bluuebunny/crossref_metadata_2025_split huggingface dataset:
Cluster Analysis of Subjects, Hierarchical Methods
Authors: Everitt Brian S. 
Published: July 2005

AbstractHierarchical cluster classification involves partitioning data into a series of groups. The first group consists ofnsingle‐member “clusters”, the last consists of a single group with allnindividuals. Hierarchical cluster classification could be represented by a diagram known as a dendrogram. Properties and problems of hierarchical clustering techniques are described. The two major types of algorithms that have been used to produce hierarchical classifications are agglomerative and divisive. Careful validation of solutions is a clear requirement in any clustering exercise. An example to illustrate hierarchical methods is presented.
Cluster Analysis of Subjects, Nonhierarchical Methods
Authors: Everitt Brian S. 
Published: July 2005

Abstract
Cluster analysis is concerned with investigating whether or not a given set of data consists of relatively distinct groups of observations. The cluster analysis methods produce a partition of individuals into a particular number of groups and a numerical index is assigned to the partition. This index indicates how successful the partition is in describing the data and therefore allows the comparison of competing partitions.
The numerical indices most commonly used arise from three matrices representing total dispersion, within‐group dispersion and between‐group dispersion. Several possible indices have been suggested which differ in the implicit assumptions made about the shape of any clusters present. Once the index has been selected, the partition that leads to its optimization is found. It is usually impractical to examine each individual partition, so algorithms designed to search for the optimum value of the clustering criterion have been developed.
Clustering, Complete Linkage
Authors: Massaro Joseph M. 
Published: July 2005

Abstract

Complete linkage clustering is used in hierarchical cluster analysis to partition a set of
n
observations into
g
groups or clusters on the basis of p variables measured on the
n
observations. The analysis is performed on an
n
×
n
matrix of pairwise distance measures between observations. The procedure starts by combining the two observations with the smallest distance between them. The procedure continues to combine clusters with the smallest distances until only one cluster, including the entire sample, remains. The number of groups,
g
, is determined to represent the final number of clusters to retain.
Covariance Matrix
Authors: Krzanowski W. J. 
Published: July 2005

Abstract
Inferential aspects of the sample covariance matrix are presented. A maximum likelihood estimator that is based on a frequentist approach as well as the other two estimators that are based on decision theoretic and Bayesian approaches are summarized. Inference is appropriate when sampling from a multivariate normal distribution. Elliptic distributions that encompass distributions other than normal distribution are described. The asymptotic distribution of the maximum likelihood statistic and its associated hypothesis tests are fully explained.
Discriminant Analysis, Linear
Authors: Hand David J. 
Published: July 2005

AbstractGiven a set of objects, each with a descriptive vector of measured variables, and each belonging to one of a finite set of classes, linear discriminant analysis is a tool for finding those linear combinations of the measured variables on which the classes are most separated. There are two main uses: using the linear combinations to predict the class membership of a new object for which only the vector of variables has been observed, and studying the vector of variables to characterize the nature of the differences between the classes. The method is based on the first and second moments of the multivariate distribution of the measured variables, and assumes that the covariance matrices of the different classes are the same. However, it is robust and can often be usefully applied in other situations. Many generalizations and extensions have been developed, and linear discriminant analysis continues to be widely used.
Factor Scores
Authors: D'AGOSTINO Ralph B. , Russell Heidy K. 
Published: July 2005

Abstract
After a set of interpretable factor loadings is determined, a next possible step is to compute factor scores. Exact factor scores can be obtained for a principal components analysis model. Methods that compute factor scores in the common factor analysis model are also presented. In general, there is limited value in the use of factor scores, for even though the factors are interpretable, the estimated factor scores are not well determined.
G
ram–
S
chmidt Process
Authors: Dukes Kimberly A. 
Published: July 2005

Abstract

The Gram–Schmidt process is a technique for constructing an orthogonal basis from a basis spanning the same subspace. The technique is used in a number of multivariate applications including battery reduction analyses and multiple regression applications. In the former, the goal is to reduce the number of variables at the same time explaining as much variance in the original variables as possible. In the latter, the goal is to reduce the
n
‐dimensional space (observations) to a
p
‐dimensional space (independent variables).
Lambda Criterion, Wilks'
Authors: Dasgupta Somesh 
Published: July 2005

AbstractWilk's Λ criterion is used to test the equality of the mean vectors ofkp‐variate normal distributions. The distribution of the test statistic can be expressed as a function of several independent beta distributions. The power function of this test is compared with the Lawley–Hotelling trace and Philbi's trace test for MANOVA.
Multivariate Analysis of Variance
Authors: Morrison Donald F. 
Published: July 2005

AbstractThe multivariate analysis of variance (MANOVA) is an extension of the univariate analysis of variance to multidimensional, or vector‐valued, observations. The same experimental design or treatment layout applies to each of the observed response variables. The univariate assumption of a normal distribution is replaced by the multivariate normal distribution for the data vectors and the random error components in the mathematical model of the design.
Multivariate Analysis,Bayesian
Authors: Press S. James 
Published: July 2005

AbstractMultivariate Bayesian Analysis uses Bayes' Theorem to make inferences about several generally correlated unknown quantities. This article explains the multivariate version of Bayes' Theorem. It explains the use of multidimensional credibility regions, hypothesis testing involving multidimensional unknown quantities, multivariate prior distributions: both multivariate vague and natural conjugate prior distributions, multivariate mixture prior distributions, exchangeability, multivariate numerical methods such as Markov Chain Monte Carlo methods, and computer‐assisted multivariate inference. There are references to some biostatistical multivariate Bayesian applications.
Multivariate Analysis, Overview
Authors: Morrison Donald F. 
Published: July 2005

AbstractThe article contains a survey of statistical methods based on the multivariate normal distribution. These include the estimators of the mean vector and covariance matrix and their distributions, hypothesis tests for the mean vector, the multivariate generalization of the analysis of variance and the general linear model, classification and discriminant functions, inferences about covariance matrices, principal components analysis, and factor analysis.
Multivariate Median and Rank Sum Tests
Authors: Sen Pranab K. 
Published: July 2005

AbstractUnivariate nonparametric procedures are extended to multivariate nonparametric procedures via the rank‐permutation principle. Univariate nonparametric procedures, such as the Wilcoxon signed‐rank test and ANCOVA, are reviewed. From this, expansion to the multivariate case is shown through emphasis on the rank‐permutation principle. This principle, based on the assets of a conditional procedure that renders conditionally distribution‐free properties, is applied to the multivariate case and allows for distribution‐freeness of a large class of rank statistics, such as the median and rank sum tests. This then carries into the development of multivariate multisample median tests and multivariate rank sum tests, such as the multivariate signed‐rank test. Furthermore, application of the principle is also used in the development of rank MANCOVA, the multivariate extension of ANCOVA.
MultivariateWeibull Distribution
Authors: Jensen D. R. 
Published: July 2005

AbstractThe univariate Weibull distribution is frequently used in accelerated life testing and failure time models. It reduces to the exponential distribution when the shape parameter is equal to one. Multivariate Weibull distributions encompass distributions exhibiting Weibull characteristics and relate to multivariate exponential distributions of various types. Applications include reliability analysis, survival analysis, and repeated failure time analysis.
Principal Components Analysis
Authors: D'agostino Ralph B. 
Published: July 2005

AbstractPrincipal components analysis is a method for transforming a set ofncorrelated variables intom(<n) uncorrelated variables. This article provides a comprehensive summary of the technique, including its mathematical derivation and the various techniques that are employed for determining the number of factors to retain, for rotation and for development of component scores. The article illustrates the application of the technique with a comprehensive example from the Framingham Heart Study. The article also outlines the many applications of principal components analysis in a variety of fields.
Data Mining, Software Packages for
Authors: Haughton Dominique 
Published: July 2005

Abstract

The term
data mining
refers to the identification—within a typically large database—of new, valid, and interesting patterns. While data mining has become most popular in the context of, for example, database marketing, most of the methods under the data mining umbrella have been widely applied in biostatistics. We describe which main applications of data mining have arisen recently in biostatistics, and introduce the reader to some of the available data mining software packages with a reference to biostatistical needs.
Computer Algebra
Authors: Kendall Wilfrid S. 
Published: July 2005

AbstractThis article begins by presenting basic common features, and by listing and giving references for current commercial computer algebra packages. There follow two simple introductory examples of the use of computer algebra in statistical contexts, and then a discussion of some typical constraints and features of computer algebra systems: it is important to be aware of these, since in this area, unrealistic expectations lead all too rapidly to frustration and disappointment. Finally, we list a few representative examples of research uses of computer algebra in statistical science, and conclude with suggestions for further reading.
Computer‐Intensive Methods
Authors: Ripley B. D. 
Published: July 2005

AbstractOne sense of “computer‐intensive” statistics is just statistical methodology that makes use of a large amount of computer time. (Examples include the bootstrap, jackknife, smoothing, image analysis, and many uses of the EM algorithm.) However, the term is usually used for methods that go beyond the minimum of calculations needed for an illuminating analysis, for example, by replacing analytic approximations by computational ones, or requiring numeric optimization or integration over high‐dimensional spaces. We introduce the subject with a very simple yet useful example, and then consider some of the areas in which computer‐intensive methods are used, to give a flavor of current research.
Optimization and Nonlinear Equations
Authors: Smyth Gordon K. 
Published: July 2005

Abstract
Optimization means finding that argument which minimizes or maximizes a given function such as a likelihood function or a sum of squares. Many optimization algorithms are derived from algorithms that solve the nonlinear equations defined by setting the derivative of the objective function equal to zero. This article discusses a number of methods for unconstrained optimization, including bisection and golden search in the univariate case and Newton's method and quasi‐Newton algorithms in the multivariate case. Applications to maximum likelihood estimation, Fisher's method of scoring, nonlinear regression, and generalized linear models are described. Restricted step modifications are discussed for preventing divergence of Newton‐type algorithms. A number of derivative‐free methods are discussed, including the Nelder–Mead simplex method, methods with numeric derivatives, conjugate methods, and the EM algorithm.
Support Vector Machines
Authors: Schölkopf Bernhard , Smola Alex 
Published: July 2005

AbstractWe describe the central ideas of Support Vector (SV) learning in a nutshell. This includes the notion of learning from data via risk minimization and the notion of kernels as an efficient means of encoding prior information. We give an overview over the optimization problems arising from SV classification and discuss various extensions such as kernel PCA and automatic margin adaptation.
Asymptotic Relative Efficiency (ARE)
Authors: Dasgupta Anirban 
Published: July 2005

AbstractThe efficiencies of two consistent estimators of a parameter may be compared by the ratio of their asymptotic variances. Alternative measures are the Pitman and Bahadur measures, which relate to the ratio of sample sizes needed to achieve equivalent asymptotic power. Topics examined are the relevance for finite samples, sensitivity to the underlying distribution, higher‐order efficiency (to compare different fully efficient estimators), and efficiency estimation in complex models.
Bayesian Methods
Authors: Dempster A. P. 
Published: July 2005

AbstractBayesian methods are used in the analysis of statistical data to provide posterior (postdata) probabilities for hypotheses. These are calculated, by Bayes' theorem, from prior (predata) probabilities and the likelihood function obtained from the observed data. Probabilities may be “objective” or “subjective”, representing degrees of belief. The history of this approach is surveyed. It fell out of fashion during the first half of the twentieth century, under the influences of the different frequentist approaches of Fisher and Neyman, but interest was maintained by the work of Jeffreys and de Finetti and revived in the mid‐1950s through the work of Savage and others. The article discusses problems arising in contemporary work, such as the involvement of many parameters, aspects of modeling, and availability of computing methods, and summarizes arguments for and against Bayesian methods.
Behrens–Fisher Problem
Authors: Cook Richard J. , Farewell Vern T. 
Published: July 2005

AbstractThe problem of testing for a difference between two normal means when no assumptions are made about the variances of the distributions, commonly known as the Behrens–Fisher problem, is presented. The properties of competing solutions to this problem are discussed. Inference when the variance ratio is fixed is outlined and the value of explicit consideration of the robustness of inferences as the variance ratio varies is explored.
Central Limit Theory
Authors: Nolan Deborah 
Published: July 2005

Abstract
The sum of a large number of none too large independent random variables is approximately normally distributed. This important result enables the normal distribution to be used in a wide range of approximately valid procedures. The history of the central limit theorem is outlined, and various versions for different conditions on the random variables are described. Topics discussed include rates of convergence, a functional central limit theorem, results for dependent random variables, and stable laws for convergence to nonnormal distributions.
Characteristic Function
Authors: Koehler Kenneth 
Published: July 2005

Abstract
The characteristic function is a complex‐valued transform of the distribution function of a random variable, closely related to the moment generating function. It may be used to derive distributions of sums and other linear functions of independent random variables, to determine limiting distributions in large samples, and to derive moments. Its natural logarithm is the cumulant generating function. Various results are illustrated in terms of the binomial distribution.
Conditional Probability
Authors: Hill B. 
Published: July 2005

Abstract
Both the Bayesian and frequentist approaches to conditional probability are presented. The undesirable consequences of using any statistical decision procedure that is not directly based upon conditional probability are discussed. These include sure loss as in the coherency theory of de Finetti; and the uniform improvement in risk of any non‐Bayes statistical decision procedure by a computable Bayesian decision procedure. By means of the evaluation game, it is then shown how the latter translates into extremely poor performance for such a non‐Bayes procedure in repeated applications such as arise in the frequentist theory. A version of these results is then presented for prediction. In all such applications, any non‐Bayes decision procedure in common use can be replaced by a uniformly better Bayes procedure using simple linear programming methods. Finally, issues regarding finite versus infinite partitions and the countably additive approach of Kolmogorov are discussed.
Consistent Estimator
Authors: Liang Kung‐Yee , Rathouz P. J. 
Published: July 2005

AbstractAn estimator of a statistical parameter is consistent if it converges in probability to the parameter as the sample size increases. Two methods of obtaining consistent estimators are described by minimizing a specific function of the data and the parameter (e.g. maximum likelihood,M‐estimation, weighted least squares), or by solving an equation involving an estimating function (e.g. quasi‐likelihood).
EmpiricalBayes
Authors: Morris Carl N. , Christiansen Cindy L. 
Published: July 2005

AbstractWhen certain estimation situations are encountered many times, the data from all these situations can be used to construct estimates for each individual case. This overview shows how empirical Bayes has evolved and expanded since its 1955 origins in order to useful practical procedures, which are good not only asymptotically but also in moderately sized samples. Various distributional models are described, as is an application to gene expression data.
Experiment‐Wise Error Rate
Authors: Iglewicz Boris 
Published: July 2005

Abstract

Multiple comparisons are frequently performed in medical experiments. These occur when dealing with multiple treatments, multiple endpoints, multiple subgroups, or multiple looks. Use of the nominal significance level for each comparison results in an inflated overall type I error rate, called the
experiment‐wise error rate
. Approaches for controlling this error rate are discussed and a number of references are provided.
Exploratory Data Analysis
Authors: Hoaglin David C. 
Published: July 2005

Abstract
Exploratory data analysis describes the attitude, approach, and techniques for flexible probing of data associated particularly with John W. Tukey. Four main themes are resistance to misbehavior in data, the importance of examining residuals, re‐expression of data in a more useful scale, and graphical displays. An example illustrates these and other points.
K
olmogorov–
S
mirnov Test
Authors: Wilcox R. 
Published: July 2005

Abstract
This is a distribution‐free method for comparing two empirical distributions, based on the largest vertical distance between the two cumulative distribution functions. The Kolmogorov test is a special case where one distribution function is known, and hence is a test of goodness‐of‐fit. Various properties, including power, are discussed.
Likelihood Ratio Tests
Authors: Birkes D. 
Published: July 2005

AbstractThe likelihood ratio test is a widely used procedure for testing hypotheses. It rejects the null hypothesis when the maximum likelihood under the null hypothesis is significantly smaller than the maximum likelihood under the alternative hypothesis. In some situations, itsPvalue can be calculated exactly, but, in general, thePvalue must be approximated, usually by using a chi‐square table. Three examples are presented. Methods have been, and continue to be, developed for improving the approximation.
Nonparametric Methods
Authors: Wolfe Douglas A. 
Published: July 2005

AbstractThe motivation behind distribution‐free hypothesis tests and confidence intervals based on signs and ranks is discussed and standard text references are provided. Distribution‐free test and confidence interval procedures for the one‐sample, two‐sample, one‐way analysis of variance, two‐way analysis of variance, and independence settings are presented. Point estimation techniques, including Hodges–Lehmann estimators and contrast estimation, and multiple comparisons procedures are described. Basic references for censored data approaches and bootstrapping are provided.
Ordered Alternatives
Authors: Lee Y. J. 
Published: July 2005

AbstractOrdered alternatives occur naturally in many experimental and observational studies. The dose‐response study is a typical one. The age‐related response is another one. Tendency to lie may increase with the age. The more the alcohol that is consumed during the pregnancy the higher is the risk of congenital malformation. There are numerous other examples of this nature. The independent variable that induces ordered response could be quantitative or ordinal (ordered categorical). The response variable observed for the ordered alternatives can be continuous counts, ordinal, dichotomous (success or failure), or even multinomial. Data may be collected in blocks or per dose group. Methods appropriate for dichotomous outcomes, Poisson counts, multinomial outcomes, and nonparametric data are reviewed. A reference for nonparametric methods appropriate for blocked data with missing observations is also given but not reviewed.
P

Value
Authors: Goodman Steven N. 
Published: July 2005

Abstract

The
P
value is the probability, under a given simple hypothesis, of the observed or a more extreme value of a test statistic. Problems discussed include that of the choice of test statistic, the relevance of alternative hypotheses, ambiguity about the sample space, and the interpretation generally. The distinction between one‐sided and two‐sided tests is a source of confusion. Bayesian considerations are discussed.
Pairwise Independence
Authors: Wermuth Nanny 
Published: July 2005

AbstractIf two explanatory variables are independent, with additive effects on a third, response, variable, then the overall effect of one explanatory variable is qualitatively the same as the effect conditional on the other explanatory variable. If the explanatory variables are dependent, reversal can occur. In multivariate analysis, pairwise independence of all variables does not imply mutual independence.
Penalized Maximum Likelihood
Authors: Simonoff Jeffrey S. 
Published: July 2005

AbstractNonparametric density estimation methods are designed to estimate the density functionfthat generates a sample of observations, without assuming a parametric form forf. Rather,fis only assumed to be smooth, where smoothness is defined as the condition that at least a specified number of derivatives are square integrable. Penalized maximum likelihood estimators accomplish this by maximizing a penalized form of the log‐likelihood, where the penalty discourages roughness in the final estimate. The estimator has a Bayesian interpretation, with the penalty function corresponding to the logged prior for the density. The resultant estimator often takes the form of a polynomial spline with knots at the order statistics, and asymptotically is approximately a local‐bandwidth kernel estimator. The method can be adapted to large sparse contingency tables, resulting in cell probability estimators that are consistent under asymptotics that approximate such tables.