bluuebunny/crossref_metadata_2025_split huggingface dataset:
Multidimensional Markov Chain Models for Image Textures
Authors: Qian W. , Titterington D. M. 
Published: December 2018

SUMMARY
Multidimensional Markov chain models are developed for texture. By suitable choice of parameters, textures can be simulated that are similar to those generated by Markov random field models, but the simulation procedure is computationally much more economical. The problem of parameter estimation is examined for non-noisy and noisy data. In the latter case, procedures are developed for simultaneous parameter estimation and image restoration. Illustrative examples are provided.
Constrained Monte Carlo Maximum Likelihood for Dependent Data
Authors: Geyer Charles J. , Thompson Elizabeth A. 
Published: December 2018

SUMMARY
Maximum likelihood estimates (MLEs) in autologistic models and other exponential family models for dependent data can be calculated with Markov chain Monte Carlo methods (the Metropolis algorithm or the Gibbs sampler), which simulate ergodic Markov chains having equilibrium distributions in the model. From one realization of such a Markov chain, a Monte Carlo approximant to the whole likelihood function can be constructed. The parameter value (if any) maximizing this function approximates the MLE. When no parameter point in the model maximizes the likelihood, the MLE in the closure of the exponential family may exist and can be calculated by a two-phase algorithm, first finding the support of the MLE by linear programming and then finding the distribution within the family conditioned on the support by maximizing the likelihood for that family. These methods are illustrated by a constrained autologistic model for DNA fingerprint data. MLEs are compared with maximum pseudolikelihood estimates (MPLEs) and with maximum conditional likelihood estimates (MCLEs), neither of which produce acceptable estimates, the MPLE because it overestimates dependence, and the MCLE because conditioning removes the constraints.
A Goodness-Of-Fit Test for Time Series with Long Range Dependence
Authors: Beran Jan 
Published: December 2018

SUMMARY
We propose a test statistic for goodness of fit in time series with slowly decaying serial correlations. The asymptotic distribution of the test statistic, originally proposed by Milhoj for time series with smooth spectra, turns out to be the same, under the null hypothesis, even if the spectrum has a pole at 0. In particular, the test is suitable to detect lack of independence in the observations, or estimated residuals, if the first few correlations are small but the decay of the correlations is slow.
Embedded Models in Non-Linear Regression
Authors: Cheng R. C. H. , Evans B. E. , Iles T. C. 
Published: December 2018

SUMMARY
A problem that is often encountered in non-linear regression is instability in the computation of parameter estimates. Such instability may arise from models with too many parameters, resulting in estimating equations that are ill conditioned and consequent problems of identification. This paper shows that in some cases these difficulties can be explained by the presence of an embedded model, a special case of the original model involving fewer parameters but one that is not readily identified from the parameterization of the model. The paper shows how an embedded model can be identified by making a suitable reparameterization. Moreover this reparameterization removes the problems of numerical instability where an embedded model turns out to be the best fit to the data. The paper suggests how the reparameterization can be chosen systematically. Numerical examples are included to illustrate these points.
On the Expected Amount of Information from a Non-Linear Model
Authors: Polson Nicholas G. 
Published: December 2018

SUMMARY
An approach to quantifying the amount of information that an experimenter expects to learn from a non-linear model is given. An expected utility for an experiment, ξ, motivated by the asymptotic form of Shannon information gain between prior and posterior, is defined. This leads to a characterization of the experimenter who expects to learn the most from a non-linear model. Such an experimenter has the design-dependent Jeffreys prior. Sufficient regularity conditions for the equivalence with asymptotic Shannon information gain are given. An application to the optimal selection of sample size from a model with exponential family errors and the Michaelis-Menten model is discussed. A link between the regularity conditions for asymptotic posterior normality and the Jeffreys prior is given.
A Type of Second-Order Asymptotic Independence
Authors: Barndorff-Nielsen O. E. , Blæsild P. 
Published: December 2018

SUMMARY
Suppose that a random vector x is partitioned into two subvectors and that generic coordinates of these subvectors are indicated by xa, xb, … and xr, xs, … respectively. If the joint cumulant (matrix) (ka,r) equals 0 then xa and xr are asymptotically independent to order O(n -1/2) under ordinary repeated sampling. When the third-order joint cumulant (array) (ka,b,r) is also 0 this independence statement may be sharpened to asymptotic independence to order O(n -1) of xr and the residuals of xa after quadratic regression on xr. Various examples where this applies to likelihood analysis are discussed.
Multivariate Regression Analyses for Categorical Data
Authors: Liang Kung-Yee , Zeger Scott L. , Qaqish Bahjat 
Published: December 2018

SUMMARY
It is common to observe a vector of discrete and/or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes. The response vector can comprise repeated observations on one variable, as in longitudinal studies or genetic studies of families, or can include observations for different variables. This paper discusses a class of models for the marginal expectations of each response and for pairwise associations. The marginal models are contrasted with log-linear models. Two generalized estimating equation approaches are compared for parameter estimation. The first focuses on the regression parameters; the second simultaneously estimates the regression and association parameters. The robustness and efficiency of each is discussed. The methods are illustrated with analyses of two data sets from public health research.
Diagnostic Results Concerning a Measure of Rotatability
Authors: Khuri André I. 
Published: December 2018

SUMMARY
The measure of rotatability introduced by Khuri is utilized to determine the closeness of the prediction variance to being constant on a sphere S(r) of radius r centred at the origin. In particular, several upper bounds on the range of the prediction variances on S(r) are obtained. These upper bounds provide information about the amount of dispersion that can exist in the prediction variances on all spheres inside a region of interest. Such information gives added insight into the nature of ‘near rotatability’ of a given response surface design. This is illustrated in an example involving four designs: the 32 factorial and three hybrid designs described by Roquemore, namely the 310, 311A and 311B designs.
Likelihood, Quasi-Likelihood and Pseudolikelihood: Some Comparisons
Authors: Nelder J. A. , Lee Y. 
Published: December 2018

SUMMARY
There is considerable interest in the fitting of models jointly to the mean and dispersion of a response. For the mean parameter, the Wedderburn estimating equations are widely accepted. However, there is some controversy about estimating the dispersion parameters. Finite sampling properties of several dispersion estimators are investigated for three models by simulation. We compare the maximum extended quasi-likelihood estimator, the maximum pseudolikelihood estimator and the maximum likelihood estimator, if it exists. Of these estimators, the maximum extended quasi-likelihood estimator is usually superior in minimizing the mean-squared error.
Estimating Dimension in Noisy Chaotic Time Series
Authors: Smith Richard L. 
Published: December 2018

SUMMARY
This paper is concerned with estimating the dimension of an attractor. The Grassberger–Procaccia procedure for estimating the correlation dimension is reviewed, and some alternative estimators considered. A particularly important problem is to estimate dimension in the presence of noise in the data. In pursuit of this, a modification of the Grassberger–Procaccia procedure is proposed, and illustrated on both artificial and real data sets.
Finding Chaos in Noisy Systems
Authors: Nychka Douglas , Ellner Stephen , Gallant A. Ronald , McCaffrey Daniel 
Published: December 2018

SUMMARYIn the past 20 years there has been much interest in the physical and biological sciences in non‐linear dynamical systems that appear to have random, unpredictable behaviour. One important parameter of a dynamical system is the dominant Lyapunov exponent (LE). When the behaviour of the system is compared for two similar initial conditions, this exponent is related to the rate at which the subsequent trajectories diverge. A bounded system with a positive LE is one operational definition of chaotic behaviour. Most methods for determining the LE have assumed thousands of observations generated from carefully controlled physical experiments. Less attention has been given to estimating the LE for biological and economic systems that are subjected to random perturbations and observed over a limited amount of time. Using nonparametric regression techniques (neural networks and thin plate splines) it is possible to estimate the LE consistently. The properties of these methods have been studied with simulated data and are applied to a biological time series: marten fur returns for the Hudson Bay Company (1820–1900). On the basis of a nonparametric analysis there is little evidence for low dimensional chaos in these data. Although these methods appear to work well for systems perturbed by small amounts of noise, finding chaos in a system with a significant stochastic component may be difficult.
A Central Limit Theorem for Latin Hypercube Sampling
Authors: Owen Art B. 
Published: December 2018

SUMMARY
Latin hypercube sampling (LHS) is a technique for Monte Carlo integration, due to McKay, Conover and Beckman. M. Stein proved that LHS integrals have smaller variance than independent and identically distributed Monte Carlo integration, the extent of the variance reduction depending on the extent to which the integrand is additive. We extend Stein's work to prove a central limit theorem. Variance estimation methods for nonparametric regression can be adapted to provide N 1/2-consistent estimates of the asymptotic variance in LHS. Moreover the skewness can be estimated at this rate. The variance reduction may be explained in terms of certain control variates that cannot be directly measured. We also show how to combine control variates with LHS. Finally we show how these results lead to a frequentist approach to computer experimentation.
Information Bounds for the Conditional Hazard Ratio in a Nested Family of Regression Models
Authors: Sasieni Peter 
Published: December 2018

SUMMARY
Information bounds are obtained for a parametric treatment effect in a nested family of models for the conditional distribution of survival given confounding variables. The family extends from the fully parametric Weibull model to a completely nonparametric model for right-censored data and includes the Cox model and the stratified version of it. It is shown that, in certain special cases, there is no loss of information about the treatment effect when going from a fully parametric to a nonparametric specification of the conditional hazard function.
Maximum Likelihood Regression on Relevant Components
Authors: Helland Inge S. 
Published: December 2018

SUMMARY
Most regression methods for multicollinear data are only based on assumptions about the conditional distribution of the dependent variable, given the explanatory variables. Here we propose a new prediction method taking a joint multinomial distribution for all the variables as the starting point. A hypothesis is formulated stating that only a fixed small number of components constructed from the explanatory variables is relevant for prediction, and maximum-likelihood-type estimates of the parameters in the model are developed under this hypothesis.
Time Series of Continuous Proportions
Authors: Grunwald Gary K. , Raftery Adrian E. , Guttorp Peter 
Published: December 2018

SUMMARY
A vector of continuous proportions consists of the proportions of some total accounted for by its constituent components. An example is the proportions of world motor vehicle production by Japan, the USA and all other countries. We consider the situation where time series data are available and where interest focuses on the proportions rather than the actual amounts. Reasons for analysing such times series include estimation of the underlying trend, estimation of the effect of covariates and interventions, and forecasting. We develop a state space model for time series of continuous proportions. Conditionally on the unobserved state, the observations are assumed to follow the Dirichlet distribution, often considered to be the most natural distribution on the simplex. The state follows the Dirichlet conjugate distribution which is introduced here. Thus the model, although based on the Dirichlet distribution, does not have its restrictive independence properties. Covariates, trends, seasonality and interventions may be incorporated in a natural way. The model has worked well when applied to several examples, and we illustrate with components of world motor vehicle production.
Spherical Median Axes
Authors: Fisher N. I. , Lunn A. D. , Davies S. J. 
Published: December 2018

SUMMARY
In an earlier paper, Fisher defined the notion of a median direction for data from a unimodal distribution of three-dimensional unit vectors and studied its statistical properties. Corresponding notions of a median axis for bipolar axial or great circle data were also suggested but not analysed. This paper gives a statistical treatment of spherical median axes, including their asymptotic relative efficiencies, and a comparison with the customary principal or polar axis estimators using asymptotic relative efficiencies. The sample spherical median axes enjoy the same sort of resistance to outlying values as do the median vector, spatial median and linear median.
Saddlepoint Approximations for Tests of Block Independence, Sphericity and Equal Variances and Covariances
Authors: Butler Ronald W. , Huzurbazar S. , Booth James G. 
Published: December 2018

SUMMARY
Approximations for the null distribution of various test statistics arising in multivariate analysis using Skovgaard's saddlepoint formula are discussed. In each case an approximation is found with such accuracy as to obviate the need for exact computation.
Simple Modifications for Signed Roots of Likelihood Ratio Statistics
Authors: Diciccio Thomas J. , Martin Michael A. 
Published: December 2018

SUMMARY
In the context of inference about a scalar parameter in the presence of nuisance parameters, some simple modifications for the signed root of the log-likelihood ratio statistic R are developed that reduce the order of error in the standard normal approximation to the distribution of R from O(n -1/2) to O(n -1). Barndorff-Nielsen has introduced a variable U such that the error in the standard normal approximation to the distribution of R + R -1 log(U/R) is of order O(n -3/2), but calculation of U requires the specification of an exact or approximate ancillary statistic A. This paper proposes an alternative variable to U, denoted by T, that is available without knowledge of A and satisfies T = U + Op(n -1) in general. Thus the standard normal approximation to the distribution of R + R -1 log(T/R) has error of order O(n -1), and it can be used to construct approximate confidence limits having coverage error of order O(n -1). In certain cases, however, T and U are identical. The derivation of T involves the Bayesian approach to constructing confidence limits considered by Welch and Peers, and Peers. Similar modifications for the signed root of the conditional likelihood ratio statistic are also developed, and these modifications are seen to be useful when a large number of nuisance parameters are present. Several examples are presented, including inference for natural parameters in exponential models and inference about location-scale models with type II censoring. In each case, the relationship between T and U is discussed. Numerical examples are also given, including inference for regression models, inference about the means of log-normal distributions and inference for exponential lifetime models with type I censoring, where Barndorff-Nielsen's variable U is not available.
Correlation Tests for Non-Linear Alternatives
Authors: Barbour A. D. , Cost M. 
Published: December 2018

SUMMARY
A new class of statistics for detecting association between two variables is proposed. The statistics improve on traditional correlation coefficients by being sensitive to U-shaped and other non-linear relationships between the variables. If both variables are one dimensional, they can be simply defined in terms of ranks, so that their null distributions can in principle be tabulated. Asymptotic discrimination of order n− 1/2 is obtained for any alternative of a continuous functional relationship between the variables. Power against trend alternatives is investigated by simulation.
Strong Collapsibility of Association Measures in Linear Models
Authors: Geng Zhi , Asano Chooichiro 
Published: December 2018

SUMMARY
A measure of association in linear models is strongly collapsible over a discrete background variable if it remains unchanged no matter how the background variable is partially pooled and if it also coincides with the corresponding marginal measure of association. Strong collapsibility implies that the measure of association can be studied no matter how the background variable is categorized and no matter whether or not it is recorded. In this paper, necessary and sufficient conditions are given for strong collapsibility of the measure of association in linear models.
Varying-Coefficient Models
Authors: Hastie Trevor , Tibshirani Robert 
Published: December 2018

SUMMARY
We explore a class of regression and generalized regression models in which the coefficients are allowed to vary as smooth functions of other variables. General algorithms are presented for estimating the models flexibly and some examples are given. This class of models ties together generalized additive models and dynamic generalized linear models into one common framework. When applied to the proportional hazards model for survival data, this approach provides a new way of modelling departures from the proportional hazards assumption.
Regional Modelling of Extreme Storms Via Max-Stable Processes
Authors: Coles Stuart G. 
Published: December 2018

SUMMARY
Asymptotic models for extremes of random processes often form the basis for estimating the extremal behaviour of environmental phenomena. Most such phenomena have a spatial dimension, and the aim of this paper is to develop a procedure for modelling in continuous space the spatial dependence within extreme events. A principal objective in the analysis—as with other current research on extremes—is to base inference on as much of the available data as possible. The modelling procedures are justified on simulated data and subsequently applied to a series of rainfall data.
Improved Estimators of Variance Components with Smaller Probability of Negativity
Authors: Kelly Robert J. , Mathew Thomas 
Published: December 2018

SUMMARY
A linear model with two variance components is considered, one variance component (say, σ 1 2 ≥ 0) corresponding to a random effect, and a second variance component (say, σ 2 &gt; 0) corresponding to the experimental errors. A class of invariant quadratic estimators (IQEs) is characterized, having uniformly smaller mean-squared error (MSE), and uniformly smaller probability of negativity, compared with the analysis-of-variance (ANOVA) estimator of σ 1 2. It turns out that for balanced models, among IQEs of σ 1 2 with uniformly smaller MSE than its ANOVA estimator, there exists an IQE with the smallest probability of being negative, uniformly in the parameters. The results are applied to the balanced one-way classification model. Numerical computations show that the MSE improvement achievable through the use of the proposed estimators is quite significant. It is noted that, for the nonnegative estimation of σ 1 2, truncation of one of the proposed estimators at 0 provides a satisfactory solution. Extension of the results to the unbalanced case, and to the general mixed model with balanced data, is also indicated.
Affine Invariant Multivariate One-Sample Sign Tests
Authors: Hettmansperger Thomas P. , Nyblom Jukka , Oja Hannu 
Published: December 2018

SUMMARY
Brown and Hettmansperger introduced an affine invariant bivariate analogue of the sign test based on the generalized median of Oja. In this paper its general multivariate extension is presented. The proposed multivariate permutation or sign change test is affine invariant with an easily computable covariance matrix. For elliptic distributions the proposed test and Randles's test are asymptotically equivalent. Formulae for calculating asymptotic relative efficiencies of the proposed test and the Oja multivariate median are given. Lower bounds for the efficiencies of the new test (and the Randles test) relative to the classical Hotelling test are established for elliptic alternatives and for unimodal elliptic alternatives. Relative efficiencies under multivariate t-distributions are also tabulated. The theory is illustrated by a simple example.
Nonparametric Estimation of Component Lifetime Based on Masked System Life Test Data
Authors: Schäbe Hendrik 
Published: December 2018

SUMMARY
In this paper we study the model of masked data sets, i.e. data sets consisting of failure times of a system and sets of failed components. Failing components can yield further failures. The initially failed component is unknown. Initial failures and later failures are indistinguishable. A nonparametric estimator of the component lifetime distribution is derived. We prove weak convergence of the estimator to a Gaussian process.
Nonparametric Conditional Inference for a Location Parameter
Authors: Severini Thomas A. 
Published: December 2018

SUMMARY
Let Y 1, ..., Yn denote independent observations of the form Yj = θ + σεj where ε 1, ..., εn are independent random variables each distributed according to a density p, and θ and σ are unknown parameters. This paper presents a method for conditional inference about the location parameter θ that does not require the specification of a parametric family of densities for p. This method uses the configuration statistic to select the density p and is based on the work of Fraser.
Boundary Estimation in Ring Recovery Models
Authors: Catchpole E. A. , Morgan B. J. T. 
Published: December 2018

SUMMARY
A simple model for avian survival often leads to boundary estimates when the model is fitted to data by maximum likelihood. Data may result from ring recovery experiments alone, or in combination with a radio tracking investigation. A study of profile likelihoods enables the conditions under which boundary estimates occur to be completely specified. Fitting an incorrect model is shown to result in inconsistent estimators of all parameters, and an asymptotic certainty of boundary estimates.