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The inverse moment's research can be used in many fields such as risk evaluation and insurance mathematics. In this paper, we consider the weighted inverse moment model based on asymptotically almost negatively associated (AANA, in short) sequences. Under some weak condition, we obtain the asymptotic approximation of inverse moments and its convergence rate. As applications of inverse moments, we study the random ratio models which contain the change-point detection models, and obtain the asymptotic moment approximation of random ratio and its convergence rate. Our conditions of inverse moment and random ratio models are very weaker than the existing models. In order to test our results, we do some simulations and real data analysis in this paper. Our results improve and general the existing works. [ABSTRACT FROM AUTHOR]

In this paper, we apply conformal prediction to time series data. Conformal prediction is a method that produces predictive regions given a confidence level. The regions outputs are always valid under the exchangeability assumption. However, this assumption does not hold for the time series data because there is a link among past, current, and future observations. Consequently, the challenge of applying conformal predictors to the problem of time series data lies in the fact that observations of a time series are dependent and therefore do not meet the exchangeability assumption. This paper aims to present a way of constructing reliable prediction intervals by using conformal predictors in the context of time series. We use the nearest neighbors method based on the fast parameters tuning technique in the weighted nearest neighbors (FPTO–WNN) approach as the underlying algorithm. Data analysis demonstrates the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The paper deals with the estimation methodology for the α-stable periodic autoregressive (PAR) models. For the classical (Gaussian) PAR time series is cyclostationary systems the periodicity is manifested in the model characteristics. One of the most common characteristics used in this context is the autocovariance function. One of the methods of the PAR model estimation utilizes the Yule-Walker equations that contain the autocovariance function of the given process. However, for the infinite variance version of the PAR model (i.e., α-stable-distributed) it is expected that the autocovariance function is not properly defined. Thus, alternative measures need to be used. In this paper, we present the general idea of the modified Yule-Walker equations for the considered model. It is proposed to replace the classical dependency measure by the dependency measures properly defined for infinite variance models. We demonstrate two possible modifications based on the covariation and fractional lower order covariance. The first approach was recently proposed in the literature while the latter is a novel algorithm. We compare the effectiveness of both estimation methods for the considered model. Finally, the results are compared with the classical Yule-Walker approach. We demonstrate the limitations of the classical method for the considered model. The possible application for real data analysis is demonstrated. [ABSTRACT FROM AUTHOR]

AbstractThis paper aims to simulate conditional samples for generalized linear models and to show their use in goodness of fit. The particular case of the natural exponential family with quadratic variance function and categorical covariates is studied. The conditional samples are drawn from the conditional distribution having conditioned on a sufficient statistic. A procedure that uses the Rao-Blackwell estimate for the cumulative distribution function is employed. The performance of the proposed procedure is shown through a simulation study and the analysis of a data set. [ABSTRACT FROM AUTHOR]

AbstractThe sampling importance resampling method is widely utilized in various fields, such as numerical integration and statistical simulation. In this paper, two modified methods are presented by incorporating two variance reduction techniques commonly used in Monte Carlo simulation, namely antithetic sampling and Latin hypercube sampling, into the process of sampling importance resampling method, respectively. Theoretical evidence is provided to demonstrate that the proposed methods significantly reduce estimation errors compared to the original approach. Furthermore, the effectiveness and advantages of the proposed methods are validated through both numerical studies and real data analysis. [ABSTRACT FROM AUTHOR]

As the alternative of Cox model, the accelerated failure time (AFT) model, which simply regresses the logarithm of the survival time over the covariates, is commonly used in the analysis of interval-censored data. In this paper, we propose a novel two-component mixture-cure model for the interval-censored failure time data in the presence of a cure fraction. Specifically, the first component is a logistic regression model that describes the cure rate, and the second component is a semiparametric accelerated failure time model that describes the failure time of interest for the uncured subjects. An efficient semiparametric procedure is developed to estimate parameters in the considered model. We propose a penalized sieve maximum likelihood estimation approach with Bernstein polynomials to estimate the regression parameters quickly and accurately and the proposed procedure does not rely on the assumption of the distribution of the measurement error. The asymptotic properties of the resulting estimators are established. Extensive simulation studies conducted indicate that the proposed procedure works well for practical situations. In addition, AIDS data analysis is provided for illustration of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a new product relative error estimation method for the partially linear multiplicative regression model (PLMM) is proposed. Both parametric and nonparametric parts are estimated by the least product relative error (LPRE) criterion and local smoothing technique. Besides, regularization conditions are given to establish the consistent and asymptotic normal properties. Finally, several numerical simulations and a real data analysis are included to show the performance of the proposed approach. [ABSTRACT FROM AUTHOR]

In recent years, clustering analysis for interval data has attracted the attention of many researchers. Nevertheless, an algorithm that can automatically determine the number of clusters, and can effectively detect the outlier intervals at the same time has not been studied so far. Therefore, in this paper, we propose a robust automatic clustering algorithm that only can automatically determine the number of clusters but also can assign the outlier intervals into separated clusters. The proposed algorithm is then applied in detecting the abnormal images consisting of the new image categories, and the images contaminated with noise. [ABSTRACT FROM AUTHOR]

In this paper, the Bayesian and Bayesian shrinkage estimators of the scale parameter of two-parameter exponential distribution are provided based on the square error and Al-Bayyati loss functions and right censoring. Both informative (inverse-Gamma) and non-informative (quasi-density) priors are considered for the scale parameter of two-parameter exponential distribution. The estimators from different loss functions are evaluated against each other via the risk and risk efficiency measures. Based on the simulation scheme and real data set, we compare the proposed estimators under both loss functions with risk and risk efficiency measures, which lead to efficiency of the Bayesian shrinkage estimates under informative prior. In real data analysis, Bayesian and Bayesian shrinkage estimation of the scale parameter for the flood stages data set is considered with both square error and Al-Bayyati loss functions under the right censoring scheme. [ABSTRACT FROM AUTHOR]

Numerous variable selection techniques have been developed for complete high-dimensional data but very few of them for censored data. The techniques for complete data must be modified if censoring is present. In this paper, we consider the variable selection technique for accelerated failure time (AFT) models by extending the ranking-based variable selection (RBVS) algorithm and its iterative procedure as proposed in the work of Baranowski et al. through the Stute's weighted least square technique. Simulation studies are conducted to demonstrate the performance of the proposed methods. We further illustrate the performance of this method with a mantle cell lymphoma microarray example. When there is no correlation among the covariates, the proposed method outperforms the iterative sure independence screening and stability selection methods in terms of overall performance for high-dimensional data. Real data analysis also suggests that the proposed method can be chosen for high-dimensional censored data analysis in parallel to other methods in the literature. [ABSTRACT FROM AUTHOR]

Competing risk analysis of time to failure data is preferred when failure of the unit occurs due to any one of several mutually exclusive causes. Masked data refer to the competing risk data with missing cause of failure. Masking in such data may depend on cause of failure or time to failure of the unit or may be independent of both. In this paper, we discuss competing risk models based on Lindley distribution assuming masking to be symmetric, cause dependent and time dependent. We consider maximum likelihood as well as Bayesian approaches for point and interval estimation of model parameters. We perform extensive simulation study to observe performance of various estimators. Finally, we analyze a real life masked data of cancer patients and select the best masking model for the same. [ABSTRACT FROM AUTHOR]

Prediction of loss reserves corresponding to dependent lines of business is one of the most important problems in the actuarial sciences. In this paper, we propose a class of copula based multivariate distributions to model the losses with the heavy tailed distribution in the run-off triangles to predict unpaid losses. We set up ANOVA, ANCOVA, and state space models with four choices of copulas, Clayton, Frank, Gumbel, and Gaussian to provide a new procedure for analyzing run-off triangle tables. We use the Hamiltonian Monte Carlo sampler to perform a Bayesian analysis to estimate the parameters. We apply the proposed models to the data set consists of two lines of business of paid losses data from the Schedule P of the National Association of Insurance Commissioners (NAIC) database. Using some well known criteria, we compare the prediction accuracy of the mean models. As a result, the ANCOVA model with the Clayton copula dominates the other models. [ABSTRACT FROM AUTHOR]

It is a common approach to dichotomize a continuous biomarker in clinical setting for the convenience of application. Analytically, results from using a dichotomized biomarker are often more reliable and resistant to outliers, bi-modal and other unknown distributions. There are two commonly used methods for selecting the best cutoff value for dichotomization of a continuous biomarker, using either maximally selected chi-square statistic or a ROC curve, specifically the Youden Index. In this paper, we explained that in many situations, it is inappropriate to use the former. By using the Maximum Absolute Youden Index (MAYI), we demonstrated that the integration of a MAYI and the Kolmogorov–Smirnov test is not only a robust non-parametric method, but also provides more meaningful p value for selecting the cutoff value than using a Mann-Whitney test. In addition, our method can be applied directly in clinical settings. [ABSTRACT FROM AUTHOR]

In the last 20 years, many of functional sufficient dimension reduction (FSDR) methods are developed. Among all of the FSDR methods, the most popular methods are functional sliced inverse regression (FSIR) and functional sliced average variance estimation (FSAVE). FSIR and FSAVE are based on the first and second moment of the functional predictor, which are not robust to outlier. A robust version of FSIR called the soft weighted FSIR (SFSIR) is proposed method, which used a trimmed and spatial median estimate to replace the classic moment estimation. The trimmed estimate is very useful and SFSIR method can deal with the outlier data very well. However, discarding the potential outlier usually leads to low efficient estimate. And the trimmed estimation method need to select two tuning parameters and to detect the potential outlier is very computational costing. Furthermore, FSIR and SFSIR methods are well-known for their poor performance when the link function is even (or symmetrically dependency). Then, a robust FSDR method with high efficient and low computation costing estimate is urgent needed in practical. In the presented paper, firstly, we will propose weighted based FSIR and FASVE methods. Secondly, we will also study the robust FSIR and FSAVE methods by series expansion, which first approximates the functional predictor by functional principal component basis, and then conduct FSDR methods on the coefficients. Numerical studies including simulation study and real data analysis show that our proposed weighted methods have wonderful performance. [ABSTRACT FROM AUTHOR]

Missing data are common in medical and social science studies and often face a serious challenge in ultrahigh-dimensional data analysis. In this paper, a nonparametric feature screening approach based on the imputation technique is proposed for ultrahigh-dimensional data with responses missing at random, where the imputation technique is used to replacing each missing value with a set of plausible values. Our approach has many advantages. On one hand, the suggested method relies only on imputation, and its impact is considerably less than that of the feature screening procedure based on the inverse probability weighting approach in missing probabilities. On the other hand, our method does not rely on any model assumption and works generally for all kinds of situations. Simulation studies are conducted to examine the performance of our approach, and a real data example is also presented for illustration. [ABSTRACT FROM AUTHOR]

Statistical models often rely on several assumptions including distributional assumptions on outcome variables as well as relational assumptions representing the relationship between outcomes and independent variables. Model diagnostics is, therefore, a crucial component of any model fitting problem. Residuals play important roles in model diagnostics and checking assumptions. In multivariate models, residuals are not commonly used in practice, although approaches have been proposed to check multivariate normality and other model assumptions. When done, ordinary residuals are often used. Nevertheless, it has been shown that ordinary residuals in the analysis of longitudinal data are correlated and are not normally distributed. Under sufficiently large sample size, a transformation of residuals were previously proposed to check the normality assumption. The transformation solely focuses on removing the correlation. In this paper, we show that the ordinary residuals in the analysis of longitudinal data are not normally distributed and should not be used for checking the normality assumption. Via extensive simulations, we also show that the transformed (de-correlated) residuals fail to provide accurate model validation, in particular in the presence of model misspecification. We consider decomposed residuals from the multivariate growth curve model, provide practical interpretations, examine their property analytically as well as via simulations, and show how the different components can be used to examine model misspecification and distributional assumptions. Extensive simulations are performed to evaluate and compare performances for normal and non-normal data. Analysis of real data sets are presented as illustrations. [ABSTRACT FROM AUTHOR]

Tweedie's compound Poisson model is a popular method to model insurance claims with probability mass at zero and nonnegative, highly right-skewed distribution. In particular, it is not uncommon to have extremely unbalanced data with excessively large proportion of zero claims, and even traditional Tweedie model may not be satisfactory for fitting the data. In this paper, we propose a boosting-assisted zero-inflated Tweedie model, called EMTboost, that allows zero probability mass to exceed a traditional model. We makes a nonparametric assumption on its Tweedie model component, that unlike a linear model, is able to capture nonlinearities, discontinuities, and complex higher order interactions among predictors. A specialized Expectation-Maximization algorithm is developed that integrates a blockwise coordinate descent strategy and a gradient tree-boosting algorithm to estimate key model parameters. We use extensive simulation and data analysis on synthetic zero-inflated auto-insurance claim data to illustrate our method's prediction performance. [ABSTRACT FROM AUTHOR]

Due to the diversity of mobile network technologies, the volume of data that has to be observed by mobile operators in a daily basis has become enormous. This huge volume has become an obstacle to mobile networks management. This paper aims to provide a simplified representation of these data for an easier analysis. A model-based co-clustering algorithm for mixed data, functional and binary, is therefore proposed. Co-clustering aims to identify block patterns in a dataset from a simultaneous clustering of rows and columns. The proposed approach relies on the latent block model, and three algorithms are compared for its inference: stochastic EM within Gibbs sampling, classification EM and variational EM. The proposed model is the first co-clustering algorithm for mixed data that deals with functional and binary features. The model has proven its efficiency on simulated data and on real data extracted from live 4G mobile networks. [ABSTRACT FROM AUTHOR]

This paper is concerned with feature screening for the ultrahigh dimensional survival data. We propose a new feature screening procedure by extending the method of Zhu et al. via inverse probability censoring weighting. The proposed procedure enjoys two appealing merits. First, it does not need to specify any model assumption between the response and the covariates. Thus, it is robust to the model mis-specification. Second, our procedure is robust in the presence of outliers or extreme values since it only uses the rank of censored outcomes. We establish the sure screening property under some regular conditions. The simulations and analysis of the real data demonstrate that our procedure exhibits favorably in comparison with the existing competitors. [ABSTRACT FROM AUTHOR]

In this paper, we caculate the probability R = P (A ′ Y 1 + B ′ Y 2 + C > 0) where A ∈ R p 1 and B ∈ R p 2 are known vectors, C is a known scalar and Y 1 ∈ R p 1 and Y 2 ∈ R p 2 are two independent random vectors that have generalized skew-elliptical distributions. In particular, we derive R for scale mixtures of multivariate skew normal distributions and multivariate skew normal-Cauchy distribution, then, by using some matrix variate distributions, the Bayes estimation of R for the multivariate skew normal distribution is obtained. Finally, a simulation study and a real data analysis are presented. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to contrast the Mantel–Haenszel estimator with an optimal estimator to better understand its specific nature, as well as some unique and interesting properties of the data setting for which it was developed. It is emphasized here that the Mantel–Haenszel estimator does not follow from optimality considerations, but nevertheless has properties similar to and often better than the optimal estimator, whose existence we demonstrate in spite of the absence of completeness. It is shown, via simulations and data analysis, that the optimal estimator outperforms the Mantel–Haenszel estimator only in certain settings with huge sample sizes. [ABSTRACT FROM AUTHOR]

Compositional data frequently arise when data refer to components which are proportions or fractions of a whole. Within the log-ratio approach, the analysis of compositional data can be conducted in terms of log-ratio transformations of components. These transformations make it possible to overcome the problem of the constant-sum constraint, making standard statistical methods applicable. In the present work, the log-ratio approach based on orthogonal log-ratio coordinates is adopted to show how it can lead to considerable improvements in the interpretation of the results of regression modeling with compositional data, both as explanatory or response variables. In order to demonstrate its practical usefulness, the methodology presented in this paper is applied to the analysis of air pollution produced by vehicles traveling through road intersections, with a specific focus on the effect of the type of traffic control (traffic signal vs. roundabout) on CO2 emissions. [ABSTRACT FROM AUTHOR]

In this paper, we first study the theory of the spatial-temporal half spectral modeling and describe some properties of recently proposed half spectral models. Next, we propose an estimation method for the estimation of spatial-temporal covariance functions in the half-spectral setting. To assess the performance of the proposed half-spectral models, we conduct two simulations, in which we compare the proposed fitting approach with respect to the other classical estimation methods. The proposed methods have great success in fitting parametric space-time covariance functions specifically for massive data sets. Finally, we apply the proposed methods for a real daily wind speed data in Iran. [ABSTRACT FROM AUTHOR]

Boosting is one of the most popular and powerful learning algorithms. However, due to its sequential nature in model fitting, the computational time of boosting algorithm can be prohibitive for big data analysis. In this paper, we proposed a parallel framework for boosting algorithm, called Ensemble of Fast Learning Stochastic Gradient Boosting (EFLSGB). The proposed EFLSGB is well suited for parallel execution, and therefore, can substantially reduce the computational time. Analysis of simulated and real datasets demonstrates that EFLSGB achieves highly competitive prediction accuracy in comparison with gradient tree boosting. [ABSTRACT FROM AUTHOR]

The use of penalized least squares based estimations in high dimensional linear regression has been received a great deal of attention during past decades and applied to variable selections under sparsity scenarios. However, it remains unclear that complex data with multiple uncertainties in measurements, such as outliers, error-in-variables and heteroscedasticity, to what extent, can influence these approaches. This paper, here, demonstrates the behaviors of least-squares based approaches in complex data problems, and suggests an alternative approach, Wald-type estimator, relying on theoretical perspectives. Numerical experiments and real data analysis are also presented to illustrate the performance of the different estimation strategies. [ABSTRACT FROM AUTHOR]

We develop some statistical methods based on tree-structured classification to assign patients from different treatment groups into subgroups with different medical recommendations. Since it is difficult to discover treatments that benefit all patients, we want to identify subgroups of patients for whom the treatment has an enhanced effect. We classify each terminal node into a subgroup by comparing the relative event rates of the node and its immediate predecessor. Given the suggested subgroup of each terminal node, we propose a method on how to identify which of the splitting variables are keen to which subgroup by tracing back along the tree. We also propose two different ways of assigning medical recommendations. Performance of the proposed method is evaluated using bagging multiple trees, and using cross validations on single trees as our benchmark model. Evaluation of the results is based on comparing the out of bag accuracy from bagging trees and the test accuracy from the cross-validated trees. Bagging trees with randomly selected features perform better than bagging trees including all features when the number of bagging trees exceeds the necessary ntree number. The bagging trees outperform the benchmark, especially when the treatment effect is more homogeneous. [ABSTRACT FROM AUTHOR]

This article proposes robust estimation via modified Cholesky decomposition for modal partially nonlinear models with longitudinal data. A new minorization-maximization algorithm is developed to calculate the modal regression estimates, and the balance between the robustness and efficiency can be achieved by choosing appropriate data adaptive bandwidth. Simulation studies and real data analysis are conducted to illustrate the finite sample performance of the proposed approach. [ABSTRACT FROM AUTHOR]

In a multiple regression model setup, we examine the effects of trimming and winsorization of regressors on the regression estimates and their efficiency. The exact results developed here to enable us to evaluate the effects of winsorizing one regressor on the estimates of the coefficients associated with another regressor. These results have important implications in accounting and finance literature wherein trimming or winsorization is frequently adopted before performing regression analysis. [ABSTRACT FROM AUTHOR]

Under ultrahigh dimensional instrumental variables, we consider the estimation for a class of partially linear models with endogenous covariates. To overcome the difficulty of ultrahigh dimensionality of the instrumental variables, we propose a double penalized regularization estimation procedure for identifying the optimal instrumental variables, and estimating covariate effects of the parametric and nonparametric components. With some regularity conditions, some asymptotic properties of the proposed estimation are derived, such as the consistency of the resulting estimators for parametric and nonparametric components. Lastly, we examine the finite sample performance of the proposed method by some simulation studies and a real data analysis. [ABSTRACT FROM AUTHOR]

In this article, we propose the median-of-means type nonparametric estimator for S-Gini index by using the idea of grouping under the massive data framework, which has been widely used in economics, finance, and insurance. Under certain condition on the growing rate of the number of subgroups, the consistency and asymptotic normality of proposed estimator are investigated. Furthermore, we construct a new method to test S-Gini index based on the empirical likelihood method for median. Our method avoids any prior estimate of variance structure of proposed estimator, which is difficult to estimate and often causes much inaccuracy. Numerical simulations and a real data analysis are designed to show the performance of our estimator. It is shown that the new proposed estimator is quite robust with respect to outliers. [ABSTRACT FROM AUTHOR]

We investigate the bi-level variable selection problem in semiparametric transformation mixture cure models (STMCM). In this type of mixture cure models, we consider a class of semiparametric transformation models for the conditional survival function and a logistic regression for the incidence component, then conduct group variable selection. The group bridge penalty is adopted for bi-level variable selection on both parts of the mixture cure models. Through simulation studies and real data analyses, we show that the proposed method can identify the important variables and groups that contribute to the cure proportion and the survival function for the uncured subjects, respectively. [ABSTRACT FROM AUTHOR]

Topological Data Analysis (TDA) is an approach to handle with big data by studying its shape. A main tool of TDA is the persistence diagram, and one can use it to compare data sets. One approach to learn on the similarity between two persistence diagrams is to use the Bottleneck and the Wasserstein distances. Another approach is to fit a parametric model for each diagram, and then to compare the model coefficients. We study the behavior of both distance measures and the RST parametric model. The theoretical behavior of the distance measures is difficult to be developed, and therefore we study their behavior numerically. We conclude that the RST model has an advantage over the Bottleneck and the Wasserstein distances in sense that it can give a definite conclusion regarding the similarity between two persistence diagrams. More of that, a great advantage of the RST is its ability to distinguish between two data sets that are geometrically different but topologically are the same, which is impossible to have by the two distance measures. [ABSTRACT FROM AUTHOR]

We study a competing risks model using Gompertz distribution under progressive Type-II censoring when probability distributions of failure causes are identically distributed with common scale and different shape parameters. Maximum likelihood estimates (MLEs) of these parameters are obtained and their uniqueness and existence behavior are also discussed. The asymptotic intervals are derived from the observed Fisher information matrix. We compare the performance of all the estimators numerically using simulations. Analysis of a real data set is presented as well. We further determine optimal censoring scheme using expected Fisher information matrix. The design parameters are selected based on suitable measures like cost-based and variance-based criteria functions. Finally, we discuss single and multi-objective optimization approaches to find optimal censoring schemes. [ABSTRACT FROM AUTHOR]

We study the effects of high-dimensional covariates in the single-index quantile regression model. An improved version of an estimation algorithm is proposed with variable selection. Finite sample performance is studied through an extensive simulation study which highlights the performance of the new procedure. A data analysis on US crime data is given that exhibits the usefulness of the proposed methodology. [ABSTRACT FROM AUTHOR]

Aggregation of large databases in a specific format is a frequently used process to make the data easily manageable. Interval-valued data is one of the data types that is generated by such an aggregation process. Using traditional methods to analyze interval-valued data results in loss of information, and thus, several interval-valued data models have been proposed to gather reliable information from such data types. On the other hand, recent technological developments have led to high dimensional and complex data in many application areas, which may not be analyzed by traditional techniques. Functional data analysis is one of the most commonly used techniques to analyze such complex datasets. While the functional extensions of much traditional statistical techniques are available, the functional form of the interval-valued data has not been studied well. This article introduces the functional forms of some well-known regression models that take interval-valued data. The proposed methods are based on the function-on-function regression model, where both the response and predictor/s are functional. Through several Monte Carlo simulations and empirical data analysis, the finite sample performance of the proposed methods is evaluated and compared with the state-of-the-art. [ABSTRACT FROM AUTHOR]

Missing data often creates complications in data analysis for any type of scientific investigations. The non response is the source of missing data and it is an unavoidable phenomenon in survey sampling. This problem becomes more severe in the case of repeated surveys because of its repetitious nature. The missing data due to random causes which we call as random non-response is an important issue which needs to be dealt with a more cautious approach. To address these thoughts, this study is an attempt to reduce the adverse impact of random non response in the estimation of population variance on the current occasion in two-occasion successive sampling. A composite class of estimators for estimation of population variance on the current occasion has been proposed and its properties are deeply examined. An empirical study is carried out to show the efficacious performances of the proposed class of estimators over an estimator defined for the complete response situation. Suitable recommendations are made to the survey practitioners for their real-life practical applications. [ABSTRACT FROM AUTHOR]

Clustering is an important task in statistics and many other scientific fields. In this note, we propose an improved K-means clustering approach called 'enhanced shrinkage K-means' based on the James-Stein estimator and learning vector quantization (LVQ) algorithm. The basic idea of this new algorithm is taking into account of the strength of both unsupervised clustering and supervised classification methods, in which we shrink the clustering centers toward the prototype vector via James-Stein estimator. We carry out extensive simulation studies and real data analysis to evaluate the performance of this new approach, and obtain encouraging results. [ABSTRACT FROM AUTHOR]