Journal of Data Science and Modeling

Abstract In various statistical model, such as density estimation and estimation of regression curves or hazard
rates, monotonicity constraints can arise naturally. A frequently encountered problem in nonparametric
statistics is to estimate a monotone density function f on a compact interval. A known estimator for
density function of f under the restriction that f is decreasing, is Grenander estimator, where is the left
derivative of the least concave majorant of the empirical distribution function of the data. Many authors
worked on this estimator and obtained very useful properties from this estimator. Grenander estimator
is a step function and as a consequence it is not smooth. In this paper, we discuss the estimation of a
decreasing density function by the kernel smoothing method. Many works have been done due to the
importance and applicability of Berry-Esseen bounds for the density estimator. In this paper, we study
a Berry- Esseen type bound for a smoothed version of Grenander estimator.

Abstract In a referendum conducted in the United Kingdom (UK) on June 23, 2016, $51.6\\%$ of the participants voted to leave the European Union (EU). The outcome of this referendum had major policy and financial impact for both UK and EU, and was seen as a surprise because the predictions consistently indicate that the ``Remain'''' would get a majority. In this paper, we investigate whether the outcome of the Brexit referendum could have been predictable by polls data.
The data consists of 233 polls which have been conducted between January 2014 and June 2016 by YouGov, Populus, ComRes, Opinion, and others. The sample size range from 500 to 20058.
We used Singular Spectrum Analysis (SSA) which is an increasingly popular and widely adopted filtering technique for both short and long time series. We found that the real outcome of the referendum is very close to our point estimate and within our prediction interval, which reinforces the usefulness of SSA to predict polls data.

Abstract 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.

Abstract This paper presents approximate confidence intervals for each function of parameters in a Banach space based on a bootstrap algorithm. We apply kernel density approach to estimate the persistence landscape. In addition, we evaluate the quality distribution function estimator of random variables using integrated mean square error (IMSE). The results of simulation studies show a significant improvement achieved by our approach compared to the standard version of confidence intervals algorithm. Finally, real data analysis shows that the accuracy of our method compared to that of previous works for computing the confidence interval.

Abstract Traditionally, the statistical quality control techniques utilize either an attributes or variables product quality measure. Recently, some methods such as three-level control chart have been developed for monitoring multi attribute processes. Control chart usually has three design parameters: the sample size (n), the sampling interval (h) and the control limit coefficient (k).The design parameters of the control chart are generally specified according to statistical or/and economic criteria. The variable sampling interval (VSI) control scheme has been shown to provide an increase to the detecting efficiency of the control chart with fixed sampling rate (FRS). In this paper a method is proposed to conduct the economic-statistical design for variable sampling interval of the three-level control charts. We use the cost model developed by Costa and Rahim and optimize this model by genetic algorithm approach. We compare the expected cost per unit time of the VSI and FRS 3-level control charts. Results indicate that the proposed chart has improved performance.

Abstract In this article, we consider the problem of estimating the stress-strength reliability $Pr (X > Y)$ based on upper record values when $X$ and $Y$ are two independent but not identically distributed random variables from the power hazard rate distribution with common scale parameter $k$. When the parameter $k$ is known, the maximum likelihood estimator (MLE), the approximate Bayes estimator and the exact confidence intervals of stress-strength reliability are obtained. When the parameter $k$ is unknown, we obtain the MLE and some bootstrap confidence intervals of stress-strength reliability. We also apply the Gibbs sampling technique to study the Bayesian estimation of stress-strength reliability and the corresponding credible interval. An example is presented in order to illustrate the inferences discussed in the previous sections. Finally, to investigate and compare the performance of the different proposed methods in this paper, a Monte Carlo simulation study is conducted.

Abstract Imprecise measurement tools produce imprecise data. Interval-valued data is usually used to deal with such imprecision. So interval-valued variables are used in estimation methods. They have recently been modeled by linear regression models. If response variable has any statistical distributions, interval-valued variables are modeled in generalized linear models framework. In this article, we propose a new consistent estimator of a parameter in generalized linear models with regard to distributions of response variable in the exponential family. A simulation study shows that the new estimator is better than others on the basis of particular distributions of response variable. We present optimal properties of the estimators in this research

Abstract A proper method of monitoring a stochastic system is to use the control charts of statistical
process control in which a drift in characteristics of output may be due to one or several assignable causes. In the establishment of X charts in statistical process control, an assumption is made that there is no correlation within the samples. However, in practice, there are many cases where the correlation does exist within the samples. It would be more appropriate to assume that each sample is a realization of a multivariate
normal random vector. Using three dierent loss functions in the concept of quality control charts with economic and economic statistical design leads to better decisions in the industry. Although some research works have considered the economic design of control charts under single assignable cause and correlated data, the economic statistical design of X control chart for multiple assignable causes and correlated data under Weibull shock model with three dierent loss functions have not been presented yet. Based on the
optimization of the average cost per unit of time and taking into account the dierent combination values
of Weibull distribution parameters, optimal design values of sample size, sampling interval and control limit
coecient were derived and calculated. Then the cost models under non-uniform and uniform sampling
scheme were compared. The results revealed that the model under multiple assignable causes with correlated
samples with non-uniform sampling integrated with three dierent loss functions has a lower cost than the
model with uniform sampling.

Abstract In the meta-analysis of clinical trials, usually the data of each trail summarized by one or more outcome measure estimates which reported along with their standard errors. In the case that summary data are multi-dimensional, usually, the data analysis will be performed in the form of a number of separated univariate analysis. In such a case the correlation between summary statistics would be ignored. In contrast, a multivariate meta-analysis model, use from these correlations synthesizes the outcomes, jointly to estimate the multiple pooled effects simultaneously. In this paper, we present a nonparametric Bayesian bivariate random effect meta-analysis.

Abstract Estimation of a quantile density function from biased data is a frequent problem in industrial life testing
experiments and medical studies.
The estimation of a quantile density function in the biased nonparametric regression model is inves-
tigated. We propose and develop a new wavelet-based methodology for this problem. In particular, an
adaptive hard thresholding wavelet estimator is constructed. Under mild assumptions on the model, we
prove that it enjoys powerful mean integrated squared error properties over Besov balls. The performance
of proposed estimator is investigated by a numerical study.
In this study, we develop two types of wavelet estimators for the quantile density function when data
comes from a biased distribution function. Our wavelet hard thresholding estimator which is introduced
as a nonlinear estimator, has the feature to be adaptive according to q(x). We show that these estimators
attain optimal and nearly optimal rates of convergence over a wide range of Besov function classes.

Abstract This paper considers an extension of the linear mixed model, called semiparametric mixed effects model, for longitudinal data, when multicollinearity is present. To overcome this problem, a new mixed ridge estimator is proposed while the nonparametric function in the semiparametric model is approximated by the kernel method. The proposed approache integrates ridge method into the semiparametric mixed effects modeling framework in order to account for both the correlation induced by repeatedly measuring an outcome on each individual over time, as well as the potentially high degree of correlation among possible predictor variables. The asymptotic normality of the exhibited estimator is established. To improve efficiency, the estimation of the covariance function is accomplished using an iterative algorithm. Performance of the proposed estimator is compared through a simulation study and analysis of CD4 data.

Abstract The Bayesian variable selection analysis is widely used as a new methodology in air quality control trials and generalized linear models. One of the important and, of course, controversial topics in this area is selection of prior distribution of unknown model parameters. The aim of this study is presenting a substitution for mixture of priors which besides
preservation of benefits and computational efficiencies obviate the available paradoxes and contradictions. In this research we pay attention to two points of view; empirical and fully Bayesian. Especially, a mixture of priors and its theoretical characteristics is introduced. Finally, the proposed model is illustrated with a real example.

Abstract The purpose of this research is to identify and introduce effective factors in adoption of e-learning based on technology adoption model. Accordingly, by considering the studies conducted in this field, several variables such as computer self-efficacy, content quality, system support, interface design, technology tools and computer anxiety as factors influencing the adoption of e-learning system were extracted and based on them, a conceptual model of research was developed. To measure the model and the relationships between the variables in the model, a questionnaire was designed and provided to users of the electronic education system of Qazvin University of Medical Sciences. The results of the data analysis confirmed the correctness of all hypotheses using the structural equation modeling method, except for the effect of technology tools on the acceptance of the e-learning system. The findings of this study will help university administrators and the professors associated with this system to encourage students to make effective use of the system by creating the necessary background for effective factors.

Abstract The purpose of this paper was to investigate the impact of audit quality on the reduction of collateral facilities, taking into account the role of major shareholders in companies listed on the Tehran Stock Exchange during the period 2017 to 2022. Considering the research conditions, 179 companies were selected as the statistical sample of the research (From a total number of 895 companies). The research method of this research is descriptive and applied research in terms of nature and content. The panel data method was used to test the research hypotheses. The findings of this research emphasized that audit quality reduces collateral facilities. The rotation of the auditor increases collateral facilities. But the auditor's expertise in the industry does not have a significant effect on collateral facilities. On the other hand, the ownership percentage of major shareholders does not affect the intensity of the impact of audit quality and expertise in the audit industry and audit turnover on collateral facilities.

Abstract ‎The recent advancements in technology have faced an increase in the growth rate of data‎.
‎According to the amount of data generated‎, ‎ensuring effective analysis using traditional approaches becomes very complicated‎.
‎One of the methods of managing and analyzing big data is classification‎.
‎%One of the data mining methods used commonly and effectively to classify big data is the MapReduce‎
‎In this paper‎, ‎the feature weighting technique to improve Bayesian classification algorithms for big data is developed based on Correlative Naive Bayes classifier and MapReduce Model‎.
‎%Classification models include Naive Bayes classifier‎, ‎correlated Naive Bayes and correlated Naive Bayes with feature weighting‎.
‎Correlated Naive Bayes classification is a generalization of the Naive Bayes classification model by considering the dependence between features‎.
‎%This paper uses the feature weighting technique and Laplace calibration to improve the correlated Naive Bayes classification‎.
‎The performance of all described methods are evaluated by considering accuracy‎, ‎sensitivity and specificity‎, ‎accuracy‎, ‎sensitivity and specificity metrics.

Abstract Accurate weather prediction plays a vital role in many sectors, such as agriculture, disaster preparedness, transportation systems, and urban planning. Traditional meteorological models face challenges in capturing complex atmospheric dynamics, leading to increased reliance on artificial neural networks (ANNs) for improved forecasting accuracy. ANNs have been widely applied in meteorology due to their ability to model nonlinear relationships and temporal dependencies. Based on the Sinc numerical methods, the modified Sinc neural network (MSNN) has been introduced recently. This model uses the advantages of the Sinc function, such as smoothness and fluctuation, and at the same time improves the ability to model nonlinear dependencies and temporal dynamics in environmental data. This work utilizes the MSNN for time series forecasting where its parameters are adjusted with a discrete-time online Lyapunov-based learning algorithm. Then, it is applied to enhance the weather forecasting. This model is evaluated on datasets containing various meteorological variables. The data used in this article is related to the city of Khorramabad in Iran. The results show that despite its simple structure, MSNN has a high efficiency in weather forecasting.

Abstract Progressive first-failure censoring schemes are potentially useful in practical applications where budget constraints exist or rapid testing is required. Moreover, several common sampling schemes such as first-failure censoring, progressive Type-II censoring, Type-II censoring, and complete sampling can be viewed as special cases of the progressive first-failure censoring scheme.
In this article, we propose a goodness-of-fit test statistic to assess whether a progressively first-failure-censored sample originates from a distribution belonging to the proportional hazard rate model. This model encompasses several well-known lifetime distributions, including the exponential, Rayleigh, Lomax, Burr Type-XII, Weibull, Gompertz, and Pareto distributions, among others.
We derive the null distribution of the proposed test statistic. Through Monte Carlo simulations, we evaluate the power of the proposed test under a range of different alternative distributions, assuming the null distribution to be exponential, Rayleigh, or Pareto. Finally, we present several numerical real-world examples to demonstrate the practical applicability of the proposed goodness-of-fit test. We also summarize the main findings and provide concluding remarks.

Abstract This paper introduces a novel semiparametric Bayesian approach for bivariate meta-regression. The method extends traditional binomial models to trinomial distributions, accounting for positive, neutral, and negative treatment effects. Using a conditional Dirichlet process, we develop a model to compare treatment and control groups across multiple clinical centers. This approach addresses the challenges posed by confounding factors in such studies. The primary objective is to assess treatment efficacy by modeling response outcomes as trinomial distributions. We employ Gibbs sampling and the Metropolis-Hastings algorithm for posterior computation. These methods generate estimates of treatment effects while incorporating auxiliary variables that may influence outcomes. Simulations across various scenarios demonstrate the model’s effectiveness. We also establish credible intervals to evaluate hypotheses related to treatment effects. Furthermore, we apply the methodology to real-world data on economic activity in Iran from 2009 to 2021. This application highlights the practical utility of our approach in meta-analytic contexts. Our research contributes to the growing body of literature on Bayesian methods in meta-analysis. It provides valuable insights for improving clinical study evaluations.

Abstract Due to the inherent complexity and increasing competition, today's business environment requires new approaches in organizing and managing. One of the new approaches is business intelligence, which is the most critical technology to help manage and deliver smart services, especially business reporting. Business intelligence enables firms to manage their business efficiently to meet the needs of businesses at different macro, middle and even operations levels. In this paper, while investigating the feasibility of implementing business intelligence in firms, designing business intelligence to report and present new services is discussed. In order to demonstrate the capabilities of this type of intelligence, an approach based on the concept of Bayesian network in the application layer of business intelligence is presented. This approach is implemented for one of the companies governed by the Iranian Industrial Development and Renovation Organization, and the effects of important accounting and financial variables on the firm goals are investigated.

Abstract Abstract
In this article, unlike recently developed methods that can only distinguish associations between pairs of variables, Bayesian Multilevel Latent Class (BMLC) model for the multiple imputation of nested categorical data is considered which is flexible enough to automatically deal with complex interactions in the joint distribution of the variables to be estimated. After presenting the model, I run the model on a real data set, that is, mathematics test of TIMSS 2015 which has missing data in itself, and at the end the completed data for both levels (Level 1, students and Level 2, schools) are obtained. To assess the performance of the BMLC model, we compare it with list wise deletion (LD) with the help of R software. Conclusion: Results show that the BMLC model has reliability and is able to cover the Bayesian estimator with lower risk in this research.
Keywords: test of TIMSS, Bayesian analysis, missing data, categorical data, Bayesian Multilevel Latent Class model.

Abstract 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.

Abstract Principal Component Analysis (PCA) is a cornerstone technique for dimensionality
reduction and data analysis. However, classic PCA can exhibit instability in
high-dimensional settings where the number of variables significantly exceeds the
number of observations. Shrinkage-based PCA addresses this limitation by incorporating
regularization into the covariance matrix estimation process, leading to
more stable and interpretable results. This paper provides a robust mathematical
and statistical foundation for shrinkage-based PCA, compares its performance with
classic PCA, and demonstrates its advantages through theoretical analysis, numerical
simulations, and real-world data experiments. It is important to note that using the idea of a contraction estimator increases the efficiency of the estimator. mean time in this paper, it is shown that the covariance matrix estimator resulting from the contraction estimator is very efficient.
It is also worth mentioning that to increase the efficiency of the contraction estimator, the recently discussed interval contraction estimator can be used.
keywords: principal component analysis, Shrinkage-based, Estimation, Covariance Structures, Simulation.

Abstract Multi-label classification assigns multiple labels to each instance, crucial for tasks like cancer detection in images and text categorization. However, machine learning methods often struggle with the complexity of real-life datasets. To improve efficiency, researchers have developed feature selection methods to identify the most relevant features. Traditional methods, requiring all features upfront, fail in dynamic environments like media platforms with continuous data streams. To address this, novel online methods have been created, yet they often neglect optimizing conflicting objectives. This study introduces an objective search approach using mutual information, feature interaction, and the NSGA-II algorithm to select relevant features from streaming data. The strategy aims to minimize feature overlap, maximize relevance to labels, and optimize online feature interaction analysis. By applying a modified NSGA-II algorithm, a set of non-dominant
solutions is identified. Experiments on eleven datasets show that the proposed approach outperforms advanced online feature selection techniques in predictive accuracy, statistical analysis, and stability assessment.

Abstract By focusing on the fuzzy Delphi technique (FDM), the current research introduces a novel approach to modeling Persian vernacular architecture. Fuzzy Delphi is a more advanced version of the Delphi Method, which utilizes triangulation statistics to determine the distance between the levels of consensus within the expert panel and deals with the measurement uncertainty of qualitative data. In this sense, the main objective of the Delphi method is to acquire the most reliable consensus of a group of expert opinions; an advantage that helps the current study to answer the main question of the research, that is, determining the efficacy of fuzzy Delphi technique in intelligent modeling of Persian vernacular architecture. Therefore, in order to identify the main factors of the research model, systematic literature reviews as well as semi-structured interviews with experts were conducted. Then, with the usage of Qualitative Content Analysis (QCA), various themes were obtained and employed as the main factors of the research model. Finally, by utilizing the fuzzy Delphi technique, the present study examined the degree of certainty and accuracy of the factors in two stages and identified 28 factors in the modeling of Persian vernacular architecture.

Abstract Interval-valued data are observed as ranges instead of single values and contain richer information than

single-valued data. Meanwhile, interval-valued data are used for interval-valued characteristics. An interval

generalized linear model is proposed for the first time in this research. Then a suitable model is presented to

estimate the parameters of the interval generalized linear model. The two models are provided on the basis of

the interval arithmetic. The estimation procedure of the parameters of the suitable model is as the estimation

procedure of the parameters of the interval generalized linear model. The least-squares (LS) estimation of the

suitable model is developed according to a nice distance in the interval space. The LS estimation is resolved

analytically through a constrained minimization problem. Then some desirable properties of the estimators

are checked. Finally, both the theoretical and the empirical performance of the estimators are investigated.