bluuebunny/crossref_metadata_2025_split huggingface dataset:
Pearson Distributions
Authors: Armitage Peter 
Published: September 2014

Abstract

This is a family of probability distributions, often called Pearson
curves
, developed by Karl Pearson in the period between 1894 and 1895 to provide flexible descriptions of the nonnormal distributions encountered in his biometric research. It includes many well‐known distributions. The types can be distinguished by the standard indices of skewness and kurtosis.
Penalized Maximum Likelihood
Authors: Simonoff Jeffrey S. 
Published: September 2014

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.
Prior Distribution
Authors: Kass R. E. 
Published: September 2014

Abstract
In Bayesian inference, the unknown parameter is given a prior distribution, and Bayes' theorem combines this with the likelihood from the observed data, to give the posterior distribution. The prior may be informative, subjective, or have a standard, reference form (usually representing vague knowledge). In hierarchical models, the prior distribution may have its own parameters that themselves have priors.
Quasi‐likelihood
Authors: Zeger Scott L. , Liang Kung‐yee 
Published: September 2014

AbstractQuasi‐likelihood is a method of estimation for regression analysis which requires the specification of only the first two moments of the response distribution, and the term refers also to the objective function analogous to the likelihood. In generalized linear models, the iterative weighted least squares algorithm for solving the score equations depends only on the mean and variance of the response. The solution of the estimating equations is consistent even when the variance expression is incorrect. Various extensions are described.
R
adon–
N
ikodym Theorem: Definitions and Applications
Authors: Alexander Kenneth S. 
Published: September 2014

Abstract
The Radon–Nikodym Theorem, in the context of probability measures, states that if all events having probability 0 under one probability measure also have probability 0 under a second measure, then the second measure is obtained by integrating some density function with respect to the first measure. Applications in probability and statistics arise in the contexts of likelihood functions, conditional expectation, Girsanov's formula, spectral measures and local time. The theorem and these applications are discussed.
Robustness
Authors: Prescott Philip 
Published: September 2014

AbstractA short history of the development of ideas of robustness is provided, from Gauss' introduction of the normal distribution in 1821 to the detailed examination of the conflicting criteria for robustness as discussed by Huber, Hampel, Tukey, and others, which led to consideration of validity robust and efficiency robust procedures. Robust estimators of location using M‐estimators (based on maximum likelihood), L‐estimators (based on order statistics), and R‐estimators (based on ranking methods) are described and examples given. These methods produce a wide range of robust estimators including trimmed means, Winsorized means, and the median of all pairwise averages. Adaptive and resistant procedures are discussed briefly.
Shrinkage Estimation
Authors: Casella George 
Published: September 2014

AbstractShrinkage estimation developed from the work of Stein for the estimation of the mean of a multivariate normal distribution. The observed vector is, from a decision theory viewpoint, inadmissible. The James–Stein estimator shrinks the observations toward zero. Later work involves estimators shrunk toward the sample mean. Shrinkage estimators are, however, not dominant in problems with a finite sample space, such as the binomial distribution. There are connections with Bayesian and empirical Bayes solutions.
Studentized Range including Neuman‐Keuls and Tukey's T Methods
Authors: Hochberg Yosef 
Published: September 2014

Abstract

In a comparison of the means of several samples of size
n
, the studentized range is the range of the sample means divided by the usual standard error of a single mean. It may be used in successive stages of a multiple comparison procedure. Two approaches are the Newman–Keuls method and Tukey's
T
‐method. In a single sample of size
n
, the internally studentized range is the ratio of the sample range to the standard deviation, and may be used in a test of normality. Various applications are discussed.
Sufficient Statistic: Theoretical Background
Authors: Strawderman William E. 
Published: September 2014

Abstract
A sufficient statistic is such that the conditional distribution of the data given the sufficient statistic does not depend on any unknown parameters. In this sense, it contains all the information in the original data. A necessary and sufficient condition is the factorization theorem. A minimal sufficient statistic is a function of every other sufficient statistic, and is conveniently found for distributions in the exponential family. Topics described here include complete sufficient statistics, minimum variance estimation, uniformly most powerful unbiased tests, Bayesian methods, and invariance.
Accelerated Failure‐time Models
Authors: James Ian 
Published: September 2014

AbstractThe accelerated failure‐time model assumes a survival function of the formS(t) = S0(θt), whereS0is an underlying survival function and θ may depend on a number of covariates. This is equivalent to a location‐shift model for the log failure time, and in particular to a loglinear regression model when θ is loglinear. Parametric and semiparametric approaches to analyses based on these models with possibly censored failure‐time responses are reviewed. The accelerated failure‐time assumption is compared and contrasted with that of proportional hazards.
Bayesian Survival Analysis
Authors: Ibrahim Joseph G. , Chen Ming‐Hui , Sinha Debajyoti 
Published: September 2014

AbstractGreat strides in the analysis of survival data using Bayesian methods have been made in the past ten years due to advances in Bayesian computation and the feasibility of such methods. In this chapter, we review Bayesian advances in survival analysis and discuss the various semiparametric modeling techniques that are now commonly used. We review parametric and semiparametric approaches to Bayesian survival analysis, with a focus on proportional hazards models. Reference to other types of models are also given.
Counting Process Methods in Survival Analysis
Authors: Chang I‐Shou , Hsiung Chao Agnes 
Published: September 2014

AbstractA brief review of the counting process approach to generalized survival analysis is given. Examples are provided to illustrate that counting processes together with their filtration‐specific intensities are excellent modeling tools for survival analysis, where data are often incompletely observed; that the associated martingale theories are useful in proposing inference procedures, analyzing their distributional properties, and studying their efficiency; that the representation of the likelihood process in terms of its intensity offers extra convenience in the data analysis. Several examples are also given to indicate that counting process may provide good statistical model but offer limited help in the analysis.
Delayed Entry
Authors: Keiding Niels 
Published: September 2014

Abstract
Methods for analyzing survival data with delayed entry are surveyed. Particular emphasis is put on the definition of random left truncation, the counting process approach and filtering, delayed entry and covariates, and independent and dependent delayed entry. As specific examples are mentioned the prevalent cohort study, confirmatory analysis of a chance finding at interim analysis, and left censoring, right truncation, time‐reversal, and the retro‐hazard.
Discrete Survival‐Time Models
Authors: Fahrmeir Ludwig 
Published: September 2014

AbstractSurvival times are rarely intrinsically discrete (an important counterexample being time to pregnancy, which is naturally measured in menstrual cycles). If times are recorded in intervals, grouped survival times methods may be relevant, but it is alternatively sometimes preferable to consider time as discrete. This leads to various forms of generalized linear models, notably repeated logistic regressions or discrete proportional hazards (complementary log–log link functions). Smoothing methods are considered.Generalizations to competing risks and to frailty models have also been studied.
Excess Mortality
Authors: Væth Michael 
Published: September 2014

Abstract
The term excess mortality is used to describe the additional hazard rate in a study population relative to that seen in a reference population with the same sex and age distributions. A formal model is introduced and a nonparametric estimate of the integrated excess mortality rate is given. As a by‐product, an estimate of the expected survival function is also obtained. For the special case with a constant excess mortality rate, simple explicit moment estimate is also available. The methodology can be generalized to both parametric and nonparametric regression models.
Expected Number of Deaths
Authors: Væth Michael 
Published: September 2014

Abstract
In epidemiological studies, the mortality in a study population is often related to that of a reference population by computing the number of deaths that is expected if the mortality rates of the reference population are applied to the follow‐up experience of the study population. This method is based on a multiplicative model for the mortality rate and is closely related to standardization techniques. Two approaches to the calculation of the expected number of deaths, the prospective model, and the person‐years method are described. In the simplest form the latter method is essentially an indirect standardization, but the model is easily generalized to include regression on covariables.
Explained Variation Measures in Survival Analysis
Authors: Graf Erika 
Published: September 2014

Abstract

In linear regression, the proportion of explained variation,
R
2
, is a familiar measure used to quantify the predictive value of a model including covariates compared to the null model of no covariate effect. Similar measures have been proposed for survival analysis where the situation is typically complicated by the presence of censored observations. In addition, squared error may not be felt to be an adequate loss function in this context. We introduce the concept of explained variation in the survival setting and illustrate it by selected measures.
Inverse Probability Weighting in Survival Analysis
Authors: Rotnitzky Andrea , Robins James M. 
Published: September 2014

AbstractSurvival studies usually incorporate high‐dimensional covariate data, but interest may focus on low‐dimensional characteristics of the survival distribution. Inverse probability weighted augmented estimation (AIPW) provides a robust approach, largely insensitive to model misspecification. The method was originally introduced to deal with coarsened (incompletely observed) data, and is discussed here with and without the assumption of random coarsening.
Length Bias
Authors: Wang Mei‐Cheng 
Published: September 2014

AbstractLength bias occurs when the sampling scheme implies that the probability of observing a positive‐valued random variable is proportional to the value of the valuable. Length bias is well documented in renewal theory, but is also important in epidemiology. Examples include prevalent cohort studies (where left truncation is an important remedy), other sampling schemes originating from cross‐sectional samples, and screening for chronical diseases.Comments are given on necessary modification of methods from nonparametric survival analysis.
Life Table: Overview
Authors: Hoem Jan M. 
Published: September 2014

Abstract
A life table is a traditional representation of estimates related to grouped survival times, sometimes called the “actuarial” method. Besides the survivor function, it usually contains estimates of residual life expectancy. There are also so‐called multiple‐decrement tables relevant for competing risks.
The history of the life table is long and well documented. Many special terms have been attached to the life table during its service in demography and actuarial mathematics.
Marker Processes
Authors: Kalbfleisch John D. 
Published: September 2014

AbstractIn longitudinal studies in survival analysis, repeated measures are often taken of more or less specific health measures. Suchmarker processesmay serve as (a) time‐dependent covariates for improving estimation of a survival distribution, (b) surrogate for survival in a comparative trial, (c) providing information on time of onset of disease, when this is not directly observable.
N
elson–
A
alen Estimator
Authors: Borgan Ørnulf 
Published: September 2014

Abstract
It is described how the Nelson–Aalen estimator can be used to provide a nonparametric estimate of the cumulative hazard rate function based on right censored and/or left truncated survival data, and how the estimator can be used to estimate the integrated transition intensities in Markovian multistate models. It is also pointed out how the Nelson–Aalen estimator can be adopted to estimate other quantities, like the integrated relative mortality in a multiplicative model with external rates and the cumulative infection rate in a simple epidemic model. It is shown that counting processes provide a framework that allows for a unified treatment of all these diverse situations, and the most important small and large sample properties of the estimator are summarized. Finally, the construction of confidence bands is considered.
Survival Analysis, Overview
Authors: Andersen Per Kragh , Keiding Niels 
Published: September 2014

AbstractSurvival analysis is the generic name for analysis of time‐to‐event data. The distinguishing feature of such data is the presence of right‐censored observations. Thus, for some subjects, instead of observing the real time to the event, only a lower limit for this time, the right‐censoring time, is known. This kind of incomplete data calls for special statistical techniques for the analysis. This article reviews such methods with cross‐references to other articles dealing with special techniques.
Survival Distributions and Their Characteristics
Authors: Klein John P. 
Published: September 2014

Abstract
The four basic functions that characterize the probability distribution of the time to an event are presented. These functions, the survival function, the density or mass function, the hazard rate, and the mean residual life function are presented, and the relationship between the functions is discussed. Classes of distributions that reflect aging properties are presented. These classes include the increasing hazard rate (IHR) class, the increasing hazard rate on the average class (IHRA), the decreasing mean residual life (DMRL) class, the new better than used (NBU) class, the new better than used in expectation class (NBUE) and the harmonic new better than used in expectation class (HNBUE).
Time‐Dependent Covariate
Authors: Andersen Per Kragh 
Published: September 2014

AbstractModels for survival data are often specified from the hazard function thereby allowing regression models to include covariates that change with time. This article reviews different types of time‐dependent covariates in survival analysis. Potential problems in connection with estimation of the survival function in models with time‐dependent covariates are discussed. Estimation in Cox's multiplicative regression model and other regression models with time‐dependent covariates, including additive models, are reviewed.
Total Time on Test
Authors: Andersen Per Kragh , Keiding Niels 
Published: September 2014

Abstract
In survival analysis, the exponential distribution plays an important role as a null hypothesis. One classical technique from reliability analysis for testing this hypothesis is based on the total time on test concept. It is explained, in the framework of counting processes, how a number of graphical and numerical test procedures may be based on this concept. These procedures are illustrated using data from a clinical trial in liver cirrhosis.
Demography
Authors: Timæus Ian M. 
Published: September 2014

AbstractDemography is the study of human populations with respect to their size and structure and of the components of population change, in particular, fertility, mortality, and migration. This article outlines the more important sources of data, substantive issues, concepts, methods, and models in demography. The discipline's central concern is to measure, explain, and model the dynamics of human populations. Thus, one crucial application of demography is the forecasting of population change by means of cohort‐component projections. Classical demographic measures and techniques of analysis were developed largely for the study of vital statistics with census‐based denominators. They include the calculation of age‐specific rates, standardization, and life‐table analysis. More recently, the growing importance of individual‐level analysis of survey data has led to convergence between demographic methods and other forms of statistical analysis.
Geographic Patterns of Disease
Authors: Elliott Paul , Best Nicola 
Published: September 2014

AbstractThe study of geographic variations in disease is a classic epidemiological technique in which location is used as a surrogate for the mix of lifestyle, environmental, and possibly genetic factors that may underlie variations in rates of disease across populations. This article reviews issues involved in disease mapping (the usual means of presenting descriptive geographic data on disease occurrence) and geographic correlation studies (where the aim is to explore geographic variation in disease in terms of underlying spatially varying “risk factors”). The emphasis is on small‐area applications, where a number of recent advances in methodology have been made.
Occupational Mortality, Background on
Authors: Lynge Elsebeth 
Published: September 2014

Abstract
The study of occupational mortality involves the systematic tabulation of mortality by occupational or socio‐economic group. Three main methods are used to conduct these studies: cross‐sectional studies, death certificate studies, and follow‐up studies. Cross‐sectional studies were undertaken in England and Wales from 1851 to 1979–1983, and these studies have provided key data on social inequalities in health. Death certificate studies have been used for identification of occupational groups with high excess risks from specific diseases. Follow‐up studies require linkage of individual records, typically from censuses and death certificates. They have been undertaken in, for example, all the Nordic countries. The follow‐up studies have shown a high mortality for all marginal groups of the labor market, a social gradient in overall mortality, low mortality among farmers, and a widening gap between the mortality rates of blue and white collar workers.
Scan Statistics for Disease Surveillance
Authors: Wallenstein S. 
Published: September 2014

AbstractScan statistics provide the researcher with a measure of unusualness (statistical significance) associated with a clustering of events in time, as would occur when observing an unexpectedly large number of events in a short time period. The statistic can also be used to detect seasonal clustering, and as a method to detect geographical, time, or space–time clustering. The scan statistic can also be generalized and then applied to the analysis of DNA sequence data focusing on detecting a certain pattern.
Multivariate Analysis, Bayesian: Overview with Examples
Authors: Press Jim 
Published: September 2014

Abstract
This article discusses Bayesian multivariate analysis. It focuses on higher‐dimensional statistical inference based upon the posterior distribution, so inference involves multidimensional prior, posterior, and predictive probability distributions. The article describes credibility intervals and regions, and hypothesis testing. There is reference to both vague and natural conjugate prior distributions. Computer‐intensive methods of numerical evaluation such as MCMC and Metropolis–Hastings algorithms are considered. There is an illustrative example involving Bayesian factor analysis.
Optimal Design for Categorical Variables
Authors: F. Berger Martijn P. 
Published: September 2014

AbstractOptimal design research is important for behavioral research because it enables efficient estimation of parameters and maximum power with minimum sample size and costs of performing a study. In this paper, an elementary introduction to the concepts of optimal design research is given and illustrated by means of four different cases, namely, linear and logistic models, with and without dummy coding. Although different models have different optimal designs, a rule‐of‐thumb may be that if the independent variables are treated as being quantitative, efficiency will increase if the variance of the independent variable increases, and if the design is as orthogonal as possible. For qualitative independent variables, a design that has equal sample sizes for all categories is often optimal.
Prediction Analysis of Cross‐Classifications
Authors: Szabat Kathryn A. 
Published: September 2014

Abstract

Prediction analysis is an approach to the analysis of cross‐classified, cross‐sectional or longitudinal data. It is a method for predicting events based on specification of predicted relations among qualitative variables and includes techniques for both stating and evaluating those event predictions. This article presents the basic methodology employed in prediction analysis and highlights approaches developed by Hildebrand, Laing, and Rosenthal (6), and by von Eye, Brandtstadter & Rovine, (12, 13). The Hildebrand et al. approach involves measuring prediction success of a set of predictions via a proportionate reduction in error (PRE) measure, known as
del
. The von Eye et al. approach models the prediction hypothesis via nonstandard log‐linear modeling and evaluates the extent to which the model adequately describes the data. Both approaches to prediction analysis provide a viable, valuable data analysis tool that researchers in the social and behavioral sciences can use in a wide range of research settings.
Goodness of Fit for Categorical Variables
Authors: Eye Alexander , Bogat G. Anne , Weber Stefan 
Published: September 2014

AbstractThe examination of frequency distributions of categorical variables often involves an evaluation of the appropriateness of probability models.Goodness‐of‐fitstatistics are suitable for this task. These statistics assess the discrepancy between the data and a probability model. Applications focus on (1) overall goodness‐of‐fit and (2) individual residuals. This entry describes the most frequently used goodness‐of‐fit statistics and presents an application in the context of logistic regression.