bluuebunny/crossref_metadata_2025_split huggingface dataset:
Collapsibility of Multidimensional Contingency Tables
Authors: Whittemore Alice S. 
Published: December 2018

Summary
Multidimensional contingency tables can be summed over factors, without affecting the log-linear parameters describing interactions of other factors, under less restrictive conditions than generally recognized. Examples are given that contradict a theorem of Bishop, Fienberg and Holland (1975). Necessary and sufficient conditions for collapsibility are given, and an example applying the results to categorical data is presented.
Block Total Response as an Alternative to the Randomized Response Method in Surveys
Authors: Raghavarao D. , Federer W. T. 
Published: December 2018

Summary
The randomized response technique appears to have been an innovative and useful procedure for eliciting reliable responses from individuals on sensitive or embarrassing questions. In this paper a new and alternative method is proposed for the same problem. Through the use of supplemented block, (v, k, r, b. λ) balanced incomplete block, and spring balance weighing designs, the individual is required to give a total of the responses to k questions, sensitive or not. From these block totals it is possible to obtain estimated responses for each of the v questions used in the survey, yet not obtain individual response to single questions. Anonymity of response for a single interviewee is thus maintained. Estimators and their variances for the estimated responses are obtained. The method allows the surveyor to obtain answers to several sensitive questions without being unduly time-consuming.
Maximum Likelihood Inference for Multiple Regression with Missing Values: A Simulation Study
Authors: Little Roderick J. A. 
Published: December 2018

Summary
Maximum likelihood inference for the coefficients of a multiple regression with missing values is studied by simulation, using artificially generated multivariate normal observations with randomly deleted missing values. The method is compared with least squares on the complete observations by mean squared error. Two methods of estimating the covariance matrix of the m.l. estimates are compared, and the applicability of large sample theory to obtain tests and confidence intervals for the regression coefficients is considered for moderate size samples.
On the Structural Representation for Polynomial-Projecting Predictor Models Based on the Kalman Filter
Authors: Godolphin E. J. , Stone J. M. 
Published: December 2018

Summary
Harrison and Stevens (1976) give a general class of dynamic linear models which incorporates a stochastic structure for describing model components and which utilizes the Kalman filter algorithm to update the system. This paper derives conditions for the dynamic linear models to yield polynomial-projecting predictors which do not have limiting constraints imposed upon them. Some examples of structurally simple models which satisfy these conditions are given, and the use of a diagonal covariance matrix for the system disturbances is discussed.
Reduced-Rank Regression and Canonical Analysis
Authors: Tso M. K.-S. 
Published: December 2018

SUMMARY
We show that maximum-likelihood analysis of the reduced-rank regression model exploits a fundamental inequality result of matrix theory when a normally distributed error structure with unknown covariance is assumed. This approach closely parallels the corresponding analysis when the covariance matrix is known (Davies and Tso, 1980) and demonstrates straightforwardly the intimate connection between reduced-rank regression and canonical analysis. A geometric interpretation of the analysis is given.
Scale Parameters: A Bayesian Treatment
Authors: Sweeting Trevor 
Published: December 2018

Summary
A definition of a scale parameter ϕ is given which includes the usual definition of a scale parameter in the exponential family. Some suggestions for the estimation of ϕ and approximations to the marginal posterior distribution of θ, a vector-valued parameter of primary interest, are made. In particular, the possibility of a χ2 approximation to the posterior distribution of ϕ, leading to h.p.d. regions for θ based on the F distribution, is explored. Two examples are discussed, where observations are from a normal and gamma distribution.
A Note on an Alternative Outlier Model
Authors: Cook R. D. , Holschuh N. , Weisberg S. 
Published: December 2018

Summary
This paper examines modelling a single outlier in the normal theory fixed effects linear model as arising from an unknown observation with inflated variance. The maximum likelihood estimates are characterized in terms of standard least squares statistics. The estimated position of the outlier does not necessarily agree with the estimated position under the usual mean slippage outlier model, and an example where they differ is presented. A sufficient and common condition for agreement is given.
Scaling Binary Data Using a Factor Model
Authors: Bartholomew D. J. 
Published: December 2018

SUMMARY
A simple method for scaling a set of binary responses is proposed using the logit factor model of Bartholomew (1980). It is shown that individuals may be ranked on the basis of a linear combination, ∑αi x i of the responses (xi = 0 or 1) where the αi's are the appropriate factor loadings. This completely avoids the need to calculate the y-scores suggested in Bartholomew (1980) and hence the heavy numerical integration which that method involves.
Multinomial Goodness-Of-Fit Tests
Authors: Cressie Noel , Read Timothy R.C. 
Published: December 2018

SUMMARY
This article investigates the family {I λ;λ ϵ ℝ} of power divergence statistics for testing the fit of observed frequencies {Xi; i = 1, …, k} to expected frequencies {Ei; i = 1, …, k}. From the definition 2nIλ=2λ(λ+1)∑i=1kXi{(XiEi)λ−1};λ∈ℝ
it can easily be seen that Pearson's X 2 (λ = 1), the log likelihood ratio statistic (λ = 0), the Freeman-Tukey statistic (λ = –½) the modified log likelihood ratio statistic (λ = –1) and the Neyman modified X 2 (λ = –2), are all special cases. Most of the work presented is devoted to an analytic study of the asymptotic difference between different I λ however finite sample results have been presented as a check and a supplement to our conclusions. A new goodness-of-fit statistic, where λ = ⅔, emerges as an excellent and compromising alternative to the old warriors, I 0 and I 1.
Estimation and Hypothesis Testing in Finite Mixture Models
Authors: Aitkin Murray , Rubin Donald B. 
Published: December 2018

SUMMARY
Finite mixture models are a useful class of models for application to data. When sample sizes are not large and the number of underlying densities is in question, likelihood ratio tests based on joint maximum likelihood estimation of the mixing parameter, λ, and the parameter of the underlying densities, θ, are problematical. Our approach places a prior distribution on λ and estimates θ by maximizing the likelihood of the data given θ with λ integrated out. Advantages of this approach, computational issues using the EM algorithm and directions for further work are discussed. The technique is applied to two examples.
The Appropriateness of the Asymptotic Distribution in a Nonlinear Regression Model in Relation to Curvature
Authors: Hougaard P. 
Published: December 2018

SUMMARY
In a non-linear regression model, correction terms for the asymptotic distribution of the maximum likelihood estimator are found. They can all be evaluated by the parameter dependent part of Beale's (1960) measure of non-linearity and some of the terms can be evaluated by Bates and Watts (1980) parameter dependent curvature in specific directions. The theory is illustrated by examples.
Bayesian Model Monitoring
Authors: West Mike 
Published: December 2018

SUMMARY
A simple method of monitoring the predictive performance of a class of Bayesian models is introduced. The models involve sequential analyses of sequences of observations and are appropriate for a variety of monitoring and forecasting applications. For any given model, the monitoring technique is based on a comparison of the predictive ability of the model, measured by the observed values of predictive densities, with that of a single alternative. The alternative is constructed sequentially and is designed, for the class of models considered, as a relatively general yet neutral alternative to the original. The monitor is used as a general diagnostic tool to detect and assess discrepancies between the data and predictions generated from the model; particular sources of such model failure of interest are the occurrence of outliers and structural change in the series. An illustration is provided and a simple method of automatically coping with outliers and adapting to change is outlined.
On the Robustness of Shrinkage Predictors in Regression to Differences between Past and Future Data
Authors: Jones M. C. , Copas J. B. 
Published: December 2018

SUMMARY
Copas (1983) investigates the shrinkage associated with prediction in the usual linear multiple regression model and proposes using Stein-type predictors which anticipate this shrinkage. Assuming that the first two (population) moments of the regressor variables associated with individuals for which predictions are to be made coincide with the first two (sample) moments of those in the construction sample, preshrunk predictors give a uniformly lower prediction mean squared error than least squares. In this paper, we investigate the robustness of these shrinkage predictors to departures from this distributional assumption. It is argued that minimaxity results are not sufficient on their own and that the applicability of shrinkage prediction should be assessed in the light of expressions involving the true regression parameters. Numerical illustrations suggest that Copas's (1983) shrinkage predictor is not only robust to small differences between the appropriate moment matrices, but can also be applicable in the case of large and systematic differences between the construction sample and future individuals.
On the Statistical Analysis of Dirty Pictures
Authors: Besag Julian 
Published: December 2018

SUMMARY
A continuous two-dimensional region is partitioned into a fine rectangular array of sites or “pixels”, each pixel having a particular “colour” belonging to a prescribed finite set. The true colouring of the region is unknown but, associated with each pixel, there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model. The aim is to reconstruct the true scene, with the additional knowledge that pixels close together tend to have the same or similar colours. In this paper, it is assumed that the local characteristics of the true scene can be represented by a non-degenerate Markov random field. Such information can be combined with the records by Bayes' theorem and the true scene can be estimated according to standard criteria. However, the computational burden is enormous and the reconstruction may reflect undesirable large-scale properties of the random field. Thus, a simple, iterative method of reconstruction is proposed, which does not depend on these large-scale characteristics. The method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field. Some complications, including parameter estimation, are discussed. Potential applications are mentioned briefly.
Binary Regression Models for Contaminated Data
Authors: Copas J. B. 
Published: December 2018

SUMMARY
The nature of outliers in the context of binary regression data is discussed. Resistant fitting procedures produce estimated regression coefficients which are numerically larger than maximum likelihood, implying the need for a shrinkage-type correction. A simple model which allows for a small number of the binary responses being misrecorded is proposed, and associated techniques for robust estimation and diagnostics developed.
Approximate Conditional Inference in Generalized Linear Models
Authors: Davison A. C. 
Published: December 2018

SUMMARY
Easily calculated and accurate approximations are developed to the conditional densities and distributions of sufficient statistics in generalized linear models with canonical link functions. They enable conditional inferences based on modified profile log-likelihoods and tail probabilities to be made using only the deviance and the variance matrix estimate based on fitted models. Examples are given in binary logistic regression and a log-linear model, and the results are applied to added variable tests of model adequacy.
Interim Analyses: The Repeated Confidence Interval Approach
Authors: Jennison Christopher , Turnbull Bruce W. 
Published: December 2018

SUMMARY
Most medical trials are monitored for early evidence of treatment differences or harmful side-effects and many sequential methods have been proposed for this. Similarly, data collected in a prospective epidemiological study are likely to be reviewed periodically in the course of the study. The repeated confidence interval approach, which combines aspects of sequential estimation and testing, allows a full exploration of the data at each interim analysis and does not depend on a rigidly enforced statistical stopping rule. In this paper we present the general principles underlying the construction of repeated confidence intervals and describe how they can be used in reaching a decision to terminate a study early. We discuss design considerations, which depend on the form of early stopping anticipated, and explain how the basic method can be adapted to cope with the problems of unpredictable group sizes or, more generally, unequal increments in information between analyses. Extensions of the method to handle survival data, categorical data, normal responses with unknown variance and multivariate normal observations are also presented.
Variance Function Estimation in Regression: The Effect of Estimating the Mean
Authors: Hall Peter , Carroll R. J. 
Published: December 2018

SUMMARY
We consider estimation of a variance function g in regression problems. Such estimation requires simultaneous estimation of the mean function f. We obtain clear results on the extent to which the smoothness of f influences best rates of convergence for estimating g. For example, in nonparametric regression with two derivatives on g, ‘classical' rates of convergence are possible if and only if the unknown f satisfies a Lipschitz condition of order 13 or more. If a parametric model is known for g, then g may be estimated n1/2 consistently if and only if f is Lipschitz of order 12 or more. Optimal rates of convergence are attained by Kernel estimators.
Generalized Linear Models with Varying Dispersion
Authors: Smyth Gordon K. 
Published: December 2018

SUMMARY
Generalized linear models are further generalized to include a linear predictor for the dispersion as well as for the mean. It is shown how the convenient structure of generalized linear models can be carried over to this more general setting by considering the mean and dispersion structure separately. Mean and dispersion submodels are formulated for this, the dependent variable for the dispersion submodel being the deviance components of the mean submodel. The fact that both submodels are essentially generalized linear models themselves is used to derive simple expressions for the likelihood equations and for asymptotic tests. Estimation algorithms are proposed which have good convergence properties. The results apply mainly to the normal, inverse Gaussian and gamma distributions but can be extended to discrete distributions by using quasi-likelihoods. The methods developed are applied to a well-known data set.
A Fast Improvement to the Em Algorithm on its Own Terms
Authors: Meilijson Isaac 
Published: December 2018

SUMMARY
The EM algorithm is a numerical technique for the evaluation of maximum likelihood estimates for parameters describing incomplete data models. It is easy to apply in many problems and is stable but slow. The algorithm fails to provide a consistent estimator of the standard errors of the maximum likelihood estimates unless the additional analysis required by the Louis method is performed. Newton-type or other gradient methods are faster and provide error estimates but tend to be unstable and require the analytical evaluation of likelihoods to derive expressions for the score function and (at least) approximations to the Fisher information matrix. The purpose of this paper is to expand on a result by Fisher that permits a unification of EM methodology and Newton methods. The evaluation of the individual observation-by-observation score functions of the incomplete data is a by-product of the application of the E step of the EM algorithm. Once these become available, the Fisher information matrix may be consistently estimated, and the M step may be replaced by a fast Newton-type step.
L-Moments: Analysis and Estimation of Distributions Using Linear Combinations of Order Statistics
Authors: Hosking J. R. M. 
Published: December 2018

SUMMARY
L-moments are expectations of certain linear combinations of order statistics. They can be defined for any random variable whose mean exists and form the basis of a general theory which covers the summarization and description of theoretical probability distributions, the summarization and description of observed data samples, estimation of parameters and quantiles of probability distributions, and hypothesis tests for probability distributions. The theory involves such established procedures as the use of order statistics and Gini's mean difference statistic, and gives rise to some promising innovations such as the measures of skewness and kurtosis described in Section 2, and new methods of parameter estimation for several distributions. The theory of L-moments parallels the theory of (conventional) moments, as this list of applications might suggest. The main advantage of L-moments over conventional moments is that L-moments, being linear functions of the data, suffer less from the effects of sampling variability: L-moments are more robust than conventional moments to outliers in the data and enable more secure inferences to be made from small samples about an underlying probability distribution. L-moments sometimes yield more efficient parameter estimates than the maximum likelihood estimates.
On Likelihood Ratio Tests for Threshold Autoregression
Authors: Chan K. S. , Tong H. 
Published: December 2018

SUMMARY
This paper addresses the null distribution of the likelihood ratio statistic for threshold autoregression with normally distributed noise. The problem is non-standard because the threshold parameter is a nuisance parameter which is absent under the null hypothesis. We reduce the problem to the first-passage probability associated with a Gaussian process which, in some special cases, turns out to be a Brownian bridge. It is also shown that, in some specific cases, the asymptotic null distribution of the test statistic depends only on the ‘degrees of freedom' and not on the exact null joint distribution of the time series.
On the Use of Nonparametric Regression for Checking Linear Relationships
Authors: Azzalini Adelchi , Bowman Adrian 
Published: December 2018

SUMMARY
The problem of checking the linearity of a regression relationship is addressed through the idea of smoothing of a residual plot. A pseudolikelihood ratio test statistic, which measures the distance between the nonparametric and the parametric models, is derived as a ratio of quadratic forms. The distribution of this statistic under the null hypothesis of linearity is calculated numerically by using Johnson curves. A power study shows the new statistic to be more sensitive to non-linearity than the Durbin-Watson statistic.
On Robustness in the Logistic Regression Model
Authors: Carroll R. J. , Pederson Shane 
Published: December 2018

SUMMARY
We investigate robustness in the logistic regression model. Copas has studied two forms of robust estimator: A robust-resistant estimate of Pregibon and an estimate based on a misclassification model. He concluded that robust-resistant estimates are much more biased in small samples than the usual logistic estimate is and recommends a bias-corrected version of the misclassification estimate. We show that there are other versions of robust-resistant estimates which have bias often approximately the same as and sometimes even less than the logistic estimate; these estimates belong to the Mallows class. In addition, the corrected misclassification estimate is inconsistent at the logistic model; we develop a simple consistent modification. The modified estimate is a member of the Mallows class but, unlike most robust estimates, it has an interpretable tuning constant. The results are illustrated on data sets featuring different kinds of outliers.
The Complex Bingham Distribution and Shape Analysis
Authors: Kent John T. 
Published: December 2018

SUMMARY
A complex version of the Bingham distribution is defined on the unit complex sphere in Ck. Various statistical properties, including asymptotic normality under high concentration, are derived. Symmetries in the distribution make it a natural tool for the analysis of the shape of landmark data in two dimensions. Strengths and weaknesses of this approach are investigated. Links and contrasts with Bookstein co-ordinates are discussed. A hybrid approach to principal component analysis based on complex and real co-ordinates is suggested.
Bayesian Model Choice: Asymptotics and Exact Calculations
Authors: Gelfand A. E. , Dey D. K. 
Published: December 2018

SUMMARY
Model determination is a fundamental data analytic task. Here we consider the problem of choosing among a finite (without loss of generality we assume two) set of models. After briefly reviewing classical and Bayesian model choice strategies we present a general predictive density which includes all proposed Bayesian approaches that we are aware of. Using Laplace approximations we can conveniently assess and compare the asymptotic behaviour of these approaches. Concern regarding the accuracy of these approximations for small to moderate sample sizes encourages the use of Monte Carlo techniques to carry out exact calculations. A data set fitted with nested non-linear models enables comparisons between proposals and between exact and asymptotic values.
Estimating the Extremal Index
Authors: Smith Richard L. , Weissman Ishay 
Published: December 2018

SUMMARY
The extremal index is an important parameter measuring the degree of clustering of extremes in a stationary process. If we consider the point process of exceedance times over a high threshold, then this can be shown to converge asymptotically to a clustered Poisson process. The extremal index, a parameter in the interval [0, 1], is the reciprocal of the mean cluster size. Apart from being of interest in its own right, it is a crucial parameter for determining the limiting distribution of extreme values from the process. In this paper we review current work on statistical estimation of the extremal index and consider an optimality criterion based on a bias-variance trade-off. Theoretical results are developed for a simple doubly stochastic process, and it is argued that the main formula obtained is valid for a much wider class of processes. The practical implications are examined through simulations and a real data example.