bluuebunny/crossref_metadata_2025_split huggingface dataset:
A Second-order Adjustment to the Profile Likelihood in the Case of a Multidimensional Parameter of Interest
Authors: Stern Steven E. 
Published: March 2003

Summary
Inference in the presence of nuisance parameters is often carried out by using the χ2-approximation to the profile likelihood ratio statistic. However, in small samples, the accuracy of such procedures may be poor, in part because the profile likelihood does not behave as a true likelihood, in particular having a profile score bias and information bias which do not vanish. To account better for nuisance parameters, various researchers have suggested that inference be based on an additively adjusted version of the profile likelihood function. Each of these adjustments to the profile likelihood generally has the effect of reducing the bias of the associated profile score statistic. However, these adjustments are not applicable outside the specific parametric framework for which they were developed. In particular, it is often difficult or even impossible to apply them where the parameter about which inference is desired is multidimensional. In this paper, we propose a new adjustment function which leads to an adjusted profile likelihood having reduced score and information biases and is readily applicable to a general parametric framework, including the case of vector-valued parameters of interest. Examples are given to examine the performance of the new adjusted profile likelihood in small samples, and also to compare its performance with other adjusted profile likelihoods.
Optimal Scaling of Discrete Approximations to Langevin Diffusions
Authors: Roberts Gareth O. , Rosenthal Jeffrey S. 
Published: March 2003

Summary
We consider the optimal scaling problem for proposal distributions in Hastings-Metropolis algorithms derived from Langevin diffusions. We prove an asymptotic diffusion limit theorem and show that the relative efficiency of the algorithm can be characterized by its overall acceptance rate, independently of the target distribution. The asymptotically optimal acceptance rate is 0.574. We show that, as a function of dimension n, the complexity of the algorithm is O(n1/3), which compares favourably with the O(n) complexity of random walk Metropolis algorithms. We illustrate this comparison with some example simulations.
Conformal Normal Curvature and Assessment of Local Influence
Authors: Poon Wai-Yin , Poon Yat Sun 
Published: March 2003

Summary
In 1986, R. D. Cook proposed differential geometry to assess local influence of minor perturbations of statistical models. We construct a conformally invariant curvature, the conformal normal curvature, for the same purpose. This curvature provides a measure of local influence ranging from 0 to 1, with objective bench-marks to judge largeness. We study various approaches to using the conformal normal curvature and the relationships between these approaches.
Bayesian Analysis of Agricultural Field Experiments
Authors: Besag Julian , Higdon David 
Published: March 2003

Summary
The paper describes Bayesian analysis for agricultural field experiments, a topic that has received very little previous attention, despite a vast frequentist literature. Adoption of the Bayesian paradigm simplifies the interpretation of the results, especially in ranking and selection. Also, complex formulations can be analysed with comparative ease, by using Markov chain Monte Carlo methods. A key ingredient in the approach is the need for spatial representations of the unobserved fertility patterns. This is discussed in detail. Problems caused by outliers and by jumps in fertility are tackled via hierarchical t formulations that may find use in other contexts. The paper includes three analyses of variety trials for yield and one example involving binary data; none is entirely straightforward. Some comparisons with frequentist analyses are made.
Time Series Analysis of Non-Gaussian Observations Based on State Space Models from Both Classical and Bayesian Perspectives
Authors: Durbin J. , Koopman S. J. 
Published: March 2003

Summary
The analysis of non-Gaussian time series by using state space models is considered from both classical and Bayesian perspectives. The treatment in both cases is based on simulation using importance sampling and antithetic variables; Markov chain Monte Carlo methods are not employed. Non-Gaussian disturbances for the state equation as well as for the observation equation are considered. Methods for estimating conditional and posterior means of functions of the state vector given the observations, and the mean-square errors of their estimates, are developed. These methods are extended to cover the estimation of conditional and posterior densities and distribution functions. The choice of importance sampling densities and antithetic variables is discussed. The techniques work well in practice and are computationally efficient. Their use is illustrated by applying them to a univariate discrete time series, a series with outliers and a volatility series.
Wavelet Processes and Adaptive Estimation of the Evolutionary Wavelet Spectrum
Authors: Nason Guy P. , Von Sachs R. , Kroisandt Gerald 
Published: March 2003

Summary
This paper defines and studies a new class of non-stationary random processes constructed from discrete non-decimated wavelets which generalizes the Cramér (Fourier) representation of stationary time series. We define an evolutionary wavelet spectrum (EWS) which quantifies how process power varies locally over time and scale. We show how the EWS may be rigorously estimated by a smoothed wavelet periodogram and how both these quantities may be inverted to provide an estimable time-localized autocovariance. We illustrate our theory with a pedagogical example based on discrete non-decimated Haar wavelets and also a real medical time series example.
Two-step Estimation of Functional Linear Models with Applications to Longitudinal Data
Authors: Fan Jianqing , Zhang Jin-Ting 
Published: March 2003

Summary
Functional linear models are useful in longitudinal data analysis. They include many classical and recently proposed statistical models for longitudinal data and other functional data. Recently, smoothing spline and kernel methods have been proposed for estimating their coefficient functions nonparametrically but these methods are either intensive in computation or inefficient in performance. To overcome these drawbacks, in this paper, a simple and powerful two-step alternative is proposed. In particular, the implementation of the proposed approach via local polynomial smoothing is discussed. Methods for estimating standard deviations of estimated coefficient functions are also proposed. Some asymptotic results for the local polynomial estimators are established. Two longitudinal data sets, one of which involves time-dependent covariates, are used to demonstrate the approach proposed. Simulation studies show that our two-step approach improves the kernel method proposed by Hoover and co-workers in several aspects such as accuracy, computational time and visual appeal of the estimators.
Expected Estimating Equations to Accommodate Covariate Measurement Error
Authors: Wang C.-Y. , Sullivan Pepe Margaret 
Published: March 2003

Summary
Estimating equations which are not necessarily likelihood-based score equations are becoming increasingly popular for estimating regression model parameters. This paper is concerned with estimation based on general estimating equations when true covariate data are missing for all the study subjects, but surrogate or mismeasured covariates are available instead. The method is motivated by the covariate measurement error problem in marginal or partly conditional regression of longitudinal data. We propose to base estimation on the expectation of the complete data estimating equation conditioned on available data. The regression parameters and other nuisance parameters are estimated simultaneously by solving the resulting estimating equations. The expected estimating equation (EEE) estimator is equal to the maximum likelihood estimator if the complete data scores are likelihood scores and conditioning is with respect to all the available data. A pseudo-EEE estimator, which requires less computation, is also investigated. Asymptotic distribution theory is derived. Small sample simulations are conducted when the error process is an order 1 autoregressive model. Regression calibration is extended to this setting and compared with the EEE approach. We demonstrate the methods on data from a longitudinal study of the relationship between childhood growth and adult obesity.
Local Influence for Incomplete Data Models
Authors: Zhu Hong-Tu , Lee Sik-Yum 
Published: March 2003

Summary
This paper proposes a method to assess the local influence in a minor perturbation of a statistical model with incomplete data. The idea is to utilize Cook's approach to the conditional expectation of the complete-data log-likelihood function in the EM algorithm. It is shown that the method proposed produces analytic results that are very similar to those obtained from a classical local influence approach based on the observed data likelihood function and has the potential to assess a variety of complicated models that cannot be handled by existing methods. An application to the generalized linear mixed model is investigated. Some illustrative artificial and real examples are presented.
Estimating the Number of Clusters in a Data Set Via the Gap Statistic
Authors: Tibshirani Robert , Walther Guenther , Hastie Trevor 
Published: March 2003

Summary
We propose a method (the ‘gap statistic’) for estimating the number of clusters (groups) in a set of data. The technique uses the output of any clustering algorithm (e.g. K-means or hierarchical), comparing the change in within-cluster dispersion with that expected under an appropriate reference null distribution. Some theory is developed for the proposal and a simulation study shows that the gap statistic usually outperforms other methods that have been proposed in the literature.
Dynamic Models for Spatiotemporal Data
Authors: Stroud Jonathan R. , Müller Peter , Sansó Bruno 
Published: March 2003

Summary
We propose a model for non-stationary spatiotemporal data. To account for spatial variability, we model the mean function at each time period as a locally weighted mixture of linear regressions. To incorporate temporal variation, we allow the regression coefficients to change through time. The model is cast in a Gaussian state space framework, which allows us to include temporal components such as trends, seasonal effects and autoregressions, and permits a fast implementation and full probabilistic inference for the parameters, interpolations and forecasts. To illustrate the model, we apply it to two large environmental data sets: tropical rainfall levels and Atlantic Ocean temperatures.
Censored Regression with the Multistate Accelerated Sojourn Times Model
Authors: Huang Yijian 
Published: March 2003

SummaryMany disease processes are characterized by two or more successive health states, and it is often of interest and importance to assess state-specific covariate effects. However, with incomplete follow-up data such inference has not been satisfactorily addressed in the literature. We model the logarithm-transformed sojourn time in each state as linearly related to the covariates; however, neither the distributional form of the error term nor the dependence structure of the states needs to be specified. We propose a regression procedure to accommodate incomplete follow-up data. Asymptotic theory is presented, along with some tools for goodness-of-fit diagnostics. Simulation studies show that the proposal is reliable for practical use. We illustrate it by application to a cancer clinical trial.
Bayesian Phylogenetic Inference from Animal Mitochondrial Genome Arrangements
Authors: Larget Bret , Simon Donald L. , Kadane Joseph B. 
Published: March 2003

SummaryThe determination of evolutionary relationships is a fundamental problem in evolutionary biology. Genome arrangement data are potentially more informative than deoxyribonucleic acid sequence data for inferring evolutionary relationships between distantly related taxa. We describe a Bayesian framework for phylogenetic inference from mitochondrial genome arrangement data using Markov chain Monte Carlo methods. We apply the method to assess evolutionary relationships between eight animal phyla.
The Two-Way Proportional Hazards Model
Authors: Efron Bradley 
Published: March 2003

SummarySurvival analysis problems often involve dual timescales, most commonly calendar date and lifetime, the latter being the elapsed time since an initiating event such as a heart transplant. In our main example attention is focused on the hazard rate of ‘death’ as a function of calendar date. Three different estimates are discussed, one each from proportional hazards analyses on the lifetime and the calendar date scales, and one from a symmetric approach called here the ‘two-way proportional hazards model’, a multiplicative hazards model going back to Lexis in the 1870s. The three are connected through a Poisson generalized linear model for the Lexis diagram. The two-way model is shown to combine the information from the two ‘one-way’ proportional hazards analyses efficiently, at the cost of more extensive parametric modelling.
Modelling Association Football Scores and Inefficiencies in the Football Betting Market
Authors: Dixon Mark J. , Coles Stuart G. 
Published: March 2003

SUMMARY
A parametric model is developed and fitted to English league and cup football data from 1992 to 1995. The model is motivated by an aim to exploit potential inefficiencies in the association football betting market, and this is examined using bookmakers’ odds from 1995 to 1996. The technique is based on a Poisson regression model but is complicated by the data structure and the dynamic nature of teams’ performances. Maximum likelihood estimates are shown to be computationally obtainable, and the model is shown to have a positive return when used as the basis of a betting strategy.
The Offender Group Reconviction Scale: A Statistical Reconviction Score for use by Probation Officers
Authors: Copas John , Marshall Peter 
Published: March 2003

SUMMARY
The criminal courts in England and Wales may request the probation service to submit pre-sentence reports which are considered by magistrates and judges before making their sentencing decision. Pre-sentence reports must include an assessment of the risk of reoffending and the risk of harm to the public which the convicted offender presents. The offender group reconviction scale is a statistical aid to such risk assessment. We describe the scale and the statistical analysis on which it is based, and we discuss some statistical aspects of its interpretation and use.
Analysis of Longitudinal Data with Non-Ignorable Non-Monotone Missing Values
Authors: Troxel Andrea B. , Harrington David P. , Lipsitz Stuart R. 
Published: March 2003

SUMMARY
A full likelihood method is proposed to analyse continuous longitudinal data with non-ignorable (informative) missing values and non-monotone patterns. The problem arose in a breast cancer clinical trial where repeated assessments of quality of life were collected: patients rated their coping ability during and after treatment. We allow the missingness probabilities to depend on unobserved responses, and we use a multivariate normal model for the outcomes. A first-order Markov dependence structure for the responses is a natural choice and facilitates the construction of the likelihood; estimates are obtained via the Nelder–Mead simplex algorithm. Computations are difficult and become intractable with more than three or four assessments. Applying the method to the quality-of-life data results in easily interpretable estimates, confirms the suspicion that the data are non-ignorably missing and highlights the likely bias of standard methods. Although treatment comparisons are not affected here, the methods are useful for obtaining unbiased means and estimating trends over time.
Modelling the Effect of Subject-Specific Covariates in Paired Comparison Studies with an Application to University Rankings
Authors: Dittrich R. , Hatzinger R. , Katzenbeisser W. 
Published: March 2003

SUMMARY
Preference decisions will usually depend on the characteristics of both the judges and the objects being judged. In the analysis of paired comparison data concerning European universities and students’ characteristics, it is demonstrated how to incorporate subject-specific information into Bradley–Terry-type models. Using this information it is shown that preferences for universities and therefore university rankings are dramatically different for different groups of students. A log-linear representation of a generalized Bradley–Terry model is specified which allows simultaneous modelling of subject- and object-specific covariates and interactions between them. A further advantage of this approach is that standard software for fitting log-linear models, such as GLIM, can be used.
Random Regression Models for Human Immunodeficiency Virus Ribonucleic Acid Data Subject to Left Censoring and Informative Drop-Outs
Authors: Lyles Robert H. , Lyles Cynthia M. , Taylor Douglas J. 
Published: March 2003

SUMMARY
Objectives in many longitudinal studies of individuals infected with the human immunodeficiency virus (HIV) include the estimation of population average trajectories of HIV ribonucleic acid (RNA) over time and tests for differences in trajectory across subgroups. Special features that are often inherent in the underlying data include a tendency for some HIV RNA levels to be below an assay detection limit, and for individuals with high initial levels or high ranges of change to drop out of the study early because of illness or death. We develop a likelihood for the observed data that incorporates both of these features. Informative drop-outs are handled by means of an approach previously published by Schluchter. Using data from the HIV Epidemiology Research Study, we implement a maximum likelihood procedure to estimate initial HIV RNA levels and slopes within a population, compare these parameters across subgroups of HIV-infected women and illustrate the importance of appropriate treatment of left censoring and informative drop-outs. We also assess model assumptions and consider the prediction of random intercepts and slopes in this setting. The results suggest that marked bias in estimates of fixed effects, variance components and standard errors in the analysis of HIV RNA data might be avoided by the use of methods like those illustrated.
Two Ways of Modelling Overdispersion in Non-Normal Data
Authors: Lee Y. , Nelder J. A. 
Published: March 2003

SUMMARY
For non-normal data assumed to have distributions, such as the Poisson distribution, which have an a priori dispersion parameter, there are two ways of modelling overdispersion: by a quasi-likelihood approach or with a random-effect model. The two approaches yield different variance functions for the response, which may be distinguishable if adequate data are available. The epilepsy data of Thall and Vail and the fabric data of Bissell are used to exemplify the ideas.
Bayesian Inference for Generalized Additive Mixed Models Based on Markov Random Field Priors
Authors: Fahrmeir Ludwig , Lang Stefan 
Published: March 2003

SUMMARY
Most regression problems in practice require flexible semiparametric forms of the predictor for modelling the dependence of responses on covariates. Moreover, it is often necessary to add random effects accounting for overdispersion caused by unobserved heterogeneity or for correlation in longitudinal or spatial data. We present a unified approach for Bayesian inference via Markov chain Monte Carlo simulation in generalized additive and semiparametric mixed models. Different types of covariates, such as the usual covariates with fixed effects, metrical covariates with non-linear effects, unstructured random effects, trend and seasonal components in longitudinal data and spatial covariates, are all treated within the same general framework by assigning appropriate Markov random field priors with different forms and degrees of smoothness. We applied the approach in several case-studies and consulting cases, showing that the methods are also computationally feasible in problems with many covariates and large data sets. In this paper, we choose two typical applications.
A Tale of Two Laws: The U.S. Congress Confronts Habeas Corpus Petitions and Section 1983 Lawsuits
Authors: Cheesman Fred , Hanson Roger , Ostrom Brian 
Published: March 2003

Actions by state prisoners have comprised a large and growing body of litigation in the U.S. federal courts over the past thirty years. State prisoners can challenge the validity of their state trial court convictions (habeas corpus petitions) and the constitutionality of the conditions of their confinement to state prisons and jails (Section 1983 lawsuits). Currently, one out of every five civil cases filed in the federal system is brought by a jail or prison inmate.When in the past did these cases begin to arise? What is the present trend? What does the future hold concerning the number of cases likely to be filed?These questions are at the heart of the current research. Care is needed in addressing these queries because it is neither easy nor obvious to know what propels the volume of litigation. Moreover, the future is especially difficult to predict in light of recent legislation adopted by the United States Congress to limit the number of habeas corpus petitions and the number of Section 1983 lawsuits filed each year.The unique contribution of the current research is threefold. First, an improved methodology is used to describe past patterns and to forecast future trends. Simply stated, prisoner litigation is hypothesized to be related to the number of prisoners. As the number of prisoners increases, the volume of litigation increases proportionately. What is not obvious about this relationship is that it has persisted over the past decades despite substantial changes in legal doctrines designed to affect the filing of the litigation. Second, the effects of two major congressional actions passed in 1996 to limit prisoner litigation are examined and assessed for their success in achieving their intended objectives. The first of these, the Antiterrorism and Effective Death Penalty Act, which sought to restrict habeas corpus petitions, is judged to have virtually no impact. The second piece of legislation, the Prisoner Litigation Reform Act, which sought to curtail lawsuits against correctional officials, appears to have lowered the volume of litigation in the short‐term, but has not disrupted the underlying link between the number of prisoners and the number of lawsuits. Finally, estimates are made of the future volume of litigation and the corresponding number of federal judges needed to resolve prisoner litigation. These estimates have the advantage of being based on significant statistical relationships and accounting for the effects of recent congressional action.
Complete Models with Stochastic Volatility
Authors: Hobson David G. , Rogers L. C. G. 
Published: March 2003

The paper proposes an original class of models for the continuous‐time price process of a financial security with nonconstant volatility. The idea is to define instantaneous volatility in terms of exponentially weighted moments of historic log‐price. The instantaneous volatility is therefore driven by the same stochastic factors as the price process, so that, unlike many other models of nonconstant volatility, it is not necessary to introduce additional sources of randomness. Thus the market is complete and there are unique, preference‐independent options prices.We find a partial differential equation for the price of a European call option. Smiles and skews are found in the resulting plots of implied volatility.