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We attempt to identify the 25 most-cited statistical papers, providing some brief commentary on each paper on our list. This list consists, to a great extent, of papers that are on non-parametric methods, have applications in the life sciences, or deal with the multiple comparisons problem. We also list the most-cited papers published in 1993 or later. In contrast to the overall most-cited papers, these are predominately papers on Bayesian methods and wavelets. We briefly discuss some of the issues involved in the use of citation counts. [ABSTRACT FROM AUTHOR]

The Cash statistic, also known as the C statistic, is commonly used for the analysis of low-count Poisson data, including data with null counts for certain values of the independent variable. The use of this statistic is especially attractive for low-count data that cannot be combined, or re-binned, without loss of resolution. This paper presents a new maximum-likelihood solution for the best-fit parameters of a linear model using the Poisson-based Cash statistic. The solution presented in this paper provides a new and simple method to measure the best-fit parameters of a linear model for any Poisson-based data, including data with null counts. In particular, the method enforces the requirement that the best-fit linear model be non-negative throughout the support of the independent variable. The method is summarized in a simple algorithm to fit Poisson counting data of any size and counting rate with a linear model, by-passing entirely the use of the traditional χ 2 statistic. [ABSTRACT FROM AUTHOR]

Researchers in statistical shape analysis often analyze outlines of objects. Even though these contours are infinite-dimensional in theory, they must be discretized in practice. When discretizing, it is important to reduce the number of sampling points considerably to reduce computational costs, but to not use too few points so as to result in too much approximation error. Unfortunately, determining the minimum number of points needed to achieve sufficiently approximate the contours is computationally expensive. In this paper, we fit regression models to predict these lower bounds using characteristics of the contours that are computationally cheap as predictor variables. However, least squares regression is inadequate for this task because it treats overestimation and underestimation equally, but underestimation of lower bounds is far more serious. Instead, to fit the models, we use the LINEX loss function, which allows us to penalize underestimation at an exponential rate while penalizing overestimation only linearly. We present a novel approach to select the shape parameter of the loss function and tools for analyzing how well the model fits the data. Through validation methods, we show that the LINEX models work well for reducing the underestimation for the lower bounds. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the mean change-point models based on associated sequences. Under some weak conditions, we obtain a limit distribution of CUSUM statistic which can be used to judge the mean change-mount δ n is satisfied or dissatisfied n 1 / 2 δ n = o (1). We also study the consistency of sample covariances and change-point location statistics. Based on Normality and Lognormality data, some simulations such as empirical sizes, empirical powers and convergence are presented to test our results. As an important application, we use CUSUM statistics to do the mean change-point analysis for a financial series. [ABSTRACT FROM AUTHOR]

The C statistic, also known as the Cash statistic, is often used in astronomy for the analysis of low-count Poisson data. The main advantage of this statistic, compared to the more commonly used χ 2 statistic, is its applicability without the need to combine data points. This feature has made the C statistic a very useful method to analyze Poisson data that have small (or even null) counts in each resolution element. One of the challenges of the C statistic is that its probability distribution, under the null hypothesis that the data follow a parent model, is not known exactly. This paper presents an effort towards improving our understanding of the C statistic by studying (a) the distribution of C statistic for a fully specified model, (b) the distribution of Cmin resulting from a maximum-likelihood fit to a simple one-parameter constant model, i.e. a model that represents the sample mean of N Poisson measurements, and (c) the distribution of the associated Δ C statistic that is used for parameter estimation. The results confirm the expectation that, in the high-count limit, both C statistic and Cmin have the same mean and variance as a χ 2 statistic with same number of degrees of freedom. It is also found that, in the low-count regime, the expectation of the C statistic and Cmin can be substantially lower than for a χ 2 distribution. The paper makes use of recent X-ray observations of the astronomical source PG 1116+215 to illustrate the application of the C statistic to Poisson data. [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]

Discrete data are collected in many application areas and are often characterised by highly-skewed distributions. An example of this, which is considered in this paper, is the number of visits to a specialist, often taken as a measure of demand in healthcare. A discrete Weibull regression model was recently proposed for regression problems with a discrete response and it was shown to possess desirable properties. In this paper, we propose the first Bayesian implementation of this model. We consider a general parametrization, where both parameters of the discrete Weibull distribution can be conditioned on the predictors, and show theoretically how, under a uniform non-informative prior, the posterior distribution is proper with finite moments. In addition, we consider closely the case of Laplace priors for parameter shrinkage and variable selection. Parameter estimates and their credible intervals can be readily calculated from their full posterior distribution. A simulation study and the analysis of four real datasets of medical records show promises for the wide applicability of this approach to the analysis of count data. The method is implemented in the R package BDWreg. [ABSTRACT FROM AUTHOR]

Adaptive designs for multi-armed clinical trials have become increasingly popular recently because of their potential to shorten development times and to increase patient response. However, developing response-adaptive designs that offer patient-benefit while ensuring the resulting trial provides a statistically rigorous and unbiased comparison of the different treatments included is highly challenging. In this paper, the theory of Multi-Armed Bandit Problems is used to define near optimal adaptive designs in the context of a clinical trial with a normally distributed endpoint with known variance. We report the operating characteristics (type I error, power, bias) and patient-benefit of these approaches and alternative designs using simulation studies based on an ongoing trial. These results are then compared to those recently published in the context of Bernoulli endpoints. Many limitations and advantages are similar in both cases but there are also important differences, specially with respect to type I error control. This paper proposes a simulation-based testing procedure to correct for the observed type I error inflation that bandit-based and adaptive rules can induce. [ABSTRACT FROM AUTHOR]

Dispersion indexes with respect to the Poisson and binomial distributions are widely used to assess the conformity of the underlying distribution from an observed sample of the count with one or the other of these theoretical distributions. Recently, the exponential variation index has been proposed as an extension to nonnegative continuous data. This paper aims to gather to study the unified definition of these indexes with respect to the relative variability of a nonnegative natural exponential family of distributions through its variance function. We establish the strong consistency of the plug-in estimators of the indexes as well as their asymptotic normalities. Since the exact distributions of the estimators are not available in closed form, we consider the test of hypothesis relying on these estimators as test statistics with their asymptotic distributions. Simulation studies globally suggest good behaviours of these tests of hypothesis procedures. Applicable examples are analysed, including the lesser-known references such as negative binomial and inverse Gaussian, and improving the very usual case of the Poisson dispersion index. Concluding remarks are made with suggestions of possible extensions. [ABSTRACT FROM AUTHOR]

Application of the exact statistical inference frequently leads to non-standard probability distributions of the considered estimators or test statistics. The exact distributions of many estimators and test statistics can be specified by their characteristic functions, as is the case for the null distribution of the Bartlett's test statistic. However, analytical inversion of the characteristic function, if possible, frequently leads to complicated expressions for computing the distribution function and the corresponding quantiles. An efficient alternative is the well-known method based on numerical inversion of the characteristic functions, which is, however, ignored in popular statistical software packages. In this paper, we present the explicit characteristic function of the corrected Bartlett's test statistic together with the computationally fast and efficient implementation of the approach based on numerical inversion of this characteristic function, suggested for evaluating the exact null distribution used for testing homogeneity of variances in several normal populations, with possibly unequal sample sizes. [ABSTRACT FROM AUTHOR]

Deciding on the best statistical method to apply when the response variable is ordinal is essential because the way the categories are ordered in the data is relevant as it could change the results of the analysis. Although the models for continuous variables have similarities to those for ordinal variables, this paper presents the advantages of the use of the ordering information on the outcomes with methods developed for modeling ordinal data such as the ordered stereotype model. The novelty of this article lies in showing the dangers of assigning equally spaced scores to ordered response categories in statistical analysis, which are illustrated with a simulation study and a case study. We propose a new way to use the score parameters, which incorporates the fitted spacing dictated by the data. Additionally, this article uses score parameter estimates in the ordered stereotype model to propose a new measure to calculate continuous medians in the raw data: the adjusted c-median. It benefits the general audience who can easily understand the median as a summary statistic. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

This paper introduces a new two-parameter exponentiated discrete Lindley distribution. A wide range of its structural properties are investigated. This includes the shape of the probability mass function, hazard rate function, moments, skewness, kurtosis, stress–strength reliability, mean residual lifetime, mean past lifetime, order statistics and L-moment statistics. The hazard rate function can be increasing, decreasing, decreasing–increasing–decreasing, increasing–decreasing–increasing, unimodal, bathtub, and J-shaped depending on its parameters values. Two methods are used herein to estimate the model parameters, namely, the maximum likelihood, and the proportion. A detailed simulation study is carried out to examine the bias and mean square error of maximum likelihood and proportion estimators. The flexibility of the proposed model is explained by using four distinctive data sets. It can serve as an alternative model to other lifetime distributions in the existing statistical literature for modeling positive real data in many areas. [ABSTRACT FROM AUTHOR]

Cluster analysis is one of the most widely used method in statistical analyses, in which homogeneous subgroups are identified in a heterogeneous population. Due to the existence of the continuous and discrete mixed data in many applications, so far, some ordinary clustering methods such as, hierarchical methods, k-means and model-based methods have been extended for analysis of mixed data. However, in the available model-based clustering methods, by increasing the number of continuous variables, the number of parameters increases and identifying as well as fitting an appropriate model may be difficult. In this paper, to reduce the number of the parameters, for the model-based clustering mixed data of continuous (normal) and nominal data, a set of parsimonious models is introduced. Models in this set are extended, using the general location model approach, for modeling distribution of mixed variables and applying factor analyzer structure for covariance matrices. The ECM algorithm is used for estimating the parameters of these models. In order to show the performance of the proposed models for clustering, results from some simulation studies and analyzing two real data sets are presented. [ABSTRACT FROM AUTHOR]

This paper considers the problem of making statistical inferences about a parameter when a narrow interval centred at a given value of the parameter is considered special, which is interpreted as meaning that there is a substantial degree of prior belief that the true value of the parameter lies in this interval. A clear justification of the practical importance of this problem is provided. The main difficulty with the standard Bayesian solution to this problem is discussed and, as a result, a pseudo-Bayesian solution is put forward based on determining lower limits for the posterior probability of the parameter lying in the special interval by means of a sensitivity analysis. Since it is not assumed that prior beliefs necessarily need to be expressed in terms of prior probabilities, nor that post-data probabilities must be Bayesian posterior probabilities, hybrid methods of inference are also proposed that are based on specific ways of measuring and interpreting the classical concept of significance. The various methods that are outlined are compared and contrasted at both a foundational level, and from a practical viewpoint by applying them to real data from meta-analyses that appeared in a well-known medical article. [ABSTRACT FROM AUTHOR]

The statistical modeling of big data bases constitutes one of the most challenging issues, especially nowadays. The issue is even more critical in case of a complicated correlation structure. Variable selection plays a vital role in statistical analysis of large data bases and many methods have been proposed so far to deal with the aforementioned problem. One of such methods is the Sure Independence Screening which has been introduced to reduce dimensionality to a relatively smaller scale. This method, though simple, produces remarkable results even under both ultra high dimensionality and big scale in terms of sample size problems. In this paper we dealt with the analysis of a big real medical data set assuming a Poisson regression model. We support the analysis by conducting simulated experiments taking into consideration the correlation structure of the design matrix. [ABSTRACT FROM AUTHOR]

Forecasting of future snow depths is useful for many applications like road safety, winter sport activities, avalanche risk assessment and hydrology. Motivated by the lack of statistical forecasts models for snow depth, in this paper we present a set of models to fill this gap. First, we present a model to do short-term forecasts when we assume that reliable weather forecasts of air temperature and precipitation are available. The covariates are included nonlinearly into the model following basic physical principles of snowfall, snow aging and melting. Due to the large set of observations with snow depth equal to zero, we use a zero-inflated gamma regression model, which is commonly used to similar applications like precipitation. We also do long-term forecasts of snow depth and much further than traditional weather forecasts for temperature and precipitation. The long-term forecasts are based on fitting models to historic time series of precipitation, temperature and snow depth. We fit the models to data from six locations in Norway with different climatic and vegetation properties. Forecasting five days into the future, the results showed that, given reliable weather forecasts of temperature and precipitation, the forecast errors in absolute value was between 3 and 7 cm for different locations in Norway. Forecasting three weeks into the future, the forecast errors were between 7 and 16 cm. [ABSTRACT FROM AUTHOR]

In this paper, we consider the notions of data depth for ordering multivariate data and propose a classification rule based on the distribution of some depth functions in . The equivalence of the proposed classification rule to optimal Bayes rule is discussed under suitable conditions. The performance of the proposed classification method is investigated in low- and high-dimensional setting using real datasets. Also, the performance of the proposed classification method is illustrated in comparison to some other depth-based classifiers using simulated data sets. [ABSTRACT FROM AUTHOR]

From the prediction viewpoint, mode regression is more attractive since it pay attention to the most probable value of response variable given regressors. On the other hand, high-dimensional data are very prevalent as the advance of the technology of collecting and storing data. Variable selection is an important strategy to deal with high-dimensional regression problem. This paper aims to propose a variable selection procedure for high-dimensional mode regression via combining nonparametric kernel estimation method with sparsity penalty tactics. We also establish the asymptotic properties under certain technical conditions. The effectiveness and flexibility of the proposed methods are further illustrated by numerical studies and the real data application. [ABSTRACT FROM AUTHOR]

In this paper, we propose a two-stage functional principal component analysis method in age-period-cohort (APC) analysis. The first stage of the method considers the age-period effect with the fitted values treated as an offset; and the second stage of the method considers the residual age-cohort effect conditional on the already estimated age-period effect. An APC version of the model in functional data analysis provides an improved fit to the data, especially when the data are sparse and irregularly spaced. We demonstrate the effectiveness of the proposed method using body mass index data stratified by gender and ethnicity. [ABSTRACT FROM AUTHOR]

A key challenge in rainfall estimation is spatio-temporal variablility. Weather radars are used to estimate precipitation with high spatial and temporal resolution. Due to the inherent errors in radar estimates, spatial interpolation has been often employed to calibrate the estimates. Kriging is a simple and popular spatial interpolation method, but the method has several shortcomings. In particular, the prediction is quite unstable and often fails to be performed when sample size is small. In this paper, we proposed a flexible and efficient spatial interpolator for radar rainfall estimation, with several advantages over kriging. The method is illustrated using a real-world data set. [ABSTRACT FROM AUTHOR]

Since the pioneering work by Koenker and Bassett [27], quantile regression models and its applications have become increasingly popular and important for research in many areas. In this paper, a random effects ordinal quantile regression model is proposed for analysis of longitudinal data with ordinal outcome of interest. An efficient Gibbs sampling algorithm was derived for fitting the model to the data based on a location-scale mixture representation of the skewed double-exponential distribution. The proposed approach is illustrated using simulated data and a real data example. This is the first work to discuss quantile regression for analysis of longitudinal data with ordinal outcome. [ABSTRACT FROM AUTHOR]

CD4 and viral load play important roles in HIV/AIDS studies, and the study of their relationship has received much attention with well-known results. However, AIDS datasets are often highly complex in the sense that they typically contain outliers, measurement errors, and missing data. These data complications can greatly affect statistical analysis results, but much of the literature fail to address these issues in data analysis. In this paper, we re-visit the important relationship between CD4 and viral load and propose methods which simultaneously address outliers, measurement errors, and missing data. We find that the strength of the relationship may be severely mis-estimated if measurement errors and outliers are ignored. The proposed methods are general and can be used in other settings, where jointly modelling several different types of longitudinal data is required in the presence of data complications. [ABSTRACT FROM PUBLISHER]

The standard regression model designed for real space is not suitable for compositional variables; it should be considered, whether the response and/or covariates are of compositional nature. There are usually three types of multiple regression model with compositional variables: Type 1 refers to the case where all the covariates are compositional data and the response is real; Type 2 is the opposite of Type 1; Type 3 relates to the model with compositional response and covariates. There have been some models for the three types. In this paper, we focus on Type 3 and propose multiple linear regression models including model in the simplex and model in isometric log-ratio (ilr) coordinates. The model in the simplex is based on matrix product, which can project a-part composition to another-part composition, and can deal with different number of parts of compositional variables. Some theorems are given to point out the relationship of parameters between the proposed models. Moreover, the inference for parameters in proposed models is also given. Real example is studied to verify the validity and usefulness of proposed models. [ABSTRACT FROM AUTHOR]

The von Mises distribution is widely used for modeling angular data. When such data are seen in a quality control setting, there may be interest in checking whether the values are in statistical control or have gone out of control. A cumulative sum (cusum) control chart has desirable properties for checking whether the distribution has changed from an in-control to an out-of-control setting. This paper develops cusums for a change in the mean direction and concentration of angular data and illustrates some of their properties. [ABSTRACT FROM AUTHOR]

Until now, various acceptance reliability sampling plans have been developed based on different life tests of items. However, the statistical effect of the acceptance sampling tests on the reliability characteristic of the lots accepted in the test has not been appropriately addressed. In this paper, we deal with an acceptance reliability sampling plan under a ‘general framework’ and discuss the corresponding statistical effect of the acceptance sampling tests. The lifetime of the population before the acceptance test and that of population ‘conditional on the acceptance’ in the sampling test are stochastically compared. The improvement of reliability characteristics of the population conditional on the acceptance in the sampling test is precisely analyzed. [ABSTRACT FROM AUTHOR]

Measurement error (ME) is the difference between the true unknown value of a variable and the data assigned to that variable during the measuring process. The multiple correlation coefficient quantifies the strength of the relationship between the dependent and independent variable(s) in regression modeling. In this paper, we show that ME in the dependent variable results in a negative bias in the multiple correlation coefficient, making the relationship appear weaker than it should. The adjusted R2 provides regression modelers an unbiased estimate of the multiple correlation coefficient. However, due to the ME induced bias in the multiple correlation coefficient, the otherwise unbiased adjusted R2 under-estimates the variance explained by a regression model. This paper proposes two statistics for estimating the multiple correlation coefficient, both of which take into account the ME in the dependent variable. The first statistic uses all unbiased estimators, but may produce values outside the [0,1] interval. The second statistic requires modeling a single data set, created by including descriptive variables on the subjects used in a gage study. Based on sums of squares, the statistic has the properties of an R2: it measures the proportion of variance explained; has values restricted to the [0,1] interval; and the endpoints indicate no variance explained and all variance explained respectively. We demonstrate the methodology using data from a study of cervical spine range of motion in children. [ABSTRACT FROM AUTHOR]

The first two stages in modelling times series are hypothesis testing and estimation. For long memory time series, the second stage was studied in the paper published in [M. Boutahar et al., Estimation methods of the long memory parameter: monte Carlo analysis and application, J. Appl. Statist. 34(3), pp. 261-301.] in which we have presented some estimation methods of the long memory parameter. The present paper is intended for the first stage, and hence completes the former, by exploring some tests for detecting long memory in time series. We consider two kinds of tests: the non-parametric class and the semi-parametric one. We precise the limiting distribution of the non-parametric tests under the null of short memory and we show that they are consistent against the alternative of long memory. We perform also some Monte Carlo simulations to analyse the size distortion and the power of all proposed tests. We conclude that for large sample size, the two classes are equivalent but for small sample size the non-parametric class is better than the semi-parametric one. [ABSTRACT FROM AUTHOR]

The aim of this paper is to provide some practical aspects of point and interval estimates of the global maximum of a function using extreme value theory. Consider a real-valued function f:D→ defined on a bounded interval D such that f is either not known analytically or is known analytically but has rather a complicated analytic form. We assume that f possesses a global maximum attained, say, at u*∈D with maximal value x*=max u f(u)≐f(u*). The problem of seeking the optimum of a function which is more or less unknown to the observer has resulted in the development of a large variety of search techniques. In this paper we use the extreme-value approach as appears in Dekkers et al. [A moment estimator for the index of an extreme-value distribution, Ann. Statist. 17 (1989), pp. 1833-1855] and de Haan [Estimation of the minimum of a function using order statistics, J. Amer. Statist. Assoc. 76 (1981), pp. 467-469]. We impose some Lipschitz conditions on the functions being investigated and through repeated simulation-based samplings, we provide various practical interpretations of the parameters involved as well as point and interval estimates for x*. [ABSTRACT FROM AUTHOR]

Surveys rely on structured questions used to map out reality, using sample observations from a population frame, into data that can be statistically analyzed. This paper focuses on the planning and design of surveys, making a distinction between individual surveys, household surveys and establishment surveys. Knowledge from cognitive science is used to provide guidelines on questionnaire design. Non-standard, but simple, statistical methods are described for analyzing survey results. The paper is based on experience gained by conducting over 150 customer satisfaction surveys in Europe, America and the Far East. [ABSTRACT FROM AUTHOR]

In this paper we use a penalized likelihood approach to image warping in the context of discrimination and averaging. The choice of average image is formulated statistically by minimizing a penalized likelihood, where the likelihood measures the similarity between images after warping and the penalty is a measure of distortion of a warping. The notions of measures of similarity are given in terms of normalized image information. The measures of distortion are landmark based. Thus we use a combination of landmark and normalized image information. The average defined in the paper is also extended by allowing random perturbation of the landmarks. This strategy improves averages for discrimination purposes. We give here real applications from medical and biological areas. [ABSTRACT FROM AUTHOR]

Consider the regression model . In a variety of situations, an estimate of VAR ( Y | X )?=?? ( X ) is needed. The paper compares the small-sample accuracy of five estimators of ? ( X ). The results suggest that the optimal estimator is a somewhat complex function of the underlying distributions. In terms of mean squared error, one of the estimators, which is based in part on a non-robust version of Cleveland's smoother, performed about as well as a bagged version of the so-called running interval smoother, but the running interval smoother was found to be preferable in terms of bias. A modification of Cleveland's smoother, stemming from Ruppert et al. (1997), achieves its intended goal of reducing bias when the error term is homoscedastic, but under heteroscedasticity, bias can be high, and in terms of mean squared error it does not compete well with the kernel method considered in the paper. When ? has a heavy-tailed distribution, a robust version of Cleveland's smoother performed particularly well except in some situations where X has a heavy-tailed distribution as well. A negative feature of using Cleveland's robust smoother is relatively high bias, and when there is heteroscedasticity and X has a heavy-tailed distribution, a kernel-type method and the running interval smoother give superior results in terms of both mean squared error and bias. [ABSTRACT FROM AUTHOR]

The propensity for military service (PMS) of young Americans is an important issue for our Armed Forces. Since the 1990s, the PMS of young Americans has steadily declined. Overtime, a declining PMS may cause military mission degradation, lowering of military recruitment standards, base closures, and reinstatement of the unpopular military draft system. This paper investigates the moderator effect of prior military service on the Generalized Exchange–PMS relationship. Generalized exchange is when indirect benefits such as preserving freedom and the American way of life accrue to the larger society because of an individual's military service. This paper uses a structural equation modelling approach to analyse the moderating effect of prior military exposure on prospective recruits regarding their PMS. Findings indicate that the group of prospective recruits with prior military exposure had higher levels of PMS than the group without such exposure, that is, the young people with prior military exposure are more likely to enlist in the military than the young Americans with no prior military exposure. [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]

Johnson (1992) developed the process loss index Le , which is defined as the ratio of the expected quadratic loss to the square of half specification width. Tsui (1997) expressed the index L e as Le = L pe+ L ot , which provides an uncontaminated separation between information concerning the potential relative expected loss ( L pe ) and the relative off-target squared ( Lot), as the ratio of the process variance and the square of the half specification width, and the square of the ratio of the deviation of mean from the target and the half specification width, respectively. In this paper, we consider these three loss function indices, and investigate the statistical properties of their natural estimators. For the three indices, we obtain their UMVUEs and MLEs, and compare the reliability of the two estimators based on the relative mean squared errors. In addition, we construct 90%, 95%, and 99% upper confidence limits, and the maximum values of L^ e for which the process is capable, 90%, 95%, and 99% of the time. The results obtained in this paper are useful to the practitioners in choosing good estimators and making reliable decisions on judging process capability. [ABSTRACT FROM AUTHOR]

Modern statistical data analysis is predominantly model-driven, seeking to decompose an observed data distribution in terms of major underlying descriptive features modified by some stochastic variation. A large part of data mining is also concerned with this exercise. However, another fundamental part of data mining is concerned with detecting anomalies amongst the vast mass of the data: the small deviations, unusual observations, unexpected clusters of observations, or surprising blips in the data, which the model does not explain. We call such anomalies patterns. For sound reasons, which are outlined in the paper, the data mining community has tended to focus on the algorithmic aspects of pattern discovery, and has not developed any general underlying theoretical base. However, such a base is important for any technology: it helps to steer the direction in which the technology develops, as well as serving to provide a basis from which algorithms can be compared, and to indicate which problems are the important ones waiting to be solved. This paper attempts to provide such a theoretical base, linking the ideas to statistical work in spatial epidemiology, scan statistics, outlier detection, and other areas. One of the striking characteristics of work on pattern discovery is that the ideas have been developed in several theoretical arenas, and also in several application domains, with little apparent awareness of the fundamentally common nature of the problem. Like model building, pattern discovery is fundamentally an inferential activity, and is an area in which statisticians can make very significant contributions. [ABSTRACT FROM AUTHOR]

In this paper, a model has been developed for the x-chart showing the shifts in the process mean and R-chart showing those in the process variability. The model involves such parameters as the sample size, n, the sampling frequency, h, and the range of the control limits, k1 and k2 minimizing the cost function. This is adequate to reach the economic objectives. However, this paper is aimed at meeting the statistical objectives. The statistical objectives include minimizing the Type I error and the enhancing the testing power. Hence, the economic model has been handled as a multi-objective optimization problem involving the statistical objectives. Nonetheless, due to the fact that it is difficult, using classical methods, to solve such economic models that have the nature of a complex function, Genetic Algorithms (GAs) were used. The results are summarized in tables after they have been compared with those in the published literature. It is understood that the results obtained by GA are better than those in the literature and that they are more likely to reach the statistical objectives [ABSTRACT FROM AUTHOR]

In this paper, we are employing the generalized linear model (GLM) in the form lij=χλ to decompose the symmetry model into the class of models discussed in Tomizawa (1992). In this formulation, the random component would be the observed counts fij with an underlying Poisson distribution. This approach utilizes the non-standard log-linear model and our focus in this paper therefore relates to models that are decompositions of the complete symmetry model. That is, models that are implied by the symmetry models. We develop factor and regression variables required for the implementation of these models in SAS PROC GENMOD and SPSS PROC GENLOG. We apply this methodology to analyse the three 4 × 4 contingency table, one of which is the Japanese Unaided distance vision data. Results obtained in this study are consistent with those from the numerous literature on the subject. We further extend our applications to the 6 × 6 Brazilian social mobility data. We found that both the quasi linear diagonal-parameters symmetry (QLDPS) and the quasi 2-ratios parameter symmetry (Q2RPS) models fit the Brazilian data very well. Parsimonious models being the QLDPS and the quasi-conditional symmetry (QCS) models. The SAS and SPSS programs for implementing the models discussed in this paper are presented in Appendices A, B and C. [ABSTRACT FROM AUTHOR]

This paper deals with the well-studied problem of how best to estimate the number of mutually exclusive and exhaustive classes in a population, based on a sample from it. Haas & Stokes review and provide non-parametric approaches, but there are associated difficulties especially for small sampling fractions and/or widely varying population class sizes. Sichel provided 'GIGP' methodology, for this problem and for other purposes; this paper utilizes the three-parameter GIGP distribution for this problem, and also for the estimation of the number of classes of size 1, as an alternative to the non-parametric approaches. Methodological and computational issues are considered, and examples indicate the potential for GIGP. [ABSTRACT FROM AUTHOR]

A relatively newer computational technique adopted by statisticians is known as independent component analysis (ICA) which is used to analyze complex multidimensional data with the objective to separate it into components that are independent to each other. Quite often the main interest for conducting ICA is to identify a small number of significant independent components (ICs) to replace the original complex dimensions with. For this, determining the order of identified ICs is a pre-requisite. The area is not unaddressed but it does deserve a careful revisiting. This is the subject matter of the paper which introduces a new method to order ICs. The proposed method is based upon regression approach. It compares the magnitude of the mixing coefficients and regression coefficients of the regression of the original series on ICs. Their compatibility determines the order. [ABSTRACT FROM PUBLISHER]

The present paper focuses on examining students' attitudes and perception of statistics in Afghanistan universities and the factor structure of the statistical anxiety rating scale (STARS). In total, 209 undergraduate students from different disciplines in different universities in Afghanistan participated in the study. In addition to testing the factor structure of the STARS, a multivariate multilevel analysis that incorporates the correlation in the data was carried out on the aggregated subscales of the STARS scores. Results showed that the original 6-factor structure did not fit the Afghanistan data well. Exploratory factor analysis identified 5-factor constructs to best fit the data and was confirmed by the fit indices as well as a likelihood ratio test. Male students showed more positive attitudes toward statistics and a higher level of statistics anxiety than their female counterparts. Female students experienced higher levels of fear of asking for help and less anxiety in computation. Students who had taken at least a previous statistics course had lower statistics anxiety than those taking the course for the first time. [ABSTRACT FROM PUBLISHER]

In many practical situations, a statistical practitioner often faces a problem of classifying an object from one of the segmented (or screened) populations where the segmentation was conducted by a set of screening variables. This paper addresses this problem, proposing and studying yet another optimal rule for classification with segmented populations. A class ofq-dimensional rectangle-screened elliptically contoured (RSEC) distributions is considered for flexibly modeling the segmented populations. Based on the properties of the RSEC distributions, a parametric procedure for the segmented classification analysis (SCA) is proposed. This includes motivation for the SCA as well as some theoretical propositions regarding its optimal rule and properties. These properties allow us to establish other important results which include an efficient estimation of the rule by the Monte Carlo expectation–conditional maximization algorithm and an optimal variable selection procedure. Two numerical examples making use of utilizing a simulation study and a real dataset application and advocating the SCA procedure are also provided. [ABSTRACT FROM PUBLISHER]

Data from longitudinal studies in which an initiating event and a subsequent event occur in sequence are called 'doubly censored' data if the time of both events is interval-censored. This paper is concerned with using doubly censored data to estimate the distribution function of the so-called 'duration time', i.e. the elapsed time between the originating event and the subsequent event. The paper proposes a generalization of the Gomez and Lagakos two-step method for the case where both the time to the initiating event and the duration time are continuous. This approach is applied to estimate the AIDS-latency time from a haemophiliacs cohort. [ABSTRACT FROM AUTHOR]

SUMMARY In long-term field trials comparing different sequences of crops and husbandry practices, the identification and understanding of trends in productivity over time is an important issue of sustainable crop production. This paper presents a statistical technique for the estimation of time trends in yield variables of a seasonal annual crop under continuous cropping. The estimation procedure incorporates the correlation structure, which is assumed to follow first-order autocorrelation in the errors that arise over time on the same plot. Because large differences in annual rainfall have a major effect on crop performance, rainfall has been allowed for in the estimation of the time trends. Expressions for the number of years (time) required to detect statistically significant time trends have been obtained. Illustrations are based on a 7-year data set of grain and straw yields from a trial in northern Syria. Although agronomic interpretation is not intended in this paper, the barley yield data indicated that a significant time trend can apparently be detected even in a suboptimal data set of 7 years' duration. [ABSTRACT FROM AUTHOR]

Inverse sampling is widely applied in studies with dichotomous outcomes, especially when the subjects arrive sequentially or the response of interest is difficult to obtain. In this paper, we investigate the rate ratio test problem under inverse sampling based on gradient statistic with the asymptotic method and parametric bootstrap technique. The gradient statistic has many advantages, for example, it is simple to calculate and competitive with Wald-type, score and likelihood ratio tests in terms of local power. Numerical studies are carried out to evaluate the performance of our gradient test and the existing tests, namely Wald-type, score and likelihood ratio tests. The simulation results suggest that the gradient test based on the parametric bootstrap method has excellent type I error control and large powers even in small sample design. Two real examples, from a heart disease study and a drug comparison study, are applied to illustrate our methods. [ABSTRACT FROM AUTHOR]

The first step in statistical analysis is the parameter estimation. In multivariate analysis, one of the parameters of interest to be estimated is the mean vector. In multivariate statistical analysis, it is usually assumed that the data come from a multivariate normal distribution. In this situation, the maximum likelihood estimator (MLE), that is, the sample mean vector, is the best estimator. However, when outliers exist in the data, the use of sample mean vector will result in poor estimation. So, other estimators which are robust to the existence of outliers should be used. The most popular robust multivariate estimator for estimating the mean vector is S-estimator with desirable properties. However, computing this estimator requires the use of a robust estimate of mean vector as a starting point. Usually minimum volume ellipsoid (MVE) is used as a starting point in computing S-estimator. For high-dimensional data computing, the MVE takes too much time. In some cases, this time is so large that the existing computers cannot perform the computation. In addition to the computation time, for high-dimensional data set the MVE method is not precise. In this paper, a robust starting point for S-estimator based on robust clustering is proposed which could be used for estimating the mean vector of the high-dimensional data. The performance of the proposed estimator in the presence of outliers is studied and the results indicate that the proposed estimator performs precisely and much better than some of the existing robust estimators for high-dimensional data. [ABSTRACT FROM PUBLISHER]

Estimation of the lifetime distribution of industrial components and systems yields very important information for manufacturers and consumers. However, obtaining reliability data is time consuming and costly. In this context, degradation tests are a useful alternative approach to lifetime and accelerated life tests in reliability studies. The approximate method is one of the most used techniques for degradation data analysis. It is very simple to understand and easy to implement numerically in any statistical software package. This paper uses time series techniques in order to propose a modified approximate method (MAM). The MAM improves the standard one in two aspects: (1) it uses previous observations in the degradation path as a Markov process for future prediction and (2) it is not necessary to specify a parametric form for the degradation path. Characteristics of interest such as mean or median time to failure and percentiles, among others, are obtained by using the modified method. A simulation study is performed in order to show the improved properties of the modified method over the standard one. Both methods are also used to estimate the failure time distribution of the fatigue-crack-growth data set. [ABSTRACT FROM PUBLISHER]

In this paper, we consider statistical diagnostic for non-parametric regression models with right-censored data based on empirical likelihood. First, the primary model is transformed to the non-parametric regression model. Then, based on empirical likelihood methodology, we define some diagnostic statistics. At last, some simulation studies show that our proposed procedure can work fairly well. [ABSTRACT FROM PUBLISHER]

The traditional standardized mortality ratio (SMR) compares the mortality rate of a study population with that of a reference population. In order to measure the performance of a surgeon or a group of surgeons in a hospital performing a particular type of surgical operation, a different SMR is used. This SMR compares the observed number of deaths in a sample with an estimated number of deaths usually calculated based on the average performance of a group of surgeons. The estimated number of deaths involved in the new SMR is not a constant but a random variable. This means that all existing results for the traditional SMR may no longer be valid for the new SMR. In this paper, the asymptotic distribution of the SMR based on an estimated number of deaths is derived. We also use the bootstrap procedure to estimate the finite-sample distribution. A simulation study is used to compare both probabilities of type I error and powers of existing confidence intervals and confidence intervals constructed using the asymptotic and bootstrap distributions of SMR. Our study reveals that, in general, existing confidence intervals are conservative in terms of probability of type I error, and the two new confidence intervals are more accurate. To perform a fair power comparison, the coverage probabilities of existing confidence intervals are recalibrated to match that based on the asymptotic distribution of SMR, and then our study shows that the powers of the asymptotic and bootstrap approaches are lower than existing approaches when the odds ratio of deathQis greater than the odds ratio of death under the null hypothesis,, but higher whenQis smaller than. The effect of patients' risk distribution on the SMR is also investigated. [ABSTRACT FROM PUBLISHER]

In recent years, there has been considerable interest in regression models based on zero-inflated distributions. These models are commonly encountered in many disciplines, such as medicine, public health, and environmental sciences, among others. The zero-inflated Poisson (ZIP) model has been typically considered for these types of problems. However, the ZIP model can fail if the non-zero counts are overdispersed in relation to the Poisson distribution, hence the zero-inflated negative binomial (ZINB) model may be more appropriate. In this paper, we present a Bayesian approach for fitting the ZINB regression model. This model considers that an observed zero may come from a point mass distribution at zero or from the negative binomial model. The likelihood function is utilized to compute not only some Bayesian model selection measures, but also to develop Bayesian case-deletion influence diagnostics based onq-divergence measures. The approach can be easily implemented using standard Bayesian software, such as WinBUGS. The performance of the proposed method is evaluated with a simulation study. Further, a real data set is analyzed, where we show that ZINB regression models seems to fit the data better than the Poisson counterpart. [ABSTRACT FROM PUBLISHER]

Ipsilateral breast tumor relapse (IBTR) often occurs in breast cancer patients after their breast conservation therapy. The IBTR status' classification (true local recurrence versus new ipsilateral primary tumor) is subject to error and there is no widely accepted gold standard. Time to IBTR is likely informative for IBTR classification because new primary tumor tends to have a longer mean time to IBTR and is associated with improved survival as compared with the true local recurrence tumor. Moreover, some patients may die from breast cancer or other causes in a competing risk scenario during the follow-up period. Because the time to death can be correlated to the unobserved true IBTR status and time to IBTR (if relapse occurs), this terminal mechanism is non-ignorable. In this paper, we propose a unified framework that addresses these issues simultaneously by modeling the misclassified binary outcome without a gold standard and the correlated time to IBTR, subject to dependent competing terminal events. We evaluate the proposed framework by a simulation study and apply it to a real data set consisting of 4477 breast cancer patients. The adaptive Gaussian quadrature tools inSASprocedureNLMIXEDcan be conveniently used to fit the proposed model. We expect to see broad applications of our model in other studies with a similar data structure. [ABSTRACT FROM AUTHOR]