influence model selection and inference. Therefore, identifying and assessing influential observations is vital in penalized methods. This article reviews measures of influence for detecting influential observations in high-dimensional lasso regression and has recently been introduced. Then, these measures under the elastic net method, which combines removing from lasso and reducing the ridge coefficients to improve the model predictions, are investigated. Through simulation and real datasets, illustrate that introduced influence measures effectively identify influential observations and can help reveal otherwise hidden relationships in the data.

Flexible Closed Skew Normal Random Field to Analysis Skew Spatial Data

Fatemeh Hosseini

Gaussian random field is usually used to model Gaussian spatial data. In practice, we may encounter non-Gaussian data that are skewed. One solution to model skew spatial data is to use a skew random field. Recently, many skew random fields have been proposed to model this type of data, some of which have problems such as complexity, non-identifiability, and non-stationarity. In this article, a flexible class of closed skew-normal distribution is introduced to construct valid stationary random fields, and some important properties of this class such as identifiability and closedness under marginalization and conditioning are examined. The reasons for developing valid spatial models based on these skew random fields are also explained. Additionally, the identifiability of the spatial correlation model based on empirical variogram is investigated in a simulation study with the stationary skew random field as a competing model. Furthermore, spatial predictions using a likelihood approach are presented on these skew random fields and a simulation study is performed to evaluate the likelihood estimation of their parameters.

Double Penalized Mixed Effects Quantile Regression Modeling Using the Maximum Likelihood Approach

Mousa Golalizadeh

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The mixed effects model is one of the powerful statistical approaches used to model the relationship between the response variable and some predictors in analyzing data with a hierarchical structure. The estimation of parameters in these models is often done following either the least squares error or maximum likelihood approaches. The estimated parameters obtained either through the least squares error or the maximum likelihood approaches are inefficient, while the error distributions are non-normal. In such cases, the mixed effects quantile regression can be used. Moreover, when the number of variables studied increases, the penalized mixed effects quantile regression is one of the best methods to gain prediction accuracy and the model's interpretability. In this paper, under the assumption of an asymmetric Laplace distribution for random effects, we proposed a double penalized model in which both the random and fixed effects are independently penalized. Then, the performance of this new method is evaluated in the simulation studies, and a discussion of the results is presented along with a comparison with some competing models. In addition, its application is demonstrated by analyzing a real example.

Spatio-Temporal Analysis Based on One-Sided Dynamic Principal Components

Mahnaz Khalafi

The analysis of spatio-temporal series is crucial but a challenge in different sciences. Accurate analyses of spatio-temporal series depend on how to measure their spatial and temporal relation simultaneously. In this article, one-sided dynamic principal components (ODPC) for spatio-temporal series are introduced and used to model the common structure of their relation. These principal components can be used in the data set, including many spatio-temporal series. In addition to spatial relations, trends, and seasonal trends, the dynamic principal components reflect other common temporal and spatial factors in spatio-temporal series. In order to evaluate the capability of one-sided dynamic principal components, they are used for clustering and forecasting in spatio-temporal series. Based on the precipitation time series in different stations of Golestan province, the efficiency of the principal components in the clustering of hydrometric stations is investigated. Moreover, forecasting for the SPI index, an essential indicator for detecting drought, is conducted based on the one-sided principal components.

Bayesian Estimation of Multi-Component Reliability Parameter Under Adaptive Hybrid Progressive Censoring

Akram Kohansal

‎In this paper, under adaptive hybrid progressive censoring samples, Bayes estimation of the multi-component reliability, with the non-identical-component strengths, in unit generalized Gompertz distribution is considered. This problem is solved in three cases. In the first case, strengths and stress variables are assumed to have unknown, uncommon parameters. In the second case, it is assumed that strengths and stress variables have two common and one uncommon parameter, so all of these parameters are unknown. In the third case, it is assumed that strengths and stress variables have two known common parameters and one unknown uncommon parameter. In each of these cases, Bayes estimation of the multi-component reliability, with the non-identical-component strengths, is obtained with different methods. Finally, different estimations are compared using the Monte Carlo simulation, and the results are implemented on one real data set.

A New Approach in Using Random Support Vector Machine Cluster in Analyzing Prostate Cancer Gene Expression Data

Nilia Mosavi

Cancer progression among patients can be assessed by creating a set of gene markers using statistical data analysis methods. Still, one of the main problems in the statistical study of this type of data is the large number of genes versus a small number of samples. Therefore, it is essential to use dimensionality reduction techniques to eliminate and find the optimal number of genes to predict the desired classes accurately. On the other hand, choosing an appropriate method can help extract valuable information and improve the machine learning model's efficiency. This article uses an ensemble learning approach, a random support vector machine cluster, to find the optimal feature set. In the current paper and in dealing with real data, it is shown that via randomly projecting the original high-dimensional feature space onto multiple lower-dimensional feature subspaces and combining support vector machine classifiers, not only the essential genes are found in causing prostate cancer, but also the classification precision is increased.