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In this paper, we propose the MulticlusterKDE algorithm applied to classify elements of a database into categories based on their similarity. MulticlusterKDE is centered on the multiple optimization of the kernel density estimator function with multivariate Gaussian kernel. One of the main features of the proposed algorithm is that the number of clusters is an optional input parameter. Furthermore, it is very simple, easy to implement, well defined and stops at a finite number of steps and it always converges regardless of the data set. We illustrate our findings by implementing the algorithm in R software. The results indicate that the MulticlusterKDE algorithm is competitive when compared to K-means, K-medoids, CLARA, DBSCAN and PdfCluster algorithms. Features such as simplicity and efficiency make the proposed algorithm an attractive and promising research field that can be used as basis for its improvement and also for the development of new density-based clustering algorithms. [ABSTRACT FROM AUTHOR]

A special source of difficulty in the statistical analysis is the possibility that some subjects may not have a complete observation of the response variable. Such incomplete observation of the response variable is called censoring. Censorship can occur for a variety of reasons, including limitations of measurement equipment, design of the experiment, and non-occurrence of the event of interest until the end of the study. In the presence of censoring, the dependence of the response variable on the explanatory variables can be explored through regression analysis. In this paper, we propose to examine the censorship problem in context of the class of asymmetric, i.e., we have proposed a linear regression model with censored responses based on skew scale mixtures of normal distributions. We develop a Monte Carlo EM (MCEM) algorithm to perform maximum likelihood inference of the parameters in the proposed linear censored regression models with skew scale mixtures of normal distributions. The MCEM algorithm has been discussed with an emphasis on the skew-normal, skew Student-t-normal, skew-slash and skew-contaminated normal distributions. To examine the performance of the proposed method, we present some simulation studies and analyze a real dataset. [ABSTRACT FROM AUTHOR]

In this paper, we consider two well-known parametric long-term survival models, namely, the Bernoulli cure rate model and the promotion time (or Poisson) cure rate model. Assuming the long-term survival probability to depend on a set of risk factors, the main contribution is in the development of the stochastic expectation maximization (SEM) algorithm to determine the maximum likelihood estimates of the model parameters. We carry out a detailed simulation study to demonstrate the performance of the proposed SEM algorithm. For this purpose, we assume the lifetimes due to each competing cause to follow a two-parameter generalized exponential distribution. We also compare the results obtained from the SEM algorithm with those obtained from the well-known expectation maximization (EM) algorithm. Furthermore, we investigate a simplified estimation procedure for both SEM and EM algorithms that allow the objective function to be maximized to split into simpler functions with lower dimensions with respect to model parameters. Moreover, we present examples where the EM algorithm fails to converge but the SEM algorithm still works. For illustrative purposes, we analyze a breast cancer survival data. Finally, we use a graphical method to assess the goodness-of-fit of the model with generalized exponential lifetimes. [ABSTRACT FROM AUTHOR]

This paper considers the vector autoregressive model of order p, VAR(p), with multivariate t error distributions, the latter being more prevalent in real life than the usual multivariate normal distribution. It is believed that the maximum-likelihood equations for the multivariate t distribution have convergence problem, hence we develop estimation procedures for VAR(p) model using the normal mean–variance mixture representation of multivariate t distribution. The procedure relies on the computational ease available in Expectation Maximization-based algorithms. The estimators obtained are explicit functions of sample observations and therefore are easy to compute. Extensive simulation experiments show that the estimators have negligible bias and are considerably more efficient than an existing method that uses the least-squares error approach. It is shown that the proposed estimators are robust to plausible deviations from an assumed distribution and hence are more advantageous when compared with the other estimator. One real-life example is given for illustration purposes. [ABSTRACT FROM AUTHOR]

This paper presents a robust extension of factor analysis model by assuming the multivariate normal mean–variance mixture of Birnbaum–Saunders distribution for the unobservable factors and errors. A computationally analytical EM-based algorithm is developed to find maximum likelihood estimates of the parameters. The asymptotic standard errors of parameter estimates are derived under an information-based paradigm. Numerical merits of the proposed methodology are illustrated using both simulated and real datasets. [ABSTRACT FROM AUTHOR]

In this paper, the estimation of unknown parameters of Chen distribution is considered under progressive Type-II censoring in the presence of competing failure causes. It is assumed that the latent causes of failures have independent Chen distributions with the common shape parameter, but different scale parameters. From a frequentist perspective, the maximum likelihood estimate of parameters via expectation–maximization (EM) algorithm is obtained. Also, the expected Fisher information matrix based on the missing information principle is computed. By using the obtained expected Fisher information matrix of the MLEs, asymptotic 95% confidence intervals for the parameters are constructed. We also apply the bootstrap methods (Bootstrap-p and Bootstrap-t) to construct confidence intervals. From Bayesian aspect, the Bayes estimates of the unknown parameters are computed by applying the Markov chain Monte Carlo (MCMC) procedure, the average length and coverage rate of credible intervals are also carried out. The Bayes inference is based on the squared error, LINEX, and general entropy loss functions. The performance of point estimators and confidence intervals is evaluated by a simulation study. Finally, a real-life example is considered for illustrative purposes. [ABSTRACT FROM AUTHOR]

The heteroscedastic nonlinear regression model (HNLM) is an important tool in data modeling. In this paper we propose a HNLM considering skew scale mixtures of normal (SSMN) distributions, which allows fitting asymmetric and heavy-tailed data simultaneously. Maximum likelihood (ML) estimation is performed via the expectation-maximization (EM) algorithm. The observed information matrix is derived analytically to account for standard errors. In addition, diagnostic analysis is developed using case-deletion measures and the local influence approach. A simulation study is developed to verify the empirical distribution of the likelihood ratio statistic, the power of the homogeneity of variances test and a study for misspecification of the structure function. The method proposed is also illustrated by analyzing a real dataset. [ABSTRACT FROM AUTHOR]

In this paper, the Rayleigh-Lindley (RL) distribution is introduced, obtained by compounding the Rayleigh and Lindley discrete distributions, where the compounding procedure follows an approach similar to the one previously studied by Adamidis and Loukas in some other contexts. The resulting distribution is a two-parameter model, which is competitive with other parsimonious models such as the gamma and Weibull distributions. We study some properties of this new model such as the moments and the mean residual life. The estimation was approached via EM algorithm. The behavior of these estimators was studied in finite samples through a simulation study. Finally, we report two real data illustrations in order to show the performance of the proposed model versus other common two-parameter models in the literature. The main conclusion is that the model proposed can be a valid alternative to other competing models well established in the literature. [ABSTRACT FROM AUTHOR]

Missing covariates data is a common issue in generalized linear models (GLMs). A model-based procedure arising from properly specifying joint models for both the partially observed covariates and the corresponding missing indicator variables represents a sound and flexible methodology, which lends itself to maximum likelihood estimation as the likelihood function is available in computable form. In this paper, a novel model-based methodology is proposed for the regression analysis of GLMs when the partially observed covariates are categorical. Pair-copula constructions are used as graphical tools in order to facilitate the specification of the high-dimensional probability distributions of the underlying missingness components. The model parameters are estimated by maximizing the weighted log-likelihood function by using an EM algorithm. In order to compare the performance of the proposed methodology with other well-established approaches, which include complete-cases and multiple imputation, several simulation experiments of Binomial, Poisson and Normal regressions are carried out under both missing at random and non-missing at random mechanisms scenarios. The methods are illustrated by modeling data from a stage III melanoma clinical trial. The results show that the methodology is rather robust and flexible, representing a competitive alternative to traditional techniques. [ABSTRACT FROM AUTHOR]

In this paper, we propose a penalized likelihood method to simultaneous select covariate, and mixing component and obtain parameter estimation in the localized mixture of experts models. We develop an expectation maximization algorithm to solve the proposed penalized likelihood procedure, and introduce a data-driven procedure to select the tuning parameters. Extensive numerical studies are carried out to compare the finite sample performances of our proposed method and other existing methods. Finally, we apply the proposed methodology to analyze the Boston housing price data set and the baseball salaries data set. [ABSTRACT FROM AUTHOR]

Singular spectrum analysis (SSA) is an increasingly popular and widely adopted filtering and forecasting technique which is currently exploited in a variety of fields. Given its increasing application and superior performance in comparison to other methods, it is pertinent to study and distinguish between the two forecasting variations of SSA. These are referred to as Vector SSA (SSA-V) and Recurrent SSA (SSA-R). The general notion is that SSA-V is more robust and provides better forecasts than SSA-R. This is especially true when faced with time series which are non-stationary and asymmetric, or affected by unit root problems, outliers or structural breaks. However, currently there exists no empirical evidence for proving the above notions or suggesting that SSA-V is better than SSA-R. In this paper, we evaluate out-of-sample forecasting capabilities of the optimised SSA-V and SSA-R forecasting algorithms via a simulation study and an application to 100 real data sets with varying structures, to provide a statistically reliable answer to the question of which SSA algorithm is best for forecasting at both short and long run horizons based on several important criteria. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new method for detecting outliers in a set of proportions. It is based on the construction of a suitable twoway contingency table and on the application of an algorithm for the detection of outlying cells in such table. We exploit the special structure of the relevant contingency table to increase the efficiency of the method. The main properties of our algorithm, together with a guide for the choice of the parameters, are investigated through simulations, and in simple cases some theoretical justifications are provided. Several examples on synthetic data and an example based on pseudo-real data from biological experiments demonstrate the good performances of our algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we present an algorithm for clustering based on univariate kernel density estimation, named ClusterKDE. It consists of an iterative procedure that in each step a new cluster is obtained by minimizing a smooth kernel function. Although in our applications we have used the univariate Gaussian kernel, any smooth kernel function can be used. The proposed algorithm has the advantage of not requiring a priori the number of cluster. Furthermore, the ClusterKDE algorithm is very simple, easy to implement, well-defined and stops in a finite number of steps, namely, it always converges independently of the initial point. We also illustrate our findings by numerical experiments which are obtained when our algorithm is implemented in the software Matlab and applied to practical applications. The results indicate that the ClusterKDE algorithm is competitive and fast when compared with the well-known Clusterdata and K-means algorithms, used by Matlab to clustering data. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a novel Max-Relevance and Min-Common-Redundancy criterion for variable selection in linear models. Considering that the ensemble approach for variable selection has been proven to be quite effective in linear regression models, we construct a variable selection ensemble (VSE) by combining the presented stochastic correlation coefficient algorithm with a stochastic stepwise algorithm. We conduct extensive experimental comparison of our algorithm and other methods using two simulation studies and four real-life data sets. The results confirm that the proposed VSE leads to promising improvement on variable selection and regression accuracy. [ABSTRACT FROM AUTHOR]

This paper discusses the bootstrap test of entropies. Since the comparison of entropies is of prime interest in applied fields, finding an appropriate way to carry out such a comparison is of utmost importance. This paper presents how resampling should be performed to obtain an accuratep-value. Although the test using a pair-wise bootstrap confidence interval (CI) has already been dealt with in few works, here the bootstrap tests are studied because it may demand quite a different resampling algorithm compared with the CI. Moreover, the multiple test is studied. The proposed tests appear to yield several appreciable advantages. The easy implementation and the power of the proposed test can be considered as advantages. Here the entropy of the discrete variable is studied. The proposed tests are examined using Monte Carlo investigations and also evaluated using various distributions. [ABSTRACT FROM PUBLISHER]

The result of feature selection for software birthmark has a direct bearing on software recognition rate. In this paper, we apply constrained clustering to analyze the software features (SF). The within-class (homogeneous software) and between-class (heterogeneous software) distances of features are measured based on mutual information. Information gain functions and penalty functions are constructed using homogeneous and heterogeneous SF, respectively; and redundancy is measured with correlation coefficients. Then the software birthmark features with high class distinction and minimum redundancy are selected. The example of extracting and detecting framework of birthmark feature is also given. The algorithm is analyzed and compared with the similar algorithms, and it is shown the algorithm provide an effective approach for software birthmark selection and optimization. [ABSTRACT FROM PUBLISHER]

This paper considers a life test under progressive type I group censoring with a Weibull failure time distribution. The maximum likelihood method is used to derive the estimators of the parameters of the failure time distribution. In practice, several variables, such as the number of test units, the number of inspections, and the length of inspection interval are related to the precision of estimation and the cost of experiment. An inappropriate setting of these decision variables not only wastes the resources of the experiment but also reduces the precision of estimation. One problem arising from designing a life test is the restricted budget of experiment. Therefore, under the constraint that the total cost of experiment does not exceed a pre-determined budget, this paper provides an algorithm to solve the optimal decision variables by considering three different criteria. An example is discussed to illustrate the proposed method. The sensitivity analysis is also studied. [ABSTRACT FROM AUTHOR]

This paper introduces an alternating conditional expectation (ACE) algorithm: a non-parametric approach for estimating the transformations that lead to the maximal multiple correlation of a response and a set of independent variables in regression and correlation analysis. These transformations can give the data analyst insight into the relationships between these variables so that this can be best described and non-linear relationships uncovered. Using the Bayesian information criterion (BIC), we show how to find the best closed-form approximations for the optimal ACE transformations. By means of ACE and BIC, the model fit can be considerably improved compared with the conventional linear model as demonstrated in the two simulated and two real datasets in this paper. [ABSTRACT FROM AUTHOR]

Electoral analysis using aggregate data relies on the availability of accurate voting statistics. One vital piece of information, often missing from official electoral returns, particularly British local government elections, is the total number of valid ballot papers. This figure is essential for the calculation of electoral turnout. When voters have a single vote and official information about the number of ballot papers issued is missing, a figure for the total vote can still be derived. However, local elections in Britain frequently use a system of multiple-member wards, where voters have as many votes as there are seats to be filled. In such cases, calculating the total vote and, hence, the turnout does present a real problem. It cannot be assumed that all voters will use their full quota of votes or that voters will cast a ballot in favour of a single party. This paper develops and tests diff erent algorithms for calculating the total vote in such circumstances. We conclude that the accuracy of an algorithm is closely related to the structure of party competition. The findings of this paper have a number of important implications. First, the difficulties in calculating the turnout in multiple-member wards are identified. This will inform the debate about public participation in the local electoral process. Second, the method for deriving a figure for the total vote has an important bearing on a number of other statistics widely employed in electoral analysis. [ABSTRACT FROM AUTHOR]

The availability of the next generation sequencing (NGS) technology in today's biomedical research has provided new opportunities in scientific discovery of genetic information. The high-throughput NGS technology, especially DNA-seq, is particularly useful in profiling a genome for the analysis of DNA copy number variants (CNVs). The read count (RC) data resulting from NGS technology are massive and information rich. How to exploit the RC data for accurate CNV detection has become a computational and statistical challenge. We provide a statistical online change point method to help detect CNVs in the sequencing RC data in this paper. This method uses the idea of online searching for change point (or breakpoint) with a Markov chain assumption on the breakpoints loci and an iterative computing process via a Bayesian framework. We illustrate that an online change-point detection method is particularly suitable for identifying CNVs in the RC data. The algorithm is applied to the publicly available NCI-H2347 lung cancer cell line sequencing reads data for locating the breakpoints. Extensive simulation studies have been carried out and results show the good behavior of the proposed algorithm. The algorithm is implemented in R and the codes are available upon request. [ABSTRACT FROM AUTHOR]

In this paper a methodology for the delineation of local labour markets (LLMs) using evolutionary algorithms is proposed. This procedure, based on that in Flórez-Revueltaet al.[13,14], introduces three modifications. First, initial groups of municipalities with a minimum size requirement are built using the travel time between them. Second, a not fully random initiation algorithm is proposed. And third, as a final stage of the procedure, a contiguity step is implemented. These modifications significantly decrease the computational times of the algorithm (up to a 99%) without any deterioration of the quality of the solutions. The optimization algorithm may give a set of potential solutions with very similar values with respect to the objective function what would lead to different partitions, both in terms of number of markets and their composition. In order to capture their common aspects an algorithm based on a cluster partitioning ofk-means type is presented. This stage of the procedure also provides a ranking of LLMs foci useful for planners and administrations in decision-making processes on issues related to labour activities. Finally, to evaluate the performance of the algorithm a toy example with artificial data is analysed. The full methodology is illustrated through a real commuting data set of the region of Aragón (Spain). [ABSTRACT FROM AUTHOR]

In this paper, we propose a solution on microaggregation problem based on the hierarchical tree equi-partition (HTEP) algorithm. Microaggregation is a family of methods for statistical disclosure control of microdata, that is, for masking microdata, so that they can be released without disclose private information on the underlying individuals. Knowing that the microaggregation problem is non-deterministic polynomial-time-hard, the goal is to partitionNgiven data into groups of at leastKitems, so that the sum of the within-partition squared error is minimized. The proposed method is general and it can be applied to any tree partition problem aiming at the minimization of a total score. The method is divisive, so that the tree with the highest ‘score’ is split into two trees, resulting in a hierarchical forest of trees with almost equal ‘score’ (equipartition). We propose a version of HTEP for microaggregation (HTEPM), that is applied on the minimum spanning tree (MST) of the graph defined by the data. The merit of the HTEPM algorithm is that it solves optimally some instances of the multivariate microaggregation problem on MST search space in. Experimental results and comparisons with existing methods from literature prove the high performance and robustness of HTEPM. [ABSTRACT FROM AUTHOR]

The detection of outliers and influential observations has received a great deal of attention in the statistical literature in the context of least-squares (LS) regression. However, the explanatory variables can be correlated with each other and alternatives to LS come out to address outliers/influential observations and multicollinearity, simultaneously. This paper proposes new influence measures based on the affine combination type regression for the detection of influential observations in the linear regression model when multicollinearity exists. Approximate influence measures are also proposed for the affine combination type regression. Since the affine combination type regression includes the ridge, the Liu and the shrunken regressions as special cases, influence measures under the ridge, the Liu and the shrunken regressions are also examined to see the possible effect that multicollinearity can have on the influence of an observation. The Longley data set is given illustrating the influence measures in affine combination type regression and also in ridge, Liu and shrunken regressions so that the performance of different biased regressions on detecting and assessing the influential observations is examined. [ABSTRACT FROM AUTHOR]

Classification and regression tree has been useful in medical research to construct algorithms for disease diagnosis or prognostic prediction. Jinet al.7 developed a robust and cost-saving tree (RACT) algorithm with application in classification of hip fracture risk after 5-year follow-up based on the data from the Study of Osteoporotic Fractures (SOF). Although conventional recursive partitioning algorithms have been well developed, they still have some limitations. Binary splits may generate a big tree with many layers, but trinary splits may produce too many nodes. In this paper, we propose a classification approach combining trinary splits and binary splits to generate a trinary–binary tree. A new non-inferiority test of entropy is used to select the binary or trinary splits. We apply the modified method in SOF to construct a trinary–binary classification rule for predicting risk of osteoporotic hip fracture. Our new classification tree has good statistical utility: it is statistically non-inferior to the optimum binary tree and the RACT based on the testing sample and is also cost-saving. It may be useful in clinical applications: femoral neck bone mineral density, age, height loss and weight gain since age 25 can identify subjects with elevated 5-year hip fracture risk without loss of statistical efficiency. [ABSTRACT FROM AUTHOR]

Quasi-optimal procedures of testing many hypotheses are described in this paper. They significantly simplify the Bayesian algorithms of hypothesis testing and computation of the risk function. The relations allowing for obtaining the estimations for the values of average risks in optimum tasks are given. The obtained general solutions are reduced to concrete formulae for a multivariate normal distribution of probabilities. The methods of approximate computation of the risk functions in Bayesian tasks of testing many hypotheses are offered. The properties and interrelations of the developed methods and algorithms are investigated. On the basis of a simulation, the validity of the obtained results and conclusions drawn is presented. [ABSTRACT FROM AUTHOR]

The EM algorithm is the standard method for estimating the parameters in finite mixture models. Yang and Pan [25] proposed a generalized classification maximum likelihood procedure, called the fuzzy c-directions (FCD) clustering algorithm, for estimating the parameters in mixtures of von Mises distributions. Two main drawbacks of the EM algorithm are its slow convergence and the dependence of the solution on the initial value used. The choice of initial values is of great importance in the algorithm-based literature as it can heavily influence the speed of convergence of the algorithm and its ability to locate the global maximum. On the other hand, the algorithmic frameworks of EM and FCD are closely related. Therefore, the drawbacks of FCD are the same as those of the EM algorithm. To resolve these problems, this paper proposes another clustering algorithm, which can self-organize local optimal cluster numbers without using cluster validity functions. These numerical results clearly indicate that the proposed algorithm is superior in performance of EM and FCD algorithms. Finally, we apply the proposed algorithm to two real data sets. [ABSTRACT FROM PUBLISHER]

In this paper,we propose a class of general partially linear varying-coefficient transformation models for ranking data. In the models, the functional coefficients are viewed as nuisance parameters and approximated by B-spline smoothing approximation technique. The B-spline coefficients and regression parameters are estimated by rank-based maximum marginal likelihood method. The three-stage Monte Carlo Markov Chain stochastic approximation algorithm based on ranking data is used to compute estimates and the corresponding variances for all the B-spline coefficients and regression parameters. Through three simulation studies and a Hong Kong horse racing data application, the proposed procedure is illustrated to be accurate, stable and practical. [ABSTRACT FROM PUBLISHER]

The aim of this paper is to present a Complete Gradient Clustering Algorithm, its applicational aspects and properties, as well as to illustrate them with specific practical problems from the subject of bioinformatics (the categorization of grains for seed production), management (the design of a marketing support strategy for a mobile phone operator) and engineering (the synthesis of a fuzzy controller). The main property of the Complete Gradient Clustering Algorithm is that it does not require strict assumptions regarding the desired number of clusters, which allows to better suit its obtained number to a real data structure. In the basic version it is possible to provide a complete set of procedures for defining the values of all functions and parameters relying on the optimization criterions. It is also possible to point out parameters, the potential change which implies influence on the size of the number of clusters (while still not giving an exact number) and the proportion between their numbers in dense and sparse areas of data elements. Moreover, the Complete Gradient Clustering Algorithm can be used to identify and possibly eliminate atypical elements (outliers). These properties proved to be very useful in the presented applications and may also be functional in many other practical problems. [ABSTRACT FROM PUBLISHER]

In this paper, we utilize normal/independent (NI) distributions as a tool for robust modeling of linear mixed models (LMM) under a Bayesian paradigm. The purpose is to develop a non-iterative sampling method to obtain i.i.d. samples approximately from the observed posterior distribution by combining the inverse Bayes formulae, sampling/importance resampling and posterior mode estimates from the expectation maximization algorithm to LMMs with NI distributions, as suggested by Tan et al. [33]. The proposed algorithm provides a novel alternative to perfect sampling and eliminates the convergence problems of Markov chain Monte Carlo methods. In order to examine the robust aspects of the NI class, against outlying and influential observations, we present a Bayesian case deletion influence diagnostics based on the Kullback–Leibler divergence. Further, some discussions on model selection criteria are given. The new methodologies are exemplified through a real data set, illustrating the usefulness of the proposed methodology. [ABSTRACT FROM AUTHOR]

In this paper, a new compounding distribution, named the Weibull–Poisson distribution is introduced. The shape of failure rate function of the new compounding distribution is flexible, it can be decreasing, increasing, upside-down bathtub-shaped or unimodal. A comprehensive mathematical treatment of the proposed distribution and expressions of its density, cumulative distribution function, survival function, failure rate function, the kth raw moment and quantiles are provided. Maximum likelihood method using EM algorithm is developed for parameter estimation. Asymptotic properties of the maximum likelihood estimates are discussed, and intensive simulation studies are conducted for evaluating the performance of parameter estimation. The use of the proposed distribution is illustrated with examples. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a Bayesian Analysis for the Block and Basu bivariate exponential distribution using Markov Chain Monte Carlo (MCMC) methods and considering lifetimes in presence of covariates and censored data. Posterior summaries of interest are obtained using the popular WinBUGS software. Numerical illustrations are introduced considering a medical data set related to the recurrence times of infection for kidney patients and a medical data set related to bone marrow transplantation for leukemia. [ABSTRACT FROM AUTHOR]

This paper evaluates the ability of a Markov regime-switching log-normal (RSLN) model to capture the time-varying features of stock return and volatility. The model displays a better ability to depict a fat tail distribution as compared with using a log-normal model, which means that the RSLN model can describe observed market behavior better. Our major objective is to explore the capability of the model to capture stock market behavior over time. By analyzing the behavior of calibrated regime-switching parameters over different lengths of time intervals, the change-point concept is introduced and an algorithm is proposed for identifying the change-points in the series corresponding to the times when there are changes in parameter estimates. This algorithm for identifying change-points is tested on the Standard and Poor's 500 monthly index data from 1971 to 2008, and the Nikkei 225 monthly index data from 1984 to 2008. It is evident that the change-points we identify match the big events observed in the US stock market and the Japan stock market (e.g., the October 1987 stock market crash), and that the segmentations of stock index series, which are defined as the periods between change-points, match the observed bear-bull market phases. [ABSTRACT FROM AUTHOR]

Likelihood-based marginalized models using random effects have become popular for analyzing longitudinal categorical data. These models permit direct interpretation of marginal mean parameters and characterize the serial dependence of longitudinal outcomes using random effects [12,22]. In this paper, we propose model that expands the use of previous models to accommodate longitudinal nominal data. Random effects using a new covariance matrix with a Kronecker product composition are used to explain serial and categorical dependence. The Quasi-Newton algorithm is developed for estimation. These proposed methods are illustrated with a real data set and compared with other standard methods. [ABSTRACT FROM AUTHOR]

Combining data of several tests or markers for the classification of patients according to their health status for assigning better treatments is a major issue in the study of diseases such as cancer. In order to tackle this problem, several approaches have been proposed in the literature. In this paper, a step-by-step algorithm for estimating the parameters of a linear classifier that combines several measures is considered. The optimization criterion is to maximize the area under the receiver operating characteristic curve. The algorithm is applied to different simulated data sets and its performance is evaluated. Finally, the method is illustrated with a prostate cancer staging database. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of robust estimation of the fractional parameter, d, in long memory autoregressive fractionally integrated moving average processes, when two types of outliers, i.e. additive and innovation, are taken into account without knowing their number, position or intensity. The proposed method is a weighted likelihood estimation (WLE) approach for which needed definitions and algorithm are given. By an extensive Monte Carlo simulation study, we compare the performance of the WLE method with the performance of both the approximated maximum likelihood estimation (MLE) and the robust M-estimator proposed by Beran (Statistics for Long-Memory Processes, Chapman & Hall, London, 1994). We find that robustness against the two types of considered outliers can be achieved without loss of efficiency. Moreover, as a byproduct of the procedure, we can classify the suspicious observations in different kinds of outliers. Finally, we apply the proposed methodology to the Nile River annual minima time series. [ABSTRACT FROM AUTHOR]

The aim of this paper is to find an optimal alternative bivariate ranked-set sample for one-sample location model bivariate sign test. Our numerical and theoretical results indicated that the optimal designs for the bivariate sign test are the alternative designs with quantifying order statistics with labels {((r+1)/2, (r+1)/2)}, when the set size r is odd and {(r/2+1, r/2), (r/2, r/2+1)} when the set size r is even. The asymptotic distribution and Pitman efficiencies of these designs are derived. A simulation study is conducted to investigate the power of the proposed optimal designs. Illustration using real data with the Bootstrap algorithm for P-value estimation is used. [ABSTRACT FROM AUTHOR]

The generalized standard two-sided power (GTSP) distribution was mentioned only in passing by Kotz and van Dorp Beyond Beta, Other Continuous Families of Distributions with Bounded Support and Applications, World Scientific Press, Singapore, 2004. In this paper, we shall further investigate this three-parameter distribution by presenting some novel properties and use its more general form to contrast the chronology of developments of various authors on the two-parameter TSP distribution since its initial introduction. GTSP distributions allow for J-shaped forms of its pdf, whereas TSP distributions are limited to U-shaped and unimodal forms. Hence, GTSP distributions possess the same three distributional shapes as the classical beta distributions. A novel method and algorithm for the indirect elicitation of the two-power parameters of the GTSP distribution is developed. We present a Project Evaluation Review Technique example that utilizes this algorithm and demonstrates the benefit of separate powers for the two branches of activity GTSP distributions for project completion time uncertainty estimation. [ABSTRACT FROM AUTHOR]

Skew-normal distribution is a class of distributions that includes the normal distributions as a special case. In this paper, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis in a multivariate, null intercept, measurement error model [R. Aoki, H. Bolfarine, J.A. Achcar, and D. Leao Pinto Jr, Bayesian analysis of a multivariate null intercept error-in-variables regression model, J. Biopharm. Stat. 13(4) (2003b), pp. 763-771] where the unobserved value of the covariate (latent variable) follows a skew-normal distribution. The results and methods are applied to a real dental clinical trial presented in [A. Hadgu and G. Koch, Application of generalized estimating equations to a dental randomized clinical trial, J. Biopharm. Stat. 9 (1999), pp. 161-178]. [ABSTRACT FROM AUTHOR]

Count data with excess zeros often occurs in areas such as public health, epidemiology, psychology, sociology, engineering, and agriculture. Zero-inflated Poisson (ZIP) regression and zero-inflated negative binomial (ZINB) regression are useful for modeling such data, but because of hierarchical study design or the data collection procedure, zero-inflation and correlation may occur simultaneously. To overcome these challenges ZIP or ZINB may still be used. In this paper, multilevel ZINB regression is used to overcome these problems. The method of parameter estimation is an expectation-maximization algorithm in conjunction with the penalized likelihood and restricted maximum likelihood estimates for variance components. Alternative modeling strategies, namely the ZIP distribution are also considered. An application of the proposed model is shown on decayed, missing, and filled teeth of children aged 12 years old. [ABSTRACT FROM AUTHOR]

Two practical degrees of complexity may arise when designing an experiment for a model of a real life case. First, some explanatory variables may not be under the control of the practitioner. Secondly, the responses may be correlated. In this paper three real life cases in this situation are considered. Different covariance structures are studied and some designs are computed adapting the theory of marginally restricted designs for correlated observations. An exchange algorithm given by Brimkulov's algorithm is also adapted to marginally restricted D-optimality and it is applied to a complex situation. [ABSTRACT FROM AUTHOR]

In order to study developmental variables, for example, neuromotor development of children and adolescents, monotone fitting is typically needed. Most methods, to estimate a monotone regression function non-parametrically, however, are not straightforward to implement, a difficult issue being the choice of smoothing parameters. In this paper, a convenient implementation of the monotone B-spline estimates of Ramsay [Monotone regression splines in action (with discussion), Stat. Sci. 3 (1988), pp. 425-461] and Kelly and Rice [Montone smoothing with application to dose-response curves and the assessment of synergism, Biometrics 46 (1990), pp. 1071-1085] is proposed and applied to neuromotor data. Knots are selected adaptively using ideas found in Friedman and Silverman [Flexible parsimonous smoothing and additive modelling (with discussion), Technometrics 31 (1989), pp. 3-39] yielding a flexible algorithm to automatically and accurately estimate a monotone regression function. Using splines also simultaneously allows to include other aspects in the estimation problem, such as modeling a constant difference between two groups or a known jump in the regression function. Finally, an estimate which is not only monotone but also has a 'levelling-off' (i.e. becomes constant after some point) is derived. This is useful when the developmental variable is known to attain a maximum/minimum within the interval of observation. [ABSTRACT FROM AUTHOR]

In this paper the issue of making inferences with misclassified data from a noisy multinomial process is addressed. A Bayesian model for making inferences about the proportions and the noise parameters is developed. The problem is reformulated in a more tractable form by introducing auxiliary or latent random vectors. This allows for an easy-to-implement Gibbs sampling-based algorithm to generate samples from the distributions of interest. An illustrative example related to elections is also presented. [ABSTRACT FROM AUTHOR]

For the data from multivariate t distributions, it is very hard to make an influence analysis based on the probability density function since its expression is intractable. In this paper, we present a technique for influence analysis based on the mixture distribution and EM algorithm. In fact, the multivariate t distribution can be considered as a particular Gaussian mixture by introducing the weights from the Gamma distribution. We treat the weights as the missing data and develop the influence analysis for the data from multivariate t distributions based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm. Several case-deletion measures are proposed for detecting influential observations from multivariate t distributions. Two numerical examples are given to illustrate our methodology. [ABSTRACT FROM AUTHOR]

Consider a random sample X 1 , X 2 ,..., X n , from a normal population with unknown mean and standard deviation. Only the sample size, mean and range are recorded and it is necessary to estimate the unknown population mean and standard deviation. In this paper the estimation of the mean and standard deviation is made from a Bayesian perspective by using a Markov Chain Monte Carlo (MCMC) algorithm to simulate samples from the intractable joint posterior distribution of the mean and standard deviation. The proposed methodology is applied to simulated and real data. The real data refers to the sugar content ( o BRIX level) of orange juice produced in different countries. [ABSTRACT FROM AUTHOR]

Taguchi (1959) introduced the concept of split-unit design to sort the factors into different groups depending upon the difficulties involved in changing the levels of factors. Li et at (1991) renamed it as split-plot design. Chen et at (1993) have given a catalogue of small designs for two- and three-level fractional factorial designs pertaining to a single type of factors. Aggarwal et al. (1997) have given a catalogue of group structure for two-level fractional factorial designs developed under the concept of split-plot design. In this paper, an algorithm has been developed for generating group structure and possible allocations for various 3n-k fractional factorial designs. [ABSTRACT FROM AUTHOR]

In this paper, we make use of an algorithm of Huffer & Lin (2001) in order to develop exact prediction intervals for failure times from one-parameter and two-parameter exponential distributions based on doubly Type-II censored samples. We show that this method yields the same results as those of Lawless (1971, 1977) and Likeŝ (1974) in the case when the available sample is Type-II right censored. We present a computational algorithm for the determination of the exact percentage points of the pivotal quantities used in the construction of these prediction intervals. We also present some tables of these percentage points for the prediction of the lth order statistic in a sample of size n for both one- and two-parameter exponential distributions, assuming that the available sample is doubly Type-II censored. Finally, we present two examples to illustrate the methods of inference developed here. [ABSTRACT FROM AUTHOR]

This paper derives an application of the minimum chi-squared (MCS) methodology to estimate the parameters of the unimodal symmetric stable distribution. The proposed method is especially suitable for large, both regular and non-standard, data sets. Monte Carlo simulations are performed to compare the efficiency of the MCS estimation with the efficiency of the McCulloch quantile algorithm. In the case of grouped observations, evidence in favour of the MCS method is reported. For the ungrouped data the MCS estimation generally performs better than McCulloch's quantile method for samples larger than 400 observations and for high alphas. The relative advantage of the MCS over the McCulloch estimators increases for larger samples. The empirical example analyses the highly irregular distributions of returns on the selected securities from the Warsaw Stock Exchange. The quantile and maximum likelihood estimates of characteristic exponents are generally smaller than the MCS ones. This reflects the bias in the traditional methods, which is due to a lack of adjustment for censored and clustered observations, and shows the flexibility of the proposed MCS approach. [ABSTRACT FROM AUTHOR]

Models for extreme values are usually based on detailed asymptotic argument, for which strong ergodic assumptions such as stationarity, or prescribed perturbations from stationarity, are required. In most applications of extreme value modelling such assumptions are not satisfied, but the type of departure from stationarity is either unknown or complex, making asymptotic calculations unfeasible. This has led to various approaches in which standard extreme value models are used as building blocks for conditional or local behaviour of processes, with more general statistical techniques being used at the modelling stage to handle the non-stationarity. This paper presents another approach in this direction based on penalized likelihood. There are some advantages to this particular approach: the method has a simple interpretation; computations for estimation are relatively straightforward using standard algorithms; and a simple reinterpretation of the model enables broader inferences, such as confidence intervals, to be obtained using MCMC methodology. Methodological details together with applications to both athletics and environmental data are given. [ABSTRACT FROM AUTHOR]

In this paper, an algorithm for Generalized Monotonic Smoothing (GMS) is developed as an extension to exponential family models of the monotonic smoothing techniques proposed by Ramsay (1988, 1998a,b). A two-step algorithm is used to estimate the coefficients of bases and the linear term. We show that the algorithm can be embedded into the iterative re-weighted least square algorithm that is typically used to estimate the coefficients in Generalized Linear Models. Thus, the GMS estimator can be computed using existing routines in S-plus and other statistical software. We apply the GMS model to the Down's syndrome data set and compare the results with those from Generalized Additive Model estimation. The choice of smoothing parameter and testing of monotonicity are also discussed. [ABSTRACT FROM AUTHOR]

Mixture models may arise for a variety of reasons in survival data analysis. This paper shows how such models that involve potentially complex cross-classification by covariates may be easily fitted using a package such as GLIM. The method employs an auxiliary Poisson-binomial model in order to find the maximum-likelihood estimates of the model parameters, and has been implemented using GLIM macros. [ABSTRACT FROM AUTHOR]