bluuebunny/crossref_metadata_2025_split huggingface dataset:
Second-Order Approach to Local Influence
Authors: Wu Xizhi , Luo Zhen 
Published: December 2018

SUMMARY
To examine global and local influence, and their relations for regression models, we study the perturbation-formed surface of a variable, such as the maximum likelihood estimate of a parameter, by evaluating the second derivative or curvature of the surface. (The corresponding slope of this surface is related to the curvature of the likelihood displacement surface of Cook.) Examples show that this approach, with the aid of plots, is helpful not only to discover influential cases including those hidden in an individual global sense but also to understand the nature of influence.
Approximate Bayesian Inference with the Weighted Likelihood Bootstrap
Authors: Newton Michael A. , Raftery Adrian E. 
Published: December 2018

SUMMARY
We introduce the weighted likelihood bootstrap (WLB) as a way to simulate approximately from a posterior distribution. This method is often easy to implement, requiring only an algorithm for calculating the maximum likelihood estimator, such as iteratively reweighted least squares. In the generic weighting scheme, the WLB is first order correct under quite general conditions. Inaccuracies can be removed by using the WLB as a source of samples in the sampling-importance resampling (SIR) algorithm, which also allows incorporation of particular prior information. The SIR-adjusted WLB can be a competitive alternative to other integration methods in certain models. Asymptotic expansions elucidate the second-order properties of the WLB, which is a generalization of Rubin's Bayesian bootstrap. The calculation of approximate Bayes factors for model comparison is also considered. We note that, given a sample simulated from the posterior distribution, the required marginal likelihood may be simulation consistently estimated by the harmonic mean of the associated likelihood values; a modification of this estimator that avoids instability is also noted. These methods provide simple ways of calculating approximate Bayes factors and posterior model probabilities for a very wide class of models.
The Linear Spatial-Temporal Interaction Process and its Relation to 1/ω-Noise
Authors: Renshaw Eric 
Published: December 2018

SUMMARY
If we are to gain an understanding of the evolutionary processes which generate pattern then time cannot be ignored, since a purely spatial viewpoint disregards the fundamental generating mechanism of the underlying process. We therefore develop a spectral approach based on a general growth–interaction model; individuals grow at intrinsic rate λ, while two individuals a distance r apart interact at rate ar times their size difference. Special cases considered involve nearest neighbour, geometric, logarithmic and Cauchy-type dependence. A separate study is made of ‘long-term persistence‘; an autoregressive binomial weight structure is used to generate processes with power law spectra ωd. We examine the effect of arranging the general process on a ring of N sites, and then use this structure to simulate nearest neighbour and binomial interaction.
Prequential Level of Impossibility with Some Applications
Authors: Vovk V. G. , V'Yugin V. V. 
Published: December 2018

SUMMARY
Within Dawid's prequential framework we introduce a quantitative measure of disagreement between a probabilistic theory and observations. Using this measure we reconsider Howard's theorem on Laplace's rule of succession and Dawid's result on the prequential efficiency of the Bayesian rule.
Adjusted Versus Conditional Likelihood: Power Properties and Bartlett-Type Adjustment
Authors: Ghosh J. K. , Mukerjee Rahul 
Published: December 2018

SUMMARY
Under contiguous alternatives the adjusted likelihood ratio (ALR) test is seen to have the same power properties as the conditional likelihood ratio test up to the third order of comparison. In particular, an optimum property of the ALR test in terms of second-order local maximinity follows. It is also seen that the ALR statistic admits a Bartlett-type adjustment.
Robust Methods for Recursive Autoregressive Moving Average Estimation
Authors: McDougall A. J. 
Published: December 2018

SUMMARY
In this paper we consider the problem of fitting, recursively in time, an autoregressive moving average (ARMA) model to time series data where outliers may be present. Although many recursive estimation procedures are available for fitting ARMA models, they are based on the recursive least squares algorithm which is known to be badly affected by additive outliers. to minimize the impact of these sort of outliers we investigate some robustified versions of the recursive maximum likelihood procedure. The problem of incorporating robust scale recursion is discussed and asymptotic properties of the procedures are examined. We also present results from simulation studies which compare adaptive versions of these procedures in the non-stationary case.
Fractional Factorial Designs for Factors with a Prime Number of Quantitative Levels
Authors: Edmondson R. N. 
Published: December 2018

SUMMARY
A technique for single degree of freedom partitioning of canonical contrasts for prime level factorials with quantitative levels is reviewed. The relationship between canonical contrasts and the polynomial contrasts of response function models is discussed. Aliasing of canonical contrasts in fractional factorials is examined and alias sets from principal fractions are shown to have a particularly simple structure. Second-order response function designs built from single principal fractions or from sums of two or four different principal fractions are discussed. The accommodation of nuisance trend effects in experiments with quantitative factor effects is exemplified. Tables of fractional factorial designs for factors with three or five quantitative levels are presented.
Dispersion Effects from Fractional Factorials in Taguchi's Method of Quality Design
Authors: Rosenbaum Paul R. 
Published: December 2018

SUMMARY
Taguchi proposed direct product designs for studying the influence of control factors on the dispersion introduced by error factors. The current paper presents several general results concerning the use of orthogonal array designs to estimate the effects of control factors on the dispersive effects of error factors. Sufficient conditions are given such that dispersion estimates are ‘undistorted’, in that they estimate the same quantity in fractional factorials as they would in complete factorials. The conditions concern the strength of the orthogonal array and the complexity of the linear model. Taguchi's designs are ‘reliable’ in that they prevent interactions among control factors from being mistaken for dispersion effects involving error effects. There are other reliable orthogonal array designs that are, in some ways, preferable to Taguchi's direct product designs in that they have greater strength or resolution with the same number of observations.
Multiple-Stage Non-Homogeneous Markov Models for the Acquired Immune Deficiency Syndrome Epidemic
Authors: Billard L. , Zhao Zhen 
Published: December 2018

SUMMARY
Numerous particular models have been introduced in recent years to explain various specific aspects of the underlying mechanism associated with the spread of the acquired immune deficiency syndrome (AIDS) epidemic. Many of these models can be classified as compartmental models. In this work we establish the mathematical framework and provide solutions for the class of compartmental stochastic models for which the transition probabilities between stages of the model are both time and state dependent. We obtain expressions for the state probabilities, and for the mean and variance of the number of AIDS cases as a function of time. to illustrate the theoretical results we compare a four- and five-stage model with the actual number of reported AIDS cases for several populations.
Inverse Problems in Fractal Construction: Hellinger Distance Method
Authors: Chen Jiahua , Kalbfleisch J. D. 
Published: December 2018

SUMMARY
Some images can be approximated by the geometry of fractals that are attractors of iterative function systems. The inverse problems to be discussed involve searching for an iterative function system that best approximates a given image. Existing methods often assume full knowledge of the image and rely on complicated computations to avoid local optima in the distance measure being used. We propose the use of a revised Hellinger distance in addressing inverse problems. It is shown that the new method does not require full knowledge of the image to be approximated and can eliminate most of the unwanted locally optimal approximations.
Non-Regular Maximum Likelihood Problems
Authors: Cheng R. C. H. , Traylor L. 
Published: December 2018

SUMMARY
Four non-regular estimation problems are reviewed and discussed. One (the unbounded likelihood problem) involves distributions with infinite spikes, for which maximum likelihood can fail to give consistent estimators. A comparison is made with modified likelihood and spacings methods which do give efficient estimators in this case. An application to the Box–Cox shifted power transform is given. The other three problems occur when the true parameter lies in some special subregion. In one (the constrained parameter problem) the subregion is a boundary. The other two (the embedded model and the indeterminate parameters problems) occur when the model takes on a special form in the subregion. These last two problems have previously been investigated separately. We show that they are equivalent in some situations. Both often arise in non-linear models and we give a directed graph approach which allows for their occurrence in nested model building. It is argued that many non-regular problems can be handled systematically without having to resort to elaborate technical assumptions. Relatively uncomplicated methods may be used provided that the underlying nature of the non-regularity is understood.
Assessment and Propagation of Model Uncertainty
Authors: Draper David 
Published: December 2018

SUMMARY
In most examples of inference and prediction, the expression of uncertainty about unknown quantities y on the basis of known quantities x is based on a model M that formalizes assumptions about how x and y are related. M will typically have two parts: structural assumptions S, such as the form of the link function and the choice of error distribution in a generalized linear model, and parameters θ whose meaning is specific to a given choice of S. It is common in statistical theory and practice to acknowledge parametric uncertainty about θ given a particular assumed structure S; it is less common to acknowledge structural uncertainty about S itself. A widely used approach involves enlisting the aid of x to specify a plausible single ‘best’ choice S* for S, and then proceeding as if S* were known to be correct. In general this approach fails to assess and propagate structural uncertainty fully and may lead to miscalibrated uncertainty assessments about y given x. When miscalibration occurs it will often result in understatement of inferential or predictive uncertainty about y, leading to inaccurate scientific summaries and overconfident decisions that do not incorporate sufficient hedging against uncertainty. In this paper I discuss a Bayesian approach to solving this problem that has long been available in principle but is only now becoming routinely feasible, by virtue of recent computational advances, and examine its implementation in examples that involve forecasting the price of oil and estimating the chance of catastrophic failure of the US space shuttle.
Covariance Structure and Convergence Rate of the Gibbs Sampler with Various Scans
Authors: Liu Jun S. , Wong Wing H. , Kong Augustine 
Published: December 2018

SUMMARY
This paper presents results on covariance structure and convergence for the Gibbs sampler with both systematic and random scans. It is shown that, under conditions that guarantee the compactness of the Markov forward operator and irreducibility of the corresponding chain, the Gibbs sampling scheme converges geometrically in terms of Pearson χ 2-distance. In particular, for the random scan, the autocovariance can be expressed as variances of iterative conditional expectations. As a consequence, the autocorrelations are all positive and decrease monotonically.
A Bandwidth Selector for Bivariate Kernel Regression
Authors: Herrmann Eva , Wand M. P. , Engel Joachim , Gasser Theo 
Published: December 2018

SUMMARY
For two and higher dimensional kernel regression, currently available bandwidth selection procedures are based on cross-validation or related penalizing ideas. However, these techniques have been shown to suffer from high sample variability and, in addition, can sometimes be difficult to implement when a vector of bandwidths needs to be selected. In this paper we propose a selector based on an iterative plug-in approach for bivariate kernel regression. It is shown to give satisfactory results and can be quickly computed. Our ideas can be extended to higher dimensions.
Local Likelihood Based on Kernel Censoring
Authors: Copas J. B. 
Published: December 2018

SUMMARY
By drawing an analogy with likelihood for censored data, a local likelihood function is proposed which gives more weight to observations near a region of interest in the sample space. Resulting methods can be used for assessing local departures from a parametric model, and for semiparametric density estimation. Some theory, and three examples, is given.
Statistical Inference for a Two-State Markov Model of a Single Ion Channel, Incorporating Time Interval Omission
Authors: Ball F. G. , Davies S. S. 
Published: December 2018

SUMMARY
A two-state Markov model of a single ion channel, in which successive open and closed sojourns follow negative exponential distributions with respective means μO and μC, is considered. Estimation of (μO μC) when brief sojourns in the open and closed states fail to be detected is studied. The moment estimating equations for (μO, μC) have no, one or two solutions, with two being the most common situation. The asymptotic behaviour of method-of-moments estimators of (μO, μC), as the number of sojourns becomes large, is determined, and the resulting confidence regions for (μO, μC) are compared with those derived by Clarke, Milne and Yeo under an approximate model. A new method of discriminating between the two solutions of the moment estimating equations is presented. The theory is illustrated by numerical examples taken from ion channel literature.
Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing
Authors: Benjamini Yoav , Hochberg Yosef 
Published: December 2018

SUMMARY
The common approach to the multiplicity problem calls for controlling the familywise error rate (FWER). This approach, though, has faults, and we point out a few. A different approach to problems of multiple significance testing is presented. It calls for controlling the expected proportion of falsely rejected hypotheses — the false discovery rate. This error rate is equivalent to the FWER when all hypotheses are true but is smaller otherwise. Therefore, in problems where the control of the false discovery rate rather than that of the FWER is desired, there is potential for a gain in power. A simple sequential Bonferronitype procedure is proved to control the false discovery rate for independent test statistics, and a simulation study shows that the gain in power is substantial. The use of the new procedure and the appropriateness of the criterion are illustrated with examples.
Regression Models with Incidental Parameters
Authors: Mak Tak K. 
Published: December 2018

SUMMARY
It is known that iterative weighted least squares (IWLS) does not merely yield a convenient way of fitting the general class of regression models considered by Green but is also a useful means of unifying techniques of model checking. However, an extension of these results to models containing nuisance or incidental parameters has made little progress beyond some special cases. Unfortunately, regression models with nuisance parameters that are not dispersion parameters arise very commonly in applications. The present paper presents a unified treatment of regression models containing incidental parameters that are permitted to contain covariates as well as being functionally dependent on the predictor or regression parameters. For the general regression model considered it is shown that Fisher's scoring algorithm can also be implemented as IWLS. Unlike the commonly suggested fitting strategy which updates the regression parameters with the nuisance parameters assumed known and set at the current values, the present approach yields the correct asymptotic covariance matrix for the regression parameter estimates. By considering simultaneous inference, residuals and influence measures which accommodate the effect of estimating the incidental parameters are outlined.
Multivariate Discriminant Analysis and Maximum Penalized Likelihood Density Estimation
Authors: Granville Vincent , Rasson Jean Paul 
Published: December 2018

SUMMARY
A new theoretical point of view is discussed in the framework of density estimation. The multivariate true density, viewed as a prior or penalizing factor in a Bayesian framework, is modelled by a Gibbs potential. Estimating the density consists in maximizing the posterior. For efficiency of time, we are interested in an approximate estimator f̂ = Bπ of the true density f, where B is a stochastic operator and π is the raw histogram. Then, we investigate the discrimination problem, introducing an adaptive bandwidth depending on the k nearest neighbours and chosen to optimize the cross-validation criterion. Our final classification algorithm referred to as APML for approximate penalized maximum likelihood compares favourably in terms of error rate and time efficiency with other algorithms tested, including multinormal, nearest neighbour and convex hull classifiers.
Some Tests Based on Extreme Values for a Parametric Survival Model
Authors: Crowder Martin 
Published: December 2018

SUMMARY
Hougaard proposed a scaled, exponentially tilted, positive stable distribution for the frailty in survival analysis. This leads to a class of survivor functions which encompasses certain special cases. Some tests based on extreme sample values are proposed for assessing the fit of these submodels within a full model. The tests are applied to some data on the breaking strengths of carbon fibres.
The Cost of Adding Parameters to a Model
Authors: Taylor Jeremy M. G. , Siqueira Arminda L. , Weiss Robert E. 
Published: December 2018

SUMMARY
For a general regression model with n independent observations we consider the variance of the estimate of a quantity of interest under two scenarios. One scenario is where all the parameters are estimated from the data; the other scenario is where a subset of the parameters is assumed known at their true values and the remaining parameters are estimated. We focus on quantities of interest which are defined on the scale of the response variable. We show that, under certain conditions, the ratio of a weighted sum across the design points of the variance of the quantity of interest is given by q/p, where q and p are the number of free parameters in the two scenarios. Thus, in this average sense, the inflation in variance associated with adding parameters, also interpreted as the cost of adding parameters to a model, is directly proportional to the number of parameters. We study models involving power transformations, non-linear models and exponential family models.
Using Bootstrap Likelihood Ratios in Finite Mixture Models
Authors: Feng Z. D. , McCulloch C. E. 
Published: December 2018

SUMMARY
Statistical inference using the likelihood ratio statistic for the number of components in a mixture model is complicated when the true number of components is less than that of the proposed model since this represents a non-regular problem: the true parameter is on the boundary of the parameter space and in some cases the true parameter is in a nonidentifiable subset of the parameter space. The maximum likelihood estimator is shown to converge to the subset characterized by the same density function, and connection is made to the bootstrap method proposed by Aitkin and co-workers and McLachlan for testing the number of components in a finite mixture and deriving confidence regions in a finite mixture.
Hierarchical Generalized Linear Models
Authors: Lee Y. , Nelder J. A. 
Published: December 2018

SUMMARY
We consider hierarchical generalized linear models which allow extra error components in the linear predictors of generalized linear models. The distribution of these components is not restricted to be normal; this allows a broader class of models, which includes generalized linear mixed models. We use a generalization of Henderson's joint likelihood, called a hierarchical or h-likelihood, for inferences from hierarchical generalized linear models. This avoids the integration that is necessary when marginal likelihood is used. Under appropriate conditions maximizing the h-likelihood gives fixed effect estimators that are asymptotically equivalent to those obtained from the use of marginal likelihood; at the same time we obtain the random effect estimates that are asymptotically best unbiased predictors. An adjusted profile h-likelihood is shown to give the required generalization of restricted maximum likelihood for the estimation of dispersion components. A scaled deviance test for the goodness of fit, a model selection criterion for choosing between various dispersion models and a graphical method for checking the distributional assumption of random effects are proposed. The ideas of quasi-likelihood and extended quasi-likelihood are generalized to the new class. We give examples of the Poisson–gamma, binomial–beta and gamma–inverse gamma hierarchical generalized linear models. A resolution is proposed for the apparent difference between population-averaged and subject-specific models. A unified framework is provided for viewing and extending many existing methods.
On Sample Reuse Methods for Dependent Data
Authors: Hall Peter , Jing Bingyi 
Published: December 2018

SUMMARY
We suggest a sample reuse method for dependent data, based on a cross between the block bootstrap and Richardson extrapolation. Instead of simulating a same size resample by resampling blocks and placing them end to end, it analyses the blocks directly and employs a variant of Richardson extrapolation to adjust for block size. A simple empirical rule, also based on Richardson extrapolation, is suggested for empirically selecting the block size. Performance in the contexts of distribution and bias estimation is discussed via theoretical analysis and numerical simulation.