bluuebunny/crossref_metadata_2025_split huggingface dataset:
Summary Measures Analysis of Longitudinal Data
Authors: Matthews John N. S. 
Published: July 2005

AbstractThere are many methods for the analysis of longitudinal data and the method of summary measures is one of the simplest and most effective. The observations on each unit are combined into a summary measure, which measures a relevant aspect of the response over time. In this way, the data from each unit is reduced to a single value and these can, within limits, be analyzed as the response of the unit. For example, two groups of individuals might be compared by performing at‐test on the summary measures. Summary measures can be whatever adequately captures the essential features of the response over time and more than one summary can be used if more than one aspect of the response is of interest. Typical summaries are the area under the curve, the slope of a regression line or the time to the maximum response. Some difficulties arise with missing data and irregular observations but these problems are generally not more severe for this approach than for other methods that analyze longitudinal data.
Axes in Multivariate Analysis
Authors: Krzanowski W.J. 
Published: July 2005

Abstract

Visualization of data is valuable in statistical analysis to reveal features that are difficult to detect in numerical summaries. When
p
variables are measured on
n
subjects it can be difficult to graphically depict patterns due to limits of dimensionality. Multivariate graphical analysis identified directions that can be projected into subspaces to highlight sample features. Projecting the original data into a subspace generated from several orthogonal linear combinations allows for low‐dimensional approximation to the full data representation.
Communality
Authors: D'agostino, Sr Ralph B. , Russell Heidy K. 
Published: July 2005

Abstract

In factor analysis, a mathematical model is used to explain the interrelationships of a set of
p
manifest variables by a smaller number of
m
underlying latent factors that cannot be observed or measured directly. If
X
1
,
X
2
, …,
X

p

represent the standardized measurement of the
p
manifest variables, then each standardized measurement can be represented as a linear combination of common factors and a unique factor. Communality is defined as the proportion of a variable's total variance that is accounted for by the common factors. The squared multiple correlation is the most commonly used estimate for the communality. It generally approaches the true communality as the number of variables increases.
Factor Analysis, Confirmatory
Authors: D'agostino Ralph B. , Russell Heidy K. 
Published: July 2005

Abstract

In factor analysis, a common‐factor analysis model involves representing each observed variable as a weighted sum of
m
common‐factor scores and one unique‐factor score. The collection of these equations for all
p
variables is called a factor pattern. Sometimes, an investigator may have a hypothesized factor pattern or there may exist a factor matrix from a previous study. An investigator might wish to estimate and test the fit of the data to the hypothesized factor pattern or to the model obtained from a previous study. Performing an analysis to find out how the estimated factor matrix from the data matches the hypothesized factor matrix is called confirmatory factor analysis. Software packages available for this analysis are highlighted.
Independence of a Set of Variables, Tests of
Authors: Krzanowski W. J. 
Published: July 2005

Abstract

If
p
variables have been divided a priori into distinct sets, then within each set, individual values for each variable may be highly correlated; however, variables in different sets could be treated as independent. Testing independence of such sets of variables is considered through development of a likelihood ratio test. Derivation from this likelihood ratio test to canonical correlation and a union–intersection test is also shown.
Multivariate Distributions, Overview
Authors: Jensen D. R. 
Published: July 2005

AbstractMultivariate distributions arise throughout statistics and applied probability and they are defined on finite‐dimensional spaces. They serve as probabilistic models for dependent outcomes of random experiments. Biometric data typically comprises observations on multiple characteristics for each experimental subject, and joint distributions are central to the modeling and analyses of such data. From multivariate distributions, the distributions of various sample statistics of note in statistical inference can be derived. Multivariate distributions also characterize the behavior of stochastic processes through properties of their finite‐dimensional projections.
Multivariate Multiple Regression
Authors: Krzanowski W. J. 
Published: July 2005

Abstract

Multivariate multiple regression analysis is used to model the relationship between
q
(>1) dependent variables and a set of explanatory variables. Maximum likelihood estimates of the parameter error matrix,
H
, and the corresponding test statistics are specified. The test of independence of dependent variables on a subset of explanatory variables, which is the basis for stepwise selection, is also described.
Multivariate Normality, Tests of
Authors: Thode Henry C. 
Published: July 2005

AbstractTesting for multivariate normality in a sample of observations presents greater difficulty than testing for univariate normality. Tests for multivariate normality are mostly based on either the unique properties of the multivariate normality, generalizations of tests for univariate normality, or generalizations of univariate tests for goodness‐of‐fit. Several methods of assessing multivariate normality are presented here, with a focus on those tests that are easily applied and/or have good power properties. Some plots that can be used for subjectively determining the normality of a sample of observations are also described.
MultivariatetDistribution
Authors: Jensen D. R. 
Published: July 2005

AbstractMultivariate versions of the Student'stdistribution derive through Studentization from multivariate normal models. Multivariatetdistributions are useful to model errors of a random experiment offering greater flexibility and heavier tails than multivariate normal models. There are two types of multivariatetdistributions. Type I distributions are derived by scaling each component of a normal vector by a single random scalar. Type II distributions involve separate scalings by elements of a further random vector, itself having a joint multivariate distribution.
Oblique Rotation
Authors: Jackson J. Edward 
Published: July 2005

Abstract

Any rotation of vectors associated with
principal components analysis
or
factor analysis
designed to produce new set approximating
simple structure
is said to be
oblique
if the resultant set of vectors are not at right angles to each other. Oblique rotations may obtain a better approximation to simple structure but with the loss of orthogonality. Some of these rotations are obtained by a general procedure called
Oblimin rotation
but some of the more widely used rotations such as
Orthoblique, Promax
and
Optres
do not use this form but instead are two‐ and three‐stage procedures, usually using orthogonal rotations as the first stage.
Pattern Recognition
Authors: Lange Nicholas 
Published: July 2005

AbstractPattern recognition refers to a technology that recognizes and analyzes patterns automatically by machine. There are some differences between pattern recognition and its relatives. Classical pattern recognition proceeds in two stages: feature detection and extraction followed by classification. One important property of feature detectors and classifiers for pattern recognition is their invariance with respect to minor pattern distortions or deformations. Pattern recognition systems built according to well‐established criteria from statistical decision and information theory are known to outperform systems built using ad hoc methods. The construction of pattern recognition systems and the evaluation of their performance usually involve some form of prediction. Artificial neural networks embody many key pattern recognition ideas and principles.
Projection Pursuit
Authors: Sun Jiayang 
Published: July 2005

AbstractThis article introduces projection pursuit and its history. It describes two basic elements of projection pursuit and ideas for choosing the elements in practice. How to judge the interestingness of a projection pursuit solution is discussed via p‐values of projection pursuit. The other variants or applications of projection pursuit, such as projection pursuit regression and projection pursuit density estimation, are also provided. The article concludes with a discussion on interactive projection pursuit.
Confidentiality and Computers
Authors: Maindonald John H. , Stott Helen P. 
Published: July 2005

AbstractComputer systems that hold data of a private or confidential nature should be designed so that data are “disclosed only to authorized persons, entities and processes at authorized times and in the authorized manner” 24. Rights of privacy and confidentiality may be enshrined in legislation. Such rights are typically not absolute; they may, especially where data is required for research purposes, be weighed against a wider public interest. Demands for privacy and confidentiality impose responsibilities on designers and managers of computer systems that store sensitive data. Advances in computer technology, and especially the use of the internet, have created huge security challenges.
Database Systems
Authors: Walker N. , Lawrence Catherine 
Published: July 2005

AbstractThe word “database” is used here in two overlapping ways to refer to a collection of related data and its storage method, or to programming system software used to organize and integrate a collection of related data. It is management, access, and control (including efficiency and recoverability), and not necessarily size, which distinguishes a database from a data set. This article concentrates on database software: choosing a database management system (DBMS), designing databases, object‐oriented approaches, and closes with an overview of resources that might be helpful.
Graphical Displays
Authors: Martin Michael A. , Welsh A. H. 
Published: July 2005

AbstractGraphical methods are fundamental tools of modern data analysis. Graphics are useful for communicating complex information quickly and easily, and are thus excellent tools for describing data and for providing direction in data analysis. They are essential tools for building statistical models from data, and for assessing model adequacy. This article surveys the use of statistical graphics in describing data and for statistical modeling, including models for relating variables, for spatiotemporal dependence, and for survival data. Graphics are also critical tools for visualizing and analyzing high‐dimensional data. The article illustrates the use of graphics in statistical modeling through numerous examples drawn from the life sciences.
Internet
Authors: Bowman Adrian W. , Crawford Ewan , Currall James , Young Stuart G. 
Published: July 2005

Abstract
The internet (lower case i) is the world's biggest computer network connecting millions of computers worldwide. The Internet (upper case I) is a term describing what can be done over the internet. It opens up new vistas for academics, the business community, and the general public, providing easier access to information and faster means of communication.
Pseudo‐Random Number Generator
Authors: Kemp C. D. 
Published: July 2005

AbstractOne of the most frequently called functions on a scientific computer is the random number generator. Random numbers are required for many purposes. A major use is in simulation. Large quantities of random numbers are needed to generate the random samples from distributions (theoretical and/or empirical) that are the basis of any stochastic simulation. Another use for random numbers is the Monte Carlo evaluation of multivariate integrals. Ideally, what is required in a simulation is a stream of independently and uniformly distributed random variables taking values between 0 and 1 [i.e. a random sample from the uniform distribution on (0,1)]. At best this ideal can only be realized approximately.
R
Authors: Venables W. N. , Maindonald John H. 
Published: July 2005

Abstract
The R system is an independent, open source, freely available implementation of a computer language that is well adapted to the development of scientific calculations, data analysis, and graphics. It has gained particular importance for developing and promulgating new statistical, data analytical, or graphical techniques. Versions of R are available for Microsoft Windows, Unix, Linux, and MacOS 8 or later.
Spline Smoothing
Authors: Turlach Berwin A. 
Published: July 2005

AbstractOver the past few decades, several methods for fitting smooth curves to data have been proposed and intensively studied. Among these methods are kernel smoothers, orthogonal series estimators, wavelet smoothers, and spline smoothers. This entry provides a brief description of the commonly used spline smoothers – regression splines, smoothing splines, and penalized splines.
S
‐
PLUS
and
S
Authors: Venables W. N. 
Published: July 2005

Abstract
S‐PLUS is a commercial software environment for data analysis and graphics based on the programming language S, designed and initially implemented by John M. Chambers at Bell Laboratories. In addition to a large suite of software for standard tasks, the system aims to provide users with the means to implement new techniques or combine standard methodology in possibly new ways. The language is interpreted rather than compiled, and has some object‐oriented features. Versions of S‐PLUS are current for Unix, Linux, and Windows. The system has a command‐line interface only, but the Windows implementation offers a graphical user interface as well.
Ancillary Statistics
Authors: Reid N. 
Published: July 2005

AbstractAn ancillary statistic is a function of the data whose distribution is free of the parameters in the model. Ancillary statistics are complementary in a certain sense to sufficient statistics. In the theory of statistics, it is often argued that inference should be conditional on ancillary statistics, when this is possible. Fisher showed that in a location model, the conditional distribution of the maximum likelihood estimator could be obtained by renormalizing the likelihood function, or, in other words, treating the likelihood function as a posterior distribution for the location parameter. This result has been generalized to provide an approximate conditional distribution to the maximum likelihood estimator, given an approximately ancillary statistic, a result known as thep* approximation.
Axioms of Probability
Authors: Rosalsky Andrew , Scheaffer Richard 
Published: July 2005

Abstract
One often thinks of probability as a limiting relative frequency; if a balanced coin is tossed often enough, the fraction of heads will be close to one half. The simple notion belies the nature and depth of mathematics that is required to make it rigorous, namely, the Kolmogorov axioms of probability and the Borel strong law of large numbers. Once the notion of long‐run relative frequency is made precise through measure theory, it can be used to build practical probability models for real‐world systems. Measure theory gives probability its rigor; repeated experimentation gives it its application and inspiration.
Delta Method
Authors: Cox C. 
Published: July 2005

Abstract
The Delta Method, also known as the Method of Propagation of Errors, refers to applications of the result that a smooth function of an asymptotically normal estimator also has an asymptotic normal distribution. The delta method has two principal groups of applications, first to the computation of a variance stabilizing transformation, and second to the computation of the asymptotic variance and confidence intervals for a nonlinear function of a set of previously estimated parameters, typically by the method of maximum likelihood. This article discusses the proof of both the univariate and multivariate versions of the theorem and gives numerous examples.
Efficiency and Efficient Estimators
Authors: Rotnitzky Andrea 
Published: July 2005

AbstractThe efficiency of a point estimator of a parameter reflects its tendency to be distributed closely around the parameter value. Asymptotic efficiency refers to the limiting distribution in large samples, which is often asymptotically normal, the minimum variance being given by the Cramér–Rao lower bound in terms of the information matrix. Concepts discussed here include asymptotic relative efficiency, semiparametric efficiency, partial likelihood, and quasi‐likelihood.
F

Distributions
Authors: Selvin S. 
Published: July 2005

Abstract

The
F
‐distribution is fundamental to much of statistical analysis, particularly the analysis of variance. The article entitled “
F
‐Distribution” is a brief but complete description of this probability distribution. Its properties are first discussed, followed by a description of the relationship between the
F
‐distribution and other common statistical distributions (e.g. beta, t‐, chi‐square, and binomial distributions). The article concludes with a typical application of this distribution to a small set of sampled observations.
Fiducial Probability
Authors: Seidenfeld Teddy 
Published: July 2005

AbstractFiducial probability was introduced by R. A. Fisher in 1930, as a method by which probability statements could (apparently) be made about an unknown parameter value without recourse to the Bayesian tools of prior and posterior probability. In a simple univariate one‐parameter case, this involves inversion of a probability statement from the distribution function. In other cases, it may involve a pivotal quantity whose distribution is independent of the parameter. The resulting statements are often similar to Bayesian posteriors with uniform priors, and fiducial intervals are often numerically equivalent to confidence intervals, although the logical structure is quite different. In some cases, notably the ratio of two normal means (the Creasy–Fieller problem) and the difference between two normal means with different variances (the Behrens–Fisher problem) fiducial and confidence intervals differ. The relationship between fiducial and Bayesian inference is discussed here in some detail.
Hypothesis Testing
Authors: Salsburg David 
Published: July 2005

AbstractA significance test of a null hypothesis involves the choice of a test statistic whose null distribution is known, and a judgment as to whether, or how well, the observed value of the statistic accords with the known distribution. The article reviews the history of this approach, with emphasis on the Neyman–Pearson formulation, taking account of the behavior of the test statistic under alternative hypotheses.
K
ullback–
L
eibler Information
Authors: Dykstra Richard 
Published: July 2005

Abstract

The Kullback–Leibler information number,
I
(
P
‖
Q
), determined for two probability measures defined on the same measurable space often serves as a type of “distance” between the two measures.

Projections (
I
‐projections) defined in terms of minimizing the Kullback–Leibler information number over appropriate sets of probability measures are often useful for finding desirable estimators.

Kullback–Leibler information numbers also play a useful role in hypothesis testing problems.
Lehmann Alternatives
Authors: Razzaghi Mehdi 
Published: July 2005

AbstractIn a nonparametric comparison of two groups, the test statistic may not be distribution‐free under alternatives to the null hypothesis. Lehmann proposed a family of alternatives under which the distribution function of the response variable in one group is a specified function of that in the other. A power relationship is usually considered. The distribution of the rank vector under the alternative then depends only on the specified function and rank statistics are distribution‐free. An extension covers the situation where a proportion of the population is unaffected by treatment.
Likelihood Principle
Authors: Lindsey J. K. 
Published: July 2005

AbstractThe likelihood function is central to all approaches to statistical inference. Principles have been proposed to justify the equivalence of inferences based on data with likelihood functions identical apart from a proportionality factor independent of parameters. The weak principle refers to replications with the same design; the more contentious strong principle refers to results from different designs. The latter, implied by Bayesian theory, needs to be supported by strong confidence in the validity of the model.
Mean Square Error
Authors: Schluchter Mark D. 
Published: July 2005

Abstract

If

is an estimator of a parameter θ, then the mean‐square(d) error (MSE) of the estimator is defined as the expectation of the squared deviation of

from θ:

. The MSE is a measure of closeness of the estimator to the true value. It can be shown that

That is, MSE reflects both the bias (accuracy) of the estimator, that is, how much its expected value deviates systematically from the true value, as well as the variance (precision) of the estimator, which indicates how much it varies about its expected value due to sampling variability.
Noncentral

t

Distribution
Authors: Rust Philip F. 
Published: July 2005

Abstract

This is the distribution of the ratio of a normally distributed variable with unit variance to the square root of a ratio of a chi‐square variable to its degrees of freedom. When the noncentrality parameter (the mean of the normal distribution) is zero, the distribution is Student's
t
distribution. The noncentral distribution provides the power function for a
t
test, and other applications concern tolerance intervals and confidence intervals. Details are given here.
Outliers
Authors: Hawkins Douglas M. 
Published: July 2005

Abstract
Outliers are observations highly discordant from the rest of the data, either in a univariate distribution or in relation to a model with explanatory variables. They may arise through contamination, errors in data gathering, or misspecification of the model. Approaches to detection include “high‐breakdown” methods involving partitions of the data into acceptable and discordant sets; and sequential identification of individual outliers by forward selection or, preferably, backward elimination. Likelihood ratios or multiple comparison methods may be used. Special cases are considered and the topic is illustrated by an example using data on body weight and brain weight of animals and dinosaurs.
Power
Authors: Muller K. E. 
Published: July 2005

Abstract
In the Neyman–Pearson approach to the theory of hypothesis testing, power is the probability of rejecting the null hypothesis when an alternative hypothesis is true.
It therefore depends on the specific alternative, and may lead to the selection of a test statistic that provides satisfactory power. In particular, one might choose a uniformly most powerful unbiased test (unbiasedness here indicating minimum power at the null hypothesis). Power considerations are often used in the determination of sample size.
Profile Likelihood
Authors: Aitkin M. 
Published: July 2005

AbstractThis is the likelihood for a set of parameters maximized over nuisance parameters. It formalizes the use of likelihood ratio tests to construct confidence regions for a parameter in the presence of nuisance parameters. It may result in overprecision by ignoring uncertainty in the nuisance parameters, and various adjustments have been proposed. The Bayesian viewpoint is discussed.