bluuebunny/crossref_metadata_2025_split huggingface dataset:
The Effect of Simulation Order on Level Accuracy and Power of Monte Carlo Tests
Authors: Hall Peter , Titterington D. M. 
Published: December 2018

SUMMARY
We discuss the effect of simulation order on level accuracy and power of Monte Carlo tests, in a very general setting. Both parametric problems, with or without nuisance parameters, and nonparametric problems are treated by a single unifying argument. It is shown that if the level of a Monte Carlo test is known only nominally, not precisely, then the level error of a Monte Carlo test is an order of magnitude less than that of the corresponding asymptotic test. This result is available whenever the test statistic is asymptotically pivotal, even if the number of simulations is held fixed as the sample size n increases. It implies that Monte Carlo methods are a real alternative to asymptotic methods. We also show that, even if the number of simulations is held fixed, a Monte Carlo test is able to distinguish between the null hypothesis and alternative hypotheses distant n– 1/2 from the null.
Jackknifing Weighted Least Squares Estimators
Authors: Shao Jun 
Published: December 2018

SUMMARY
In a heteroscedastic linear regression model, the ordinary jackknife estimator of the asymptotic covariance matrix of the weighted least squares estimator is proved to be inconsistent. A modified jackknife procedure is proposed and shown to produce consistent estimators of the asymptotic covariance matrix. Finite sample performances of the jackknife, the modified jackknife and the customary S method are discussed. Some empirical results are also presented.
Exact Maximum A Posteriori Estimation for Binary Images
Authors: Greig D. M. , Porteous B. T. , Seheult A. H. 
Published: December 2018

SUMMARY
In this paper, for a degraded two-colour or binary scene, we show how the image with maximum a posteriori (MAP) probability, the MAP estimate, can be evaluated exactly using efficient variants of the Ford–Fulkerson algorithm for finding the maximum flow in a certain capacitated network. Availability of exact estimates allows an assessment of the performance of simulated annealing and of MAP estimation itself in this restricted setting. Unfortunately, the simple network flow algorithm does not extend in any obvious way to multicolour scenes. However, the results of experiments on two-colour images suggest that, in general, simulated annealing, according to practicable ‘temperature’ schedules, can produce poor approximations to the MAP estimate to which it converges.
Spatial Clustering for Inhomogeneous Populations
Authors: Cuzick Jack , Edwards Robert 
Published: December 2018

SUMMARY
A new method for detecting spatial clustering of events in populations with non-uniform density is proposed. The method is based on selecting controls from the population at risk and computing interpoint distances for the combined sample. Nonparametric tests are developed which are based on the number of cases among the k nearest neighbours of each case and the number of cases nearer than the k nearest control. The performance of these tests is evaluated analytically and by simulation and the method is applied to a data set on the locations of cases of childhood leukaemia and lymphoma in a defined geographical area. In particular the impact on power of the choice of k and of the ratio of cases to controls is examined. Modifications of the procedure to study distances from predefined objects, to match for known risk factors which would produce unwanted clustering and issues related to estimation are also discussed.
Nonparametric Estimation of Intensities for Sampled Counting Processes
Authors: Guttorp Peter , Thompson Mary Lou 
Published: December 2018

SUMMARY
Sampled counting processes are often studied using methods for the analysis of stationary time series. We express some time series parameters as smoothed versions of corresponding point process parameters and use these relations to suggest estimates of the point process parameters. In addition, we propose a reconstructive approach to the estimation problem. We derive some properties of the estimators and apply them to data from meteorology, entomology and particle physics. A simulation study indicates which estimators perform better in different situations.
Disaggregation of Time Series Models
Authors: Wei William W. S. , Stram Daniel O. 
Published: December 2018

SUMMARY
We develop a model disaggregation method to derive a disaggregate model from a given aggregate model, which is then used to perform data disaggregation. Since a time series model and its autocovariance structure are closely related, we approach the problem by exploring the possibility of estimating the autocovariance structure for the unobserved disaggregated series from the available autocovariances of an aggregate model. Let the time series aggregates be the non-overlapping sums of m consecutive disaggregated observations. Given an aggregate autoregressive integrated moving average ARIMA(p, d, r) model with r ≤ p + d + 1, assume that there is no hidden periodicity of order m. It is shown that, if m is odd or if m is even but all the real roots of the autoregressive polynomial of the given aggregate model are positive, then there exists a disaggregate model whose autocovariances can be uniquely derived from the autocovariances of the given aggregate model. Both non-seasonal and seasonal models are discussed. Empirical examples are presented to illustrate the method.
A Sample Reuse Method for Accurate Parametric Empirical Bayes Confidence Intervals
Authors: Carlin Bradley P. , Gelfand Alan E. 
Published: December 2018

SUMMARY
Parametric empirical Bayes (EB) methods of point estimation for a vector of unknown parameters date to the landmark paper of James and Stein (1961). The usual approach is to use the mean of the estimated posterior distribution of each parameter, where the estimation of the prior parameters (‘hyperparameters’) is accomplished through the marginal distribution of the data. While point estimates computed this way usually perform well, interval estimates based on the estimated posterior (called ‘naive’ EB intervals) do not. They fail to account for the variability in the estimation of the hyperparameters, generally resulting in subnominal coverage probability in the EB sense defined in Morris (1983a). In this paper we extend our earlier work in which we proposed a conditional bias correction method for developing EB intervals which corrects the deficiencies in the naive intervals. We show how bias correction can be implemented in general via a type III parametric bootstrap procedure, a sample reuse method first employed by Laird and Louis (1987). Theoretical and simulation work indicates that the resulting intervals are accurate with respect to nominal coverage. We give a specific application (to Poisson failure rate data) where we compute simultaneous point and bias-corrected interval estimates.
Jackknifing Linear Estimating Equations: Asymptotic Theory and Applications in Stochastic Processes
Authors: Lele Subhash 
Published: December 2018

SUMMARY
Let (X 1, X 2, ..., Xn) be a vector of (possibly dependent) random variables having distribution F(X, θ). Let θn be an estimating equation for θ, e.g. the score function or the maximum pseudolikelihood estimating equation in spatial processes. Let θn be the estimator obtained from G such that θn → θ0 in probability and n1/2(θn−θ0)→N(0,V) in distribution. In many situations, it is difficult to derive an analytical expression for V, e.g. for maximum pseudolikelihood estimators for the spatial processes. In this paper, we give a jackknife estimator of V and show that it is weakly consistent. The method consists of deleting one estimating equation (instead of one observation) at a time and thus obtaining the pseudovalues. The method of proof and conditions are similar to those of Reeds with some modifications. The method applies equally to independent and identically distributed random variables, independent but not identically distributed random variables, time- or space-dependent stochastic processes. Our conditions are less severe than Carlstein's who deals with a similar problem of estimating V for dependent observations. We also give some simulation results.
Procrustes Methods in the Statistical Analysis of Shape
Authors: Goodall Colin 
Published: December 2018

SUMMARY
Two geometrical figures, X and Y, in RK, each consisting of N landmark points, have the same shape if they differ by at most a rotation, a translation and isotropic scaling. This paper presents a model-based Procrustes approach to analysing sets of shapes. With few exceptions, the metric geometry of shape spaces is quite complicated. We develop a basic understanding through the familiar QR and singular value decompositions of multivariate analysis. The strategy underlying the use of Procrustes methods is to work directly with the N x K co-ordinate matrix, while allowing for an arbitrary similarity transformation at all stages of model formulation, estimation and inference. A Gaussian model for landmark data is defined for a single population and generalized to two-sample, analysis-of-variance and regression models. Maximum likelihood estimation is by least squares superimposition of the figures; we describe generalizations of Procrustes techniques to allow non-isotropic errors at and between landmarks. Inference is based on an N x K linear multivariate Procrustes statistic that, in a double-rotated co-ordinate system, is a simple but singular linear transformation of the errors at landmarks. However, the superimposition metric used for fitting, and the model metric, or covariance, used for testing, may not coincide. Estimates of means are consistent for many reasonable choices of superimposition metric. The estimates are efficient (maximum likelihood estimates) when the metrics coincide. F-ratio and Hotelling's R 2-tests for shape differences in one- and two-sample data are derived from the distribution of the Procrustes statistic. The techniques are applied to the shapes associated with hydrocephaly and nutritional differences in young rats.
Identifying Multiple Outliers in Multivariate Data
Authors: Hadi Ali S. 
Published: December 2018

SUMMARY
We propose a procedure for the detection of multiple outliers in multivariate data. Let X be an n × p data matrix representing n observations on p variates. We first order the n observations, using an appropriately chosen robust measure of outlyingness, then divide the data set into two initial subsets: A ‘basic’ subset which contains p +1 ‘good’ observations and a ‘non-basic’ subset which contains the remaining n - p - 1 observations. Second, we compute the relative distance from each point in the data set to the centre of the basic subset, relative to the (possibly singular) covariance matrix of the basic subset. Third, we rearrange the n observations in ascending order accordingly, then divide the data set into two subsets: A basic subset which contains the first p + 2 observations and a non-basic subset which contains the remaining n - p - 2 observations. This process is repeated until an appropriately chosen stopping criterion is met. The final non-basic subset of observations is declared an outlying subset. The procedure proposed is illustrated and compared with existing methods by using several data sets. The procedure is simple, computationally inexpensive, suitable for automation, computable with widely available software packages, effective in dealing with masking and swamping problems and, most importantly, successful in identifying multivariate outliers.
A Comparison of Variance Estimators in Nonparametric Regression
Authors: Carter C. K. , Eagleson G. K. 
Published: December 2018

SUMMARY
We compare two estimators of error variance, both based on quadratic forms in the residuals about smoothing spline fits to data. The estimators are compared over the whole range of values of the smoothing parameter as well as for data-based choices of the smoothing parameter. We show that the commonly used estimator of variance has the serious drawback of underestimating the error variance for small choices of the smoothing parameter. This drawback is not shared by a simple, but more computationally intensive, alternative.
Bayesian and Frequentist Bartlett Corrections for Likelihood Ratio and Conditional Likelihood Ratio Tests
Authors: Ghosh J. K. , Mukerjee Rahul 
Published: December 2018

SUMMARY
This paper characterizes priors under which the Bayesian and frequentist Bartlett corrections for the likelihood ratio and the conditional likelihood ratio (CLR) statistics differ by o(1). It is seen that, except for sample points with negligible probability, the CLR statistic has a posterior distribution for which a posterior Bartlett correction exists. This observation leads to an alternative proof of the existence of a frequentist Bartlett correction for the CLR statistic.
The Identity of Armitage's Two Tests of Heterogeneity of Proportions for Proportional Subclass Numbers
Authors: Gart John J. 
Published: December 2018

SUMMARY
Armitage discusses two χ2 -tests for heterogeneity of proportions after adjustment for stratification. One is based on a quadratic form of the deviations from expected values and the other is a more easily calculated Pearson χ2 -test. We show, for proportional subclass numbers (or balanced designs), that the two test statistics are identical.
Chaos and Deterministic Versus Stochastic Non-Linear Modelling
Authors: Casdagli Martin 
Published: December 2018

SUMMARY
An exploratory technique is introduced for investigating how much of the irregularity in an aperiodic time series is due to low dimensional chaotic dynamics, as opposed to stochastic or high dimensional dynamics. Non-linear models are constructed with a variable smoothing parameter which at one extreme defines a non-linear deterministic model, and at the other extreme defines a linear stochastic model. The accuracy of the resulting short-term forecasts as a function of the smoothing parameter reveals much about the underlying dynamics generating the time series. The technique is applied to a variety of experimental and naturally occurring time series data, and the results are compared with dimension calculations.
On Consistent Nonparametric Order Determination and Chaos
Authors: Cheng B. , Tong H. 
Published: December 2018

SUMMARY
We give a brief introduction to deterministic chaos and a link between chaotic deterministic models and stochastic time series models. We argue that it is often natural to determine the embedding dimension in a noisy environment first in any systematic study of chaos. Setting the stochastic models within the framework of non-linear autoregression, we introduce the notion of a generalized partial autocorrelation and an order. We approach the estimation of the embedding dimension via order determination of an unknown non-linear autoregression by cross-validation, and give justification by proving its consistency under global boundedness. As a by-product, we provide a theoretical justification of the final prediction error approach of Auestad and Tjøstheim. Some illustrations based on the Hénon map and several real data sets are given. The bias of the residual sum of squares as essentially a noise variance estimator is quantified.
Modelling Agent Forecast Distributions
Authors: West Mike 
Published: December 2018

SUMMARY
Problems in the analysis and interpretation of uncertain inferences obtained from individuals, or agents, are considered in the context of forecasting a scalar random quantity. Based on new theoretical results presented by West and Crosse, Bayesian updating is developed for cases in which agents' opinions are provided in terms of full forecast distributions (discrete or continuous), or partial summaries such as forecast means and variances. A particular focus is on problems in which partial agent information is communicated in terms of a few summary probabilities or, alternatively, quantiles of the agent's distribution. Example models highlight the key features of the theory and illustrate applications.
Spatial Statistics and Bayesian Computation
Authors: Besag Julian , Green Peter J. 
Published: December 2018

SUMMARY
Markov chain Monte Carlo (MCMC) algorithms, such as the Gibbs sampler, have provided a Bayesian inference machine in image analysis and in other areas of spatial statistics for several years, founded on the pioneering ideas of Ulf Grenander. More recently, the observation that hyperparameters can be included as part of the updating schedule and the fact that almost any multivariate distribution is equivalently a Markov random field has opened the way to the use of MCMC in general Bayesian computation. In this paper, we trace the early development of MCMC in Bayesian inference, review some recent computational progress in statistical physics, based on the introduction of auxiliary variables, and discuss its current and future relevance in Bayesian applications. We briefly describe a simple MCMC implementation for the Bayesian analysis of agricultural field experiments, with which we have some practical experience.
Modelling Complexity: Applications of Gibbs Sampling in Medicine
Authors: Gilks W. R. , Clayton D. G. , Spiegelhalter D. J. , Best N. G. , McNeil A. J. , Sharples L. D. , Kirby A. J. 
Published: December 2018

SUMMARY
We review applications of Gibbs sampling in medicine, involving longitudinal, spatial, covariate measurement and survival models. Applications in immunology, pharmacology, transplantation, cancer screening, industrial epidemiology and genetic epidemiology are discussed.
Estimating Logistic Regression Parameters for Bivariate Binary Data
Authors: McDonald Barry W. 
Published: December 2018

SUMMARY
Consider bivariate binary data, with possibly different covariates for each marginal binary observation. Suppose that the correlation between paired observations is a nuisance, and the interest lies in estimating logistic regression parameters associated with the covariates. We consider the estimator obtained by using the independence estimating equation, with corrected variance. This estimator can be very efficient and robust compared with maximum likelihood or the estimator of Liang and Zeger. Some comments are made concerning higher dimensional multivariate data.
Modelling Marginal Hazards in Multivariate Failure Time Data
Authors: Liang Kung-Yee , Self Steven G. , Chang Yue-Cune 
Published: December 2018

SUMMARY
We consider the problem of estimating relative risk parameters in the marginal distribution of failure times from a sample in which individuals are grouped into clusters and failure times for individuals within clusters may be dependent. We assume that the marginal hazard of failure for individuals within a cluster is specified by a relative risk regression model and the structure of dependence between individuals within a cluster is left unspecified. Estimating equations for the regression parameters and an estimator for the cumulative base-line marginal hazard are described. Large sample distribution theory based on a representation of the estimating functions as U-statistics is developed and results from a small simulation study are described. Two examples which originally motivated this work are presented.
Fitting Multivariate Regression Functions by Interaction Spline Models
Authors: Chen Zehua 
Published: December 2018

SUMMARY
In nonparametric multivariate regression analysis, we seek methods to reduce the dimensionality of the regression function to bypass the difficulty caused by the curse of dimensionality. The original additive models approximate a regression function by additive univariate functions, which overcome successfully the difficulty caused by the curse of dimensionality and have a clear interpretation. But since they ignore any interactions between regressors they are not sufficiently flexible to cope with the case where interactions are of concern. In this paper, we study interactive models in which the regression function is approximated by an analysis-of-variance-type function. The models retain all the advantages of the original additive models but are much more flexible. We study ways of fitting an interactive model by the smoothing spline method. We relate the well-known backfitting algorithm to a typical penalized least squares problem in the context of the smoothing spline method. We develop a non-standard method based on bootstrap methodology for model selection in the interaction spline modelling.
Duality Principle in Order Statistics
Authors: Balasubramanian K. , Balakrishnan N. 
Published: December 2018

SUMMARY
We establish a duality principle for order statistics in the arbitrary case, using which many known dual results on order statistics can be deduced without a formal proof. The literature on order statistics is rich with such dual pairs derived under different assumptions such as continuity, absolute continuity, exchangeability, etc.
Multiregression Dynamic Models
Authors: Queen Catriona M. , Smith Jim Q. 
Published: December 2018

SUMMARY
Multiregression dynamic models are defined to preserve certain conditional independence structures over time across a multivariate time series. They are non-Gaussian and yet they can often be updated in closed form. The first two moments of their one-step-ahead forecast distribution can be easily calculated. Furthermore, they can be built to contain all the features of the univariate dynamic linear model and promise more efficient identification of causal structures in a time series than has been possible in the past.
Heterogeneity in Models for Bivariate Survival: The Importance of the Mixing Distribution
Authors: Lindeboom Maarten , Van den Berg Gerard J. 
Published: December 2018

SUMMARY
We consider bivariate survival models in which the dependence between two survival times is by way of stochastically related unobserved components. We analyse the role of the mixing or heterogeneity distribution in such models and examine how this distribution affects the correlation between the two survival times. We derive explicit expressions for the correlation between the survival times and examine some properties of this correlation. Furthermore we examine to what extent the choice of this heterogeneity distribution is important for the hazards in the sample and their time paths. The time path of the hazard among the survivors is determined by the moments of the distribution describing the heterogeneity among the survivors. We consider particular published mixing distributions. Simulations show that it may be hazardous to estimate bivariate survival models in which the mixing distribution is parameterized univariate, in that a univariate random variable may not be able to account both for the mutual dependence of the survival times and for the change in the composition of the sample over time owing to unobserved heterogeneity.
Completely Randomized Designs for Comparing Dual with Single Treatments
Authors: Gerami A. , Lewis S. M. 
Published: December 2018

SUMMARY
This paper considers n × m completely randomized factorial experiments in which one treatment combination, labelled 00, is excluded. The aim of the experiments is to compare the effects of having both factors at non-zero labelled levels with the effects of having only one factor at a non-zero labelled level. A necessary and sufficient condition is given for an A-optimal allocation of units to treatments, and a series of equireplicate, A-optimal designs is derived.
On Estimating Linear Relationships When Both Variables are Subject to Errors
Authors: Cheng Chi-Lun , Van Ness John W. 
Published: December 2018

SUMMARY
This paper discusses the problem of estimating a linear relationship between two variables observed with errors. It focuses on confidence intervals for the slope parameter and confidence regions for the intercept and slope parameters in Gaussian models. A compendium of existing results as well as new results are presented.