bluuebunny/crossref_metadata_2025_split huggingface dataset:
On Some Smoothing Techniques Used in Image Restoration
Authors: Hall Peter , Titterington D. M. 
Published: December 2018

SUMMARY
The problem is considered of restoring a blurred and/or noisy image using various regularization prescriptions. Preliminary work concerns the invertibility of point spread functions and the construction of a stochastic model for images. A simple linear regularization procedure is introduced, as well as the special cases of constrained deconvolution, maximum entropy restoration and least-squares filtering. Optimal choices for the degree of smoothing are obtained for the case of low noise-to-signal ratios. Certain techniques, prevalent in the image-restoration literature for choosing the degree of smoothing, are shown to oversmooth, in a well-defined sense.
Cross-Validation Shrinkage of Regression Predictors
Authors: Copas J. B. 
Published: December 2018

SUMMARY
Copas (1983) suggests that shrinkage of predictors can be related to the least squares slope of actual on predicted values in a new set of data. Considering multiple regression in a crossvalidatory setting, this shrinkage slope is approximated by an estimable function of the fitted residuals. Patterns of heteroscedasticity of residual variance can lead to more, or less, shrinkage of least squares. A new predictor using a nonparametric shrinkage multiplier is proposed.
Common Structure of Techniques for Choosing Smoothing Parameters in Regression Problems
Authors: Hall Peter , Titterington D. M. 
Published: December 2018

SUMMARY
Two general methods have been used for choosing the degree of smoothing in both linear ridge-regression and nonparametric regression. One is based on a criterion of minimum risk and the other is based on a measure of fit to the data as summarised by a statistic based on the residuals. The comparative effects of these two approaches are investigated and one popular version of the second method is shown to oversmooth quite drastically. The work also generates alternative suggestions for data-based smoothing prescriptions, and elucidates the heuristic argument of Wahba (1983).
On Posterior Asymptotic Normality and Asymptotic Normality of Estimators for the Galton-Watson Process
Authors: Scott David 
Published: December 2018

SUMMARY
For a Galton-Watson process with offspring distribution pθ, where θ is an unknown parameter, asymptotic posterior normality is established for θ and for the mean of the offspring distribution. A form of asymptotic normality for the mean of the offspring distribution is also obtained, without restriction on whether the process is supercritical or not, provided that the total number of offspring increases to infinity. A non-Bayesian procedure is suggested for testing for supercriticality of the Galton-Watson process.
Statistical Models of Chemical Kinetics in Liquids
Authors: Clifford Peter , Green N. J. B. , Pilling M. J. 
Published: December 2018

SUMMARY
Statistical methods are used increasingly in theoretical chemistry. Applications range from the use of stochastic relaxation techniques in determining minimum energy molecular configurations to dynamical Monte Carlo simulations of molecular motion in liquids. This paper focuses on diffusion-controlled reactions in radiation chemistry. Here the interest is in describing the evolution of isolated clusters, containing a few chemically active particles, resulting from the passage of ionising radiation through a liquid. The subsequent chemistry is determined by the rate at which these particles can encounter each other, pairwise, in the course of their random motion. Classically the trajectories of the particles are described as sample paths of a continuous stochastic process, which in many cases can be assumed to be a diffusion. We have devised an approximate theory based on the approximation that pair distances evolve independently. The effect of this geometric distortion has been studied for small systems by simulation. The extension of this work to a wider class of realistic chemical processes poses many problems. Analytical progress is difficult and methods of simulating large spatial systems are not well developed. Problems which remain to be solved relate to the random geometry of the cluster as its constituent particles diffuse, the development of good approximations to first passage time distributions for diffusions with inhomogeneous drift and methods for the analysis of random motion in a liquid on the basis of detailed non-Markovian models of molecular movement.
Parametric Collapsibility and the Lack of Moderating Effects in Contingency Tables with a Dichotomous Response Variable
Authors: Wermuth Nanny 
Published: December 2018

SUMMARY
We consider contingency tables having one variable specified as a response with just two categories. We look at conditions for collapsibility of a symmetric and a directed measure of association, the odds-ratio and the relative risk: situations are discussed under which equal partial associations coincide with the corresponding marginal association. Contrary to the odds-ratio the relative risk is collapsible, if there are independencies in the marginal distribution of the influencing variables. This fact is exploited to derive conditions for the lack of a moderating effect, the latter being a much discussed concept in the social science literature.
Does Simple Random Sampling Provide Adequate Balance?
Authors: Cumberland W. G. , Royall R. M. 
Published: December 2018

SUMMARY
Theoretical arguments imply that, as the sample size increases, simple random sampling does not force balance fast enough to provide robust inference for a finite population total using the ratio estimator. An empirical study shows that under simple random sampling, confidence intervals for the total can have conditional coverage probabilities that are persistently awful as the sample size grows.
Adjusting Belief Structures
Authors: Goldstein Michael 
Published: December 2018

SUMMARY
Suppose that we have made various belief statements, but not a full probability specification, about a collection of random quantities. How do we modify uncertainties over one subset of the quantities, when given the values of another subset? We suggest an approach in which belief statements are organised into belief structures which are adjusted by observation on related belief structures and derive various properties of such adjustments. We give two examples. In the first example, belief adjustments are related to case statistics for regression diagnostics. In the second example adjusted structures are used to suggest designs for the localised regression model.
Local Computations with Probabilities on Graphical Structures and Their Application to Expert Systems
Authors: Lauritzen S. L. , Spiegelhalter D. J. 
Published: December 2018

SUMMARY
A causal network is used in a number of areas as a depiction of patterns of ‘influence’ among sets of variables. In expert systems it is common to perform ‘inference’ by means of local computations on such large but sparse networks. In general, non-probabilistic methods are used to handle uncertainty when propagating the effects of evidence, and it has appeared that exact probabilistic methods are not computationally feasible. Motivated by an application in electromyography, we counter this claim by exploiting a range of local representations for the joint probability distribution, combined with topological changes to the original network termed ‘marrying’ and ‘filling-in‘. The resulting structure allows efficient algorithms for transfer between representations, providing rapid absorption and propagation of evidence. The scheme is first illustrated on a small, fictitious but challenging example, and the underlying theory and computational aspects are then discussed.
A Generalization of a Nonparametric Test for Stochastically Ordered Distributions to Censored Survival Data
Authors: Mau Jochen 
Published: December 2018

SUMMARY
Currently used test statistics for stochastically increasing survival times in a k-sample problem are linear combinations of either Gehan (generalized Wilcoxon) or generalized Savage score sums. The power of these tests depends on a priori knowledge about the true form of the alternative. When isotonic regression is applied to these score sums, it yields a new trend test for right-censored survival data which generalizes to left-truncated survival data and to counting processes. In a Monte Carlo study, its empirical power is at least comparable with that of the linear trend tests in their standard form (without prior information), and it is markedly superior if only the last survival distribution turns out to be stochastically smaller or larger than the control distribution.
Collapsed Two-Way Contingency Tables and the Chi-Square Reduction Principle
Authors: Gilula Zvi , Krieger Abba M. 
Published: December 2018

SUMMARY
The value of the chi-square statistic for homogeneity of rows and columns in a contingency table remains unchanged if the table is collapsed (grouped) over homogeneous rows and columns. The difference between the chi-square values pertaining to the original table and to the collapsed table (the ‘chi-square reduction‘) is shown to have a meaningful canonical decomposition which can guide the researcher in detecting homogeneous rows and columns. The methodology proposed generalizes an earlier methodology suggested by Gilula for the same problem.
Shape Analysis of Triangles Through Directional Techniques
Authors: Mardia K. V. 
Published: December 2018

SUMMARY
Kendall has shown how the shape variables of a labelled triangle can be mapped to a point on a sphere. Using Mardia and Dryden's method, we obtain the shape distribution of triangles under Bookstein's model. Various properties are discussed and in particular we show that this distribution, transformed to the sphere, is approximately the Fisher distribution. In particular, we examine the reduction of this distribution when the shape space is reduced to a subset of the sphere. Some practical examples are given, and the hypothesis of central place theory for a geographical data set is reassessed.
A Multivariate Distribution with Weibull Connections
Authors: Crowder Martin 
Published: December 2018

SUMMARY
A simple form of multivariate distribution is defined which, for certain parameter values, has Weibull marginals. The distribution has a single parameter governing association between the variates, which may be positive, negative or zero. The simple forms for marginal and conditional distributions, hazard functions and densities make it attractive for practical application and interpretation.
Partial Separation in Logistic Discrimination
Authors: Lesaffre E. , Albert A. 
Published: December 2018

SUMMARY
The problem of maximum likelihood estimates in logistic discrimination is receiving growing attention in the literature. The existence is known to be highly dependent on the data configuration observed. Here we focus on the practically important case where the group samples form a set of clusters that are completely separated from each other, which we call ‘partial separation'. The classical Fisher iris data set is a good example of the problem discussed. A non-existence theorem is proven and a general algorithm is developed to help to distinguish separation from multicollinearity given divergence in maximum likelihood estimation.
Spherical Regression on Matched Pairs of Orientation Statistics
Authors: Prentice Michael J. 
Published: December 2018

SUMMARY
The matched pairs section of the analysis of 3 times 3 orientation statistics in Prentice (1986) may be improved on by constructing a rotational regression model, an analogue of spherical regression. The results obtained are relatively simple consequences of the work of Chang and are therefore presented here for general orientation statistics—rigid orthogonal m frames in p dimensions—before application to the matched pairs of vectorcardiogram orientations (m = p = 3) which provided the original motivation for this paper.
Chebyshev Polynomial Approximations for Characteristic Function Estimation: Some Theoretical Supplements
Authors: Madan D. B. , Seneta E. 
Published: December 2018

SUMMARY
Densities for the angle Θ = uX(mod 2π) and the cosine Y = cos(uX) can be expressed, through Fourier methods, in terms of the characteristic function of X. Thus, if X has a characteristic function of closed form, the parameters of its distribution may be estimated by maximum likelihood. The paper addresses the problems of estimability of asymmetric distributions and situations where the method may not apply.
Best Conditional Tests for Separate Families of Hypotheses
Authors: Pace L. , Salvan A. 
Published: December 2018

SUMMARY
We consider, from the viewpoint of hypotheses testing, the problem of assigning the probability density function of a random variable X to one of two separate families of distributions. Our aim is to study the possibility of constructing best similar tests. For this, we characterize sufficient statistics for the union of the two families; completeness is also studied. We state conditions under which the test statistics are easily obtainable when both families are of the generalized exponential type. As an illustration, many examples are given solving both new and previously worked problems of choice between separate families of hypotheses. The relative merits of the exact best test and of asymptotic tests are empirically investigated in small samples when testing for the log-normal versus the gamma distribution.
Computation of Theoretical Autocovariance Matrices of Multivariate Autoregressive Moving Average Time Series
Authors: Mittnik Stefan 
Published: December 2018

SUMMARY
Matrix expressions relating the theoretical autocovariances of autoregressive moving average (ARMA) processes to their parameters are derived and used to design an efficient procedure for computing autocovariance sequences of multivariate ARMA processes. The method proposed is more efficient than others suggested in the literature and, in particular, reduces the computational burden associated with exact maximum likelihood estimation of ARMA models. The closed form expressions facilitate the implementation of algorithms for computing multivariate autocovariances.
A New Approach to Frequency Analysis with Amplified Harmonics
Authors: Truong-Van B. 
Published: December 2018

SUMMARY
For stationary time series having a mixed spectrum, we introduce a new method for estimating the discrete frequencies based on amplification of the sine waves in the time series and on minimization of least squares regressions on amplified waves. Under the assumption that the continuous part of the spectrum arises from a stationary autoregressive moving average process, we show that the estimators for the discrete frequencies obtained with this method are strongly consistent: more precisely, as the serial length n tends to infinity, their bias almost surely converges to zero with the rate n−3/2(logn)δ,δ&gt;12. We also establish a central limit theorem which shows that these estimators have exactly the same asymptotic variance as that given by Whittle's method, which is known to yield the most accurate frequency estimates. However, the new technique has two advantages over Whittle's method. First, it yields an algorithm that is both robust against improper starting estimates and computationally efficient. Secondly, it gives rise to a simple tool based on its amplified harmonics for identifying the number of sine waves in a time series. A simulation study is also reported that gives statistical results on the properties of the new method on simulated series as well as comparative results with Whittle's method.
Continuum Regression: Cross-Validated Sequentially Constructed Prediction Embracing Ordinary Least Squares, Partial Least Squares and Principal Components Regression
Authors: Stone M. , Brooks R. J. 
Published: December 2018

SUMMARY
The paper addresses the evergreen problem of construction of regressors for use in least squares multiple regression. In the context of a general sequential procedure for doing this, it is shown that, with a particular objective criterion for the construction, the procedures of ordinary least squares and principal components regression occupy the opposite ends of a continuous spectrum, with partial least squares lying in between. There are two adjustable ‘parameters’ controlling the procedure: ‘alpha’, in the continuum [0, 1], and ‘omega’, the number of regressors finally accepted. These control parameters are chosen by cross-validation. The method is illustrated by a range of examples of its application.
Uniform Saddlepoint Approximations and Log-Concave Densities
Authors: Jensen Jens Ledet 
Published: December 2018

SUMMARY
For a one-dimensional variable with a log-concave density it is shown that the saddlepoint approximations to the density and the distribution function of the mean are uniformly valid. A double-saddlepoint approximation to a conditional distribution function is introduced, which is uniformly valid for a two-dimensional log-concave density. The results are illustrated with the log-normal distribution and the gamma distribution.
Existence of Maximum Likelihood Estimates for Interval-Censored Data from Some Three-Parameter Models with a Shifted Origin
Authors: Nakamura T. 
Published: December 2018

SUMMARY
Given data in the form of interval-censored observations from a three-parameter distribution, practical criteria are established for the existence of maximum likelihood estimates for three kinds of parameter space. These criteria can be derived by analysing the behaviour of the log-likelihood near a type of boundary of the parameter space, called the probability contents inner boundary. The effectiveness of the criteria is discussed. In the case where the underlying distribution is a three-parameter log-normal distribution, the efficiency of the criteria is evaluated by simulation.
Estimating the Mean and Covariance Structure Nonparametrically When the Data are Curves
Authors: Rice John A. , Silverman B. W. 
Published: December 2018

SUMMARY
We develop methods for the analysis of a collection of curves which are stochastically modelled as independent realizations of a random function with an unknown mean and covariance structure. We propose a method of estimating the mean function non-parametrically under the assumption that it is smooth. We suggest a variant on the usual form of cross-validation for choosing the degree of smoothing to be employed. This method of cross-validation, which consists of deleting entire sample curves, has the advantage that it does not require that the covariance structure be known or estimated. In the estimation of the covariance structure, we are primarily concerned with models in which the first few eigenfunctions are smooth and the eigenvalues decay rapidly, so that the variability is predominantly of large scale. We propose smooth nonparametric estimates of the eigenfunctions and a suitable method of cross-validation to determine the amount of smoothing. Our methods are applied to data on the gaits of a group of 5-year-old children.
Nonparametric Regression: Optimal Local Bandwidth Choice
Authors: Vieu Philippe 
Published: December 2018

SUMMARY
Kernel estimators of a regression function are investigated. The bandwidths are locally chosen by a data-driven method based on the minimization of a local cross-validation criterion. This method is shown to be asymptotically optimal with respect to local quadratic measures of errors. Monte Carlo experiments are presented, and finally the method is applied to some data of medical interest.
Exponential Linear Models: A Two-Pass Procedure for Saddlepoint Approximation
Authors: Fraser D. A. S. , Reid N. , Wong A. 
Published: December 2018

SUMMARY
For an exponential linear model, the saddlepoint method gives accurate approximations for the density of the minimal sufficient statistic or maximum likelihood estimate, and for the corresponding distribution functions. In this paper we describe a simple numerical procedure that constructs such approximations for a real parameter in an exponential linear model, using only a two-pass calculation on the observed likelihood function for the original data. Simple examples of the numerical procedure are discussed, but we take the general accuracy of the saddlepoint procedure as given. An immediate application of this is to exponential family models, where inference for a component of the canonical parameter is to be based on the conditional density of the corresponding component of the sufficient statistic, given the remaining components. This conditional density is also of exponential family form, but its functional form and cumulant-generating function may not be accessible. The procedure is applied to the corresponding likelihood, approximated as the full likelihood divided by an approximate marginal likelihood obtained from Barndorff-Nielsen's formula. A double saddlepoint approximation provides another means of bypassing this difficulty. The computational procedure is also examined as a numerical procedure for obtaining the saddlepoint approximation to the Fourier inversion of a characteristic function. As such it is a two-pass calculation on a table of the cumulant-generating function.
Likelihood and Cost as Path Integrals
Authors: Whittle P. 
Published: December 2018

SUMMARY
We consider the optimal estimation, prediction and control etc. of time series. The essence of a path integral characterization is considered to be that optimal estimates and decisions etc. are obtained by the free extremization of some form. In Sections 2–5 it is shown for some stock situations that this property is ensured by the direct maximization of likelihood (rather than by appeal to the formally equivalent but operationally contrasting least square principle). In Sections 6–9 a risk-sensitive criterion is taken, in that the criterion is an exponential function of cost rather than cost itself. It is shown that this class of problems admits a natural path integral treatment, in which extremization of stress replaces separate extremization of likelihood and cost. A stochastic maximum principle is derived. For the linear–quadratic–Gaussian (LQG) case, results are exact and depend on proof of a certainty equivalence principle. In the non-LQG case they are valid as large deviation approximations, depending on a formalism going back to Bartlett. Finally, in Sections 10 and 11 we note the efficacy (if not indeed the necessity) of direct likelihood arguments in two other time series areas: recursive estimation and structural models.
A Note on the Construction of Row-And-Column Designs with Two Replicates
Authors: Bailey R. A. , Patterson H. D. 
Published: December 2018

SUMMARY
This paper shows that useful designs for variety trials with two replicates, each arranged in a compact array of plots, can be derived from existing row-and-column designs for two non-interacting sets of treatments. Combinatorial and statistical properties are preserved; in particular, if the original design is efficient, then so is the new design.
Inferences on Multivariate Measures of Interclass and Intraclass Correlations in Familial Data
Authors: Konishi Sadanori , Khatri C. G. , Rao C. Radhakrishna 
Published: December 2018

SUMMARY
Multivariate measures of interclass and intraclass correlations are introduced to assess the degree of resemblance between family members with respect to more than one characteristic. Unified estimators for the multivariate measures are proposed as the eigenvalues of certain random matrices constructed by the matrices of the weighted sums of squares and products of observations. Asymptotic distributions of the proposed estimators are derived under the assumption of multivariate normality. The asymptotic results produce approximate confidence intervals and test procedures in a simple way.