bluuebunny/crossref_metadata_2025_split huggingface dataset:
An Affine Invariant Bivariate Version of the Sign Test
Authors: Brown B. M. , Hettmansperger T. P. 
Published: December 2018

SUMMARY
The generalized median of Oja yields a notion of bivariate quantile and, in turn, an affine invariant bivariate analogue of the sign test. its properties include a simple null covariance formula, facilitating a permutation or sign change test in the case of bivariate symmetry, normal efficiency coinciding with that of the Oja median and bounded influence, and hence strong robustness.
An Exact Decomposition Theorem for a Sample from the Three-Dimensional Hyperboloid Distribution
Authors: Massam Hélène 
Published: December 2018

SUMMARY
Consider a sample (v 1, ..., vn) from the three-dimensional hyperboloid distribution. The joint probability distribution function (PDF) of (v 1 ..., vn) can be expressed as the product of the PDF of n independent quantities. Each of these quantities has an exponential κ distribution. The splitting is done in such a way that the data points vi are incorporated into the successive quantities one at a time. A similar result has been proved in the literature for the normal and the inverse Gaussian distributions. Since the normal, gamma and inverse Gaussian distributions are the only one-dimensional distributions which are reproductive and are equal to their saddlepoint approximation, a parallel result was to be expected for the gamma distribution. We also prove this result and an application to recursive testing is presented.
Quasisymmetric Models for the Analysis of Square Contingency Tables
Authors: Becker Mark P. 
Published: December 2018

SUMMARY
A parametric model is presented for the analysis of square contingency tables where there is a one-to-one correspondence between the categories of the row variable and the categories of the column variable. The model is applicable to cross-classifications where the categories are unordered, partially ordered or completely ordered, but the interpretation of the model and associated parameters is most straightforward when the categories are at least partially ordered. Connections with the mover-stayer model and the usual model of quasisymmetry are described. Two data sets are used to illustrate the utility of the model.
Approximate Interval Probabilities
Authors: Barndorff-Nielsen O. E. 
Published: December 2018

SUMMARY
For models of parametric dimension 1 two parameterization invariant approximations to the conditional distribution function of the maximum likelihood estimator are considered. The first is derived by partial integration of a formula for the conditional density given an ancillary statistic (the p*-formula), a technique which in addition yields a useful expression for the error term. For exponential models of order 1 the approximation specializes to the Lugannani–Rice formula. The second approximation is based on an adjusted version (denoted r*) of the signed log-likelihood ratio statistic, which was also derived from p*. These two approximations generally agree closely, even in the far tails of the distribution. A third approximation is a modification of the first that avoids the specification of an ancillary. Some numerical comparisons are given.
A Graphical Procedure for Comparing Goodness-Of-Fit Tests
Authors: Mudholkar Govind S. , Kollia Georgia D. , Lin C. Thomas , Patel Kartik R. 
Published: December 2018

SUMMARY
A method for comparing tests of normality using their ‘isotones‘, i.e. contours on the surfaces representing p-values, is proposed. Select a family of distributions labelled by two parameters λ1 and λ2 to represent the null and alternative hypotheses. For each (λ1, λ2) take an ‘ideal sample’ from that distribution, calculate the value of the goodness-of-fit statistic and determine the corresponding P-value under the normality assumption. This generates a surface of the p-values of the ‘values of the test statistic' in the (λ1, λ2) plane. In this paper the construction and interpretation of the isotones, the contours on the above surfaces, for competing tests, is illustrated using the Shapiro–Wilk W, Vasicek's entropy test and Lin and Mudholkar's Zp-test of the composite hypothesis of normality.
Asymptotic Properties of Some Estimators for the Infection Rate in the General Stochastic Epidemic Model
Authors: Rida Wasima N. 
Published: December 2018

SUMMARY
Some estimators for the infection rate in the general stochastic epidemic model are presented. The first estimator follows the approach of maximum likelihood. However, this approach requires us to observe most if not all of the epidemic process. As an alternative, an estimator which uses less detailed data is derived from a suitable martingale. Both estimators are shown to be consistent only when a major outbreak of disease is observed. Minor out-breaks do not provide enough information on the infection rate. The asymptotic distributions of these estimators are also obtained. Asymptotic normality holds only for a major outbreak. Finally, the estimators are applied to data on a smallpox outbreak.
Weighted Kaplan-Meier Statistics: Large Sample and Optimality Considerations
Authors: Pepe Margaret Sullivan , Fleming Thomas R. 
Published: December 2018

SUMMARY
We propose a cumulative weighted difference in the Kaplan-Meier estimates as a test statistic for equality of distributions in the two-sample censored data survival analysis problem. For stability of such a statistic, the absolute value of the possibly random weight function must be bounded above by a multiple of (C −)1/2 + δ where 1 – C − is the left continuous censoring distribution function and δ &gt; 0. For these weighted Kaplan–Meier (WKM) statistics, asymptotic distribution theory is presented along with expressions for the efficacy under a sequence of local alternatives. A simple censored data generalization of the two-sample difference in means test (z-test) is a member of this class and in large samples is seen to be quite efficient relative to the popular log-rank test under a range of alternatives including the proportional hazards alternative. Optimal weight functions are also calculated. The optimal WKM statistic is as efficient as the optimal weighted log-rank statistic for any particular sequence of local alternatives. Stratified statistics and trend statistics are also presented.
Error Model Diagnostics in the General Linear Model Relevant to the Analysis of Repeated Measurements and Field Experiments
Authors: Cullis B. R. , McGilchrist C. A. , Gleeson A. C. 
Published: December 2018

SUMMARY
The large sample distribution of the recursive residual maximum likelihood residuals from the general linear model with dependent errors is derived. Further results are obtained from this distribution to aid the identification of an appropriate error model in the general linear model.
Sound Confidence Intervals in the Heteroscedastic Linear Model Through Releveraging
Authors: Dorfman Alan H. 
Published: December 2018

SUMMARY
Under heteroscedasticity, ordinary least squares regression can fail to yield adequate inference on parameter coefficients with respect to hypothesis testing or confidence intervals. For example, confidence intervals can have coverage well below that claimed. This is especially the case in small or moderate-sized imbalanced samples and holds even if the ordinary least squares variance estimator is replaced by a robust-against-heteroscedasticity variance estimator. A new simple weighting scheme corrects this problem, although at possibly serious cost in efficiency. Inefficient methods have been rated as useful at the data exploration stage of analysis. The present method is also useful as an adjunct to least squares regression, at the stage of regression diagnostics. As such, it can sometimes replace the need for them altogether.
Minimum Distance Methods Based on Quadratic Distances for Transforms in Simple Linear Regression Models
Authors: Luong Andrew 
Published: December 2018

SUMMARY
Minimum distance estimators and test statistics based on quadratic distances for transforms are introduced in simple linear regression models. Asymptotic properties of quadratic distance estimators and tests for the error distributions are derived. The modified quadratic distance estimator is shown to be efficient provided that the error distribution is symmetric and the derivative of the logarithm of the error density is a linear combination of the transforms.
Bias Correction in Generalized Linear Models
Authors: Cordeiro Gauss M. , McCullagh Peter 
Published: December 2018

SUMMARY
In this paper we derive general formulae for first-order biases of maximum likelihood estimates of the linear parameters, linear predictors, the dispersion parameter and fitted values in generalized linear models. These formulae may be implemented in the GLIM program to compute bias-corrected maximum likelihood estimates to order n −1, where n is the sample size, with minimal effort by means of a supplementary weighted regression. For linear logistic models it is shown that the asymptotic bias vector of β^ is almost collinear with β. The approximate formula βp/m+ for the bias of β^ in logistic models, where p = dim(β) and m+ = ∑ mi is the sum of the binomial indices, is derived and checked numerically.
Multivariate Mean Parameter Estimation by Using a Partly Exponential Model
Authors: Zhao Lue Ping , Prentice Ross L. , Self Steven G. 
Published: December 2018

SUMMARY
A class of partly exponential models is proposed for the regression analysis of multivariate response data. The class is parameterized in terms of the response mean and a general shape parameter. It includes the generalized linear error model and exponential dispersion models as special cases. Maximum likelihood equations for mean parameters are shown to be of the same form as certain generalized estimating equations, and maximum likelihood estimates of mean and shape parameters are asymptotically independent. Some results are given on the efficiency of the estimating equation procedure under misspecification of the response covariance matrix.
Semiparametric Additive Regression
Authors: Cuzick Jack 
Published: December 2018

SUMMARY
A simple estimator for β is proposed for the model y = x'β + g(t)+ error, g smooth but unknown. The approach is to approximate the estimating equation obtained from a ***semiparametric likelihood and in the simplest case reduces to minimizing the distance between the 'pseudoresiduals' y - x'β and a local linear cross-validated estimate of them. When the errors are independent with finite variance, the bias and variance of the estimate are computed and compared against the least squares estimate with g known. It is shown that n 1/2-consistent estimates are possible when the bandwidth contains only a finite number of points and their asymptotic relative efficiency is computed in special cases. When the error distribution is known up to a scale factor and the design points (X, T) are assumed to be drawn as independent samples from a bivariate distribution, the Hajek-LeCam lower bound for the variance of any regular estimator of β is computed and a sequence of estimators is exhibited which achieves this bound. When X and T are independent these estimators do as well asymptotically as the maximum likelihood estimator with g known.
Maximum Entropy and the Nearly Black Object
Authors: Donoho David L. , Johnstone Iain M. , Hoch Jeffrey C. , Stern Alan S. 
Published: December 2018

SUMMARY
Maximum entropy (ME) inversion is a non-linear inversion technique for inverse problems where the object to be recovered is known to be positive. It has been applied in areas ranging from radio astronomy to various forms of spectroscopy, sometimes with dramatic success. In some cases, ME has attained an order of magnitude finer resolution and/or an order of magnitude smaller noise level than that obtainable by standard linear methods. The dramatic successes all seem to occur in cases where the object to be recovered is ‘nearly black‘: essentially zero in the vast majority of samples. We show that near-blackness is required, both for signal-to-noise enhancements and for superresolution. However, other methods—in particular, minimum l 1-norm reconstruction—may exploit near-blackness to an even greater extent.
Jackknife-After-Bootstrap Standard Errors and Influence Functions
Authors: Efron Bradley 
Published: December 2018

SUMMARY
This paper shows how to derive more information from a bootstrap analysis, information about the accuracy of the usual bootstrap estimates. Suppose that we observe data x = (x 1 x 2, . . ., xn), compute a statistic of interest s(x) and further compute B bootstrap replications of s, say s(x*1) s(x*2), . . ., s(x*B), where B is some large number like 1000. Various accuracy measures for s(x) can be obtained from the bootstrap values, e.g. the bootstrap estimates of standard error and bias, or the length and shape of bootstrap confidence intervals. We might wonder how accurate these accuracy measures themselves are, or how sensitive they are to small changes in the individual data points xi. It turns out that these questions can be answered from the information in the original bootstrap sample s* 1 s* 2, . . ., s*B, with no further resampling required. The answers, which make use of the jackknife and delta method influence functions, are easy to apply and can give informative results, as shown by several examples.
Approximate Bayes Factors and Orthogonal Parameters, with Application to Testing Equality of Two Binomial Proportions
Authors: Kass Robert E. , Vaidyanathan Suresh K. 
Published: December 2018

SUMMARY
We use asymptotic expansions to approximate Bayes factors, improving on a method used by Jeffreys. Suppose that the hypothesis H 0: ψ = ψ0 is to be tested against H A: ψ ≠ ψ0 in the presence of a nuisance parameter β, and initially priors π0(β) under H 0 and π(β, ψ) under H A are used. We consider the problem of assessing sensitivity of the Bayes factor to small changes in π0 and π. We show that for local alternatives (which, for moderate sample sizes, are consistent with small or moderately large values of the Bayes factor in favour of the alternative), if β and ψ are what we call ‘null orthogonal’ parameters, then alterations in π0 have no effect on the Bayes factor up to order O(n –1). Under similar conditions we also derive an order O(n –1) approximation to the minimum Bayes factor over all priors π under H A such that the marginal prior on ψ is normal with mean ψ0. We then go on to consider sensitivity to specific changes in the marginal prior on ψ and show how asymptotics may be used for this, applying a second-order approximation due to Tierney and Kadane. We illustrate the results with a test of equality of two binomial proportions and briefly investigate the accuracy of the approximations is this context.
Testing for Parameter Variation in Non-Linear Regression Models
Authors: McCabe B. P. M. , Leybourne S. J. 
Published: December 2018

SUMMARY
This paper addresses the problem of testing for purely random parameter variation in nonlinear regression models. Based on different approximations to the true density of the data, score-type tests are constructed and their asymptotic distributions are derived. The local power of the tests is investigated both theoretically and via Monte Carlo simulation. An empirical testing example, involving a well-known non-linear aggregate demand for money function, is also given.
Convergence Rates of the Gibbs Sampler, the Metropolis Algorithm and Other Single-Site Updating Dynamics
Authors: Frigessi Arnoldo , Stefano Patrizia , Hwang Chii-Ruey , Sheu Shuenn-Jyi 
Published: December 2018

SUMMARY
Sampling from a Markov random field II can be performed efficiently via Monta Carlo methods by simulating a Markov chain that converges weakly to II. We consider a class of local updating dynamics that are reversible with respect to II. It includes the Metropolis algorithm (MA) and the Gibbs sampler (GS). We investigate the speed of weak convergence of these Markov chains in terms of their second-largest eigenvalues in absolute value. We study the general algebraic structure and then the stochastic Ising model in detail. We conclude the following: the GS is faster than locally updating twice by the MA; in the Ising case, the MA is the best at low temperature but the worst at high temperature; there are dynamics faster than the GS at high temperature. The results clear up some intuitive misconceptions.
Nearly Orthogonal Randomized Designs
Authors: Hooper Peter M. 
Published: December 2018

SUMMARY
A new method of experimental randomization is presented that is suitable under additive general linear models for treatment and unit effects. The method is designed for a standard normal theory analysis of the data. The method is motivated by thinking of the randomization strategy, which may be represented as a distribution on the group of n × n permutation matrices, as a discrete approximation to a fictitious, ideal randomization strategy corresponding to a continuous distribution on the group of n × n orthogonal matrices. Designs are generated by using a simulated annealing algorithm. The method requires the selection of a tuning constant that determines a trade-off between validity and efficiency. The tuning constant is chosen with the aid of a new diagnostic measure of validity. The ideas are illustrated by using continuous, piecewise linear models of potential use in field experiments.
On the Empirical Validity of the Bayesian Method
Authors: Vovk V. G. , V'Yugin V. V. 
Published: December 2018

SUMMARY
The ideas in Kolmogorov's programme for algorithmic substantiation of applications of probability make it possible to define a measure of disagreement between the probability distribution representing the attitude of a coherent individual towards a random experiment and the outcome of the experiment. When there is agreement we say that the probability distribution is empirically valid. We prove quantitatively that formulae of Bayesian statistics transform empirically valid probability distributions into other empirically valid distributions.
Computing Theoretical Autocovariances of Multivariate Autoregressive Moving Average Models by Using a Block Levinson Method
Authors: Mittnik Stefan 
Published: December 2018

SUMMARY
A closed form expression relating the theoretical autocovariances of a multivariate autoregressive moving average (ARMA) model to the ARMA parameters in terms of a system of linear equations has been presented recently. Using this result and the special Hankel plus Toeplitz structure of the coefficient matrix obtained after suitable partitioning, this paper presents a method for computing multivariate autocovariance functions that is based on a block Levinson procedure. The method is particularly advantageous for models with high order autoregressive components and/or a large number of variables.
A Fourier Approach to Nonparametric Deconvolution of a Density Estimate
Authors: Diggle Peter J. , Hall Peter 
Published: December 2018

SUMMARY
We consider the problem of constructing a nonparametric estimate of a probability density function h from independent random samples of observations from densities a and f, when a represents the convolution of h and f. Our approach is based on truncated Fourier inversion, in which the truncation point plays the role of a smoothing parameter. We derive the asymptotic mean integrated squared error of the estimate and use this formula to suggest a simple practical method for choosing the truncation point from the data. Strikingly, when the smoothing parameter is chosen in this way then in many circumstances the estimator behaves, to first order, as though the true f were known. Simulated data sets are used to demonstrate that the method can give good results in practice.
Interpolated Nonparametric Prediction Intervals and Confidence Intervals
Authors: Beran Rudolf , Hall Peter 
Published: December 2018

SUMMARY
In several important statistical problems, prediction intervals and confidence intervals can be constructed with coverage levels which are known precisely but cannot be rendered equal to predetermined levels such as 0.95. One solution to this difficulty is to interpolate between such intervals. We show that simple linear interpolation reduces the order of coverage error, but that higher orders of interpolation produce no further improvement. The error is reduced by a factor n −1 for prediction intervals and n −1/2 for confidence intervals, where n denotes sample size. In the case of confidence intervals for quantiles, linear interpolation provides particularly accurate intervals which err on the side of conservatism.
Shape Analysis for the Anisotropic Corpuscle Problem
Authors: Girling A. J. 
Published: December 2018

SUMMARY
The problem of inferring the shape distribution of anisotropically oriented spheroidal particles from their elliptical traces in planar samples is addressed by generalizing a size-shape independence condition suggested by Wicksell in his original discussion of the corpuscle problem. Shape statistics are introduced through which the eccentricities of the sampled ellipses may be related to some suitably defined moments of the underlying particle shape distribution, taking account of particle orientation. Practical methods which employ bootstrap resampling of shape statistics are developed with reference to data from a recent neurological study.
Systematic Row-And-Column Designs Balanced for Low Order Polynomial Interactions between Rows and Columns
Authors: Edmondson R. N. 
Published: December 2018

SUMMARY
Systematic row-and-column designs intended to accommodate low order polynomial rows × columns interaction effects are discussed. Latin square, Graeco-Latin square and quasi-Latin square designs of size 2N × 2M and size 9 × 9 are examined by using plot pseudofactor methods. Latin square and Graeco-Latin square designs of size 5 × 5 and 7 × 7 are examined by using a published technique for the design of quantitative factorial experiments with a prime number of factor levels. A 6 × 6 Latin square design is constructed by trial and error. Finally, the control of positional effects by fitted quadratic response surfaces is discussed.
A Contamination Model and Resistant Estimation Within the Sampling Paradigm
Authors: Titterington D. M. 
Published: December 2018

SUMMARY
Copas's model for contamination in binary regression structures is translated into the sampling paradigm approach that is familiar in discriminant analysis. A parallel treatment of the two models is afforded by a common expression of the log-likelihood. Resistant parameter estimation is discussed for prevalence rates and for parameters, including discriminant functions, within component distributions. The methods are illustrated on a breast cancer example.
High Breakdown Methods of Time Series Analysis
Authors: Tatum Lawrence G. , Hurvich Clifford M. 
Published: December 2018

SUMMARY
A robust form of the discrete Fourier transform is developed that can handle large amounts of contamination and patchy outliers. We use robust regression to fit a sine and cosine coefficient at each Fourier frequency, and these coefficients are then inverse Fourier transformed to give a filtered version of the data. The filtered series can then be analysed with conventional methods. The limiting breakdown bound of the filter is 50%. Other properties of the filter are also given. The performance of our method is compared by a Monte Carlo study with that of a data cleaner of Martin and Thomson. A comparison of the methods, including an outlier detection procedure, is also done by using a real data set with patchy outliers.