bluuebunny/crossref_metadata_2025_split huggingface dataset:
Schläflian Rotatability
Authors: Draper Norman R. 
Published: December 2018

SUMMARY
Suppose that a polynomial of order d is to be fitted to data from a designed experiment and that V(·) is any selected variance function. For example, if ŷ(x) is the fitted value at a location x = (x 1, x 2, …, xk)′ in the k-dimensional predictor space, V{ŷ(x)}, which we shall also write V(ŷ), denotes the usual variance function. Design rotatability of order d is the property that V{ŷ(x)} has spherical contours in the x space. Here, a more general definition, Schläflian rotatability, is made with respect to any V(·), by requiring that the contours of F(·) are spherical in the space of the model predictors, specified in the usual Schläflian form. It is shown that Schläflian rotatability for V(ŷ) implies ordinary rotatability, and vice versa. The selection of a particular Schläflian variance profile for V(·) for a second order rotatable design implies a choice of the number of center points and the consequences of this are explored.
Optimal Sequential Estimation for Ergodic Birth-Death Processes
Authors: Manjunath S. M. 
Published: December 2018

SUMMARY
For ergodic birth-death processes a lower bound for the variance of an unbiased estimator of a function of birth and death parameters is obtained under an arbitrary stopping rule. All efficiently estimable functions and closed efficient sampling schemes are characterized. The processes treated here include random walk with reflecting barriers, immigration-death process, M/M/1 and M/M/S queues with limited or unlimited waiting space.
Some Aspects of the Spline Smoothing Approach to Non-Parametric Regression Curve Fitting
Authors: Silverman B. W. 
Published: December 2018

SUMMARY
Non-parametric regression using cubic splines is an attractive, flexible and widely-applicable approach to curve estimation. Although the basic idea was formulated many years ago, the method is not as widely known or adopted as perhaps it should be. The topics and examples discussed in this paper are intended to promote the understanding and extend the practicability of the spline smoothing methodology. Particular subjects covered include the basic principles of the method; the relation with moving average and other smoothing methods; the automatic choice of the amount of smoothing; and the use of residuals for diagnostic checking and model adaptation. The question of providing inference regions for curves – and for relevant properties of curves – is approached via a finite-dimensional Bayesian formulation.
Modelling Data Containing Exact Zeroes Using Zero Degrees of Freedom
Authors: Siegel Andrew F. 
Published: December 2018

SUMMARY
The noncentral chi-squared distribution with zero degrees of freedom can be used to model continuous data of a variety of shapes that also contain exact zero values. Existence and uniqueness of the maximum likelihood estimates for the scaled non-central chi-squared distribution with zero degrees of freedom are established, computational methods are considered, and an illustrative example is given.
Recursive Estimation of Dynamic Linear Models
Authors: Snyder R. D. 
Published: December 2018

SUMMARY
A dynamic, linear model for the analysis of univariate time series is proposed. It encompasses many of the common statistical models as special cases such as multiple regression, exponential smoothing and mixed autoregressive-moving average processes. its distinguishing feature is that it relies on only one primary source of randomness. It therefore not only provides a simpler framework for the study of dynamic models but also eliminates the need for the contentious system variance matrix which has been credited with hampering the use of recursive forecasting methods in practice. The associated Kalman filter is also derived.
Exponential Dispersion Models
Authors: Jørgensen Bent 
Published: December 2018

SUMMARY
We study general properties of the class of exponential dispersion models, which is the multivariate generalization of the error distribution of Nelder and Wedderburn’s (1972) generalized linear models. Since any given moment generating function generates an exponential dispersion model, there exists a multitude of exponential dispersion models, and some new examples are introduced. General results on convolution and asymptotic normality of exponential dispersion models are presented. Asymptotic theory is discussed, including a new small-dispersion asymptotic framework, which extends the domain of application of large-sample theory. Procedures for constructing new exponential dispersion models for correlated data are introduced, including models for longitudinal data and variance components. The results of the paper unify and generalize standard results for distributions such as the Poisson, the binomial, the negative binomial, the normal, the gamma, and the inverse Gaussian distributions.
Kernel Smoothing in Partial Linear Models
Authors: Speckman Paul 
Published: December 2018

SUMMARY
Kernel smoothing is studied in partial linear models, i.e. semiparametric models of the form yi=ξi′β+f(ti)+εi(1⩽i⩽n), where the ξi are fixed known p vectors, β is an unknown vector parameter and f is a smooth but unknown function. Two methods of estimating β and f are considered, one related to partial smoothing splines and the other motivated by partial residual analysis. Under suitable assumptions, the asymptotic bias and variance are obtained for both methods, and it is shown that estimating β by partial residuals results in improved bias with no asymptotic loss in variance. Application to analysis of covariance is made, and several examples are presented.
Hierarchical Statistical Models and a Generalized Likelihood Ratio Test
Authors: Hosoya Yuzo 
Published: December 2018

SUMMARY
This paper deals with statistical inference for statistical models which have a nested structure. The emphasis here is on the use of a classical test of significance and on a confidence set construction approach for model identification, and the paper proposes a generalized likelihood ratio test with equal marginal error rate as a basic tool. The power performance of this test is characterized and some applications are illustrated.
A Smoothed Em Approach to Indirect Estimation Problems, with Particular Reference to Stereology and Emission Tomography
Authors: Silverman B. W. , Jones M. C. , Wilson J. D. , Nychka D. W. 
Published: December 2018

SUMMARY
There are many practical problems where the observed data are not drawn directly from the density g of real interest, but rather from another distribution derived from g by the application of an integral operator. The estimation of g then entails both statistical and numerical difficulties. A natural statistical approach is by maximum likelihood, conveniently implemented using the EM algorithm, but this provides unsatisfactory reconstructions of g. In this paper, we modify the maximum likelihood–EM approach by introducing a simple smoothing step at each EM iteration. In our experience, this algorithm converges in relatively few iterations to good estimates of g that do not depend on the choice of starting configuration. Some theoretical background is given that relates this smoothed EM algorithm to a maximum penalized likelihood approach. Two applications are considered in detail. The first is the classical stereology problem of determining particle size distributions from data collected on a plane section through a composite medium. The second concerns the recovery of the structure of a section of the human body from external observations obtained by positron emission tomography; for this problem, we also suggest several technical improvements on existing methodology.
Gene Hunting with Gradients of Likelihoods
Authors: Thomas Alun 
Published: December 2018

SUMMARY
When analysing the mode of inheritance of a genetic trait, or mapping its location on the human genome, computationally intensive likelihood calculations are required. The standard method, called peeling, is reviewed here and an extension to the calculation of gradients is implemented. The gradients are used for numerical searches for maximum likelihood estimates, and also for producing contour plots of log-likelihood surfaces. This is illustrated with an analysis of the mode of inheritance, of the eye disease blue dot cataract, and of its proximity to a genetic marker on chromosome 16.
Computing Extended Maximum Likelihood Estimates for Linear Parameter Models
Authors: Clarkson Douglas B. , Jennrich Robert I. 
Published: December 2018

SUMMARY
Methods are given for computing extended maximum likelihood estimates in which one or more parameter estimates are infinite at the supremum of the likelihood. The results are given for a broad class of regression-like models based on independent observations with linearly related parameters including, in particular, the generalized linear models. The estimation consists of two steps: A linear programming step to identify the infinite components and a more conventional function optimization step to optimize the remaining finite components. Provision is made for nuisance parameters. Two algorithms are presented and examples illustrating their use are given.
Semiparametric Estimation in Logistic Measurement Error Models
Authors: Carroll R. J. , Wand M. P. 
Published: December 2018

SUMMARY
We describe semiparametric estimation and inference in a logistic regression model with measurement error in the predictors. The particular measurement error model consists of a primary data set in which only the response Y and a fallible surrogate W of the true predictor X are observed, plus a smaller validation data set for which (Y, X, W) are observed. Except for the underlying assumption of a logistic model in the true predictor, no parametric distributional assumption is made about the true predictor or its surrogate. We develop a semiparametric parameter estimate of the logistic regression parameter which is asymptotically normally distributed and computationally feasible. The estimate relies on kernel regression techniques. For scalar predictors, by a detailed analysis of the mean-squared error of the parameter estimate, we obtain a representation for an optimal bandwidth.
A Characterization of Optimal Designs for Observational Studies
Authors: Rosenbaum Paul R. 
Published: December 2018

SUMMARY
Subclassification and matching are often used to adjust for covariates in observational studies. Here, the form of an ‘optimal’ subclassification is determined, i.e. a subclassification which makes the treated and control subjects in the same subclass as similar as possible. This optimal form is simple, intuitive and quite practical, though it is rarely used. The optimal form has several consequences. First, it suggests that theoretical investigations may assume that observational studies have this form, for if they do not they may be changed to this form without a loss, and often with a gain. Second, in searching for an optimal subclassification, the search may be confined to subclassifications of this form, for one is sure to be optimal. Finally, it is shown that finding an optimal subclassification of this form may often be reduced to finding the minimum cost flow in a certain network, i.e. to a standard combinatorial optimization problem for which good algorithms exist.
A New Method of Prediction for Spatial Regression Models with Correlated Errors
Authors: Vecchia A. V. 
Published: December 2018

SUMMARY
This paper deals with minimum mean-squared error, unbiased linear interpolation of a continuous domain spatial process based on a sparse set of irregularly spaced observations. The process is assumed to be governed by a linear regression model with errors that follow a second-order stationary Gaussian random field. A new method of prediction is developed that is compatible with the parameter estimation procedures of Vecchia. The result is a new likelihood-based method for joint parameter estimation and prediction that can be applied to large or small data sets with irregularly spaced data. Simulated and observed data sets are analysed to illustrate the methods.
Pooling 2 Times 2 Tables: Asymptotic Moments of Estimators
Authors: Gart John J. 
Published: December 2018

SUMMARY
Consider J independent pairs of mutually independent binomial variates which can be considered as 72 times 2 tables. We assume a common measure of association, such as the odds ratio, between the tables. This paper studies the asymptotic moments of the ‘pooled' estimators, i.e. those constructed from the data summed over all the tables. For balanced designs, or proportional subclass numbers, it is shown that the pooled estimator of the common odds ratio is asymptotically biased towards 1, while those of the common ratio and difference are asymptotically unbiased. The asymptotic variances are also compared. A simple test for complete homogeneity is suggested. The various results are illustrated in numerical examples.
Bayesian Computation Via the Gibbs Sampler and Related Markov Chain Monte Carlo Methods
Authors: Smith A. F. M. , Roberts G. O. 
Published: December 2018

SUMMARY
The use of the Gibbs sampler for Bayesian computation is reviewed and illustrated in the context of some canonical examples. Other Markov chain Monte Carlo simulation methods are also briefly described, and comments are made on the advantages of sample-based approaches for Bayesian inference summaries.
Semiparametric Analysis of Variance with Tensor Product Thin Plate Splines
Authors: Gu Chong , Wahba Grace 
Published: December 2018

SUMMARY
We consider fitting multivariate models to response data based on analysis-of-variance (ANOVA)-like decompositions of functions of several variables, f(t 1,..., td) = C + σα f α(ta + σα &lt; β f αβ(t α, t β) + · · · · A theory for fitting (some components of) these models with polynomial smoothing splines exists when each tα is in a subset of the real line. In this case the various estimated components turn out to be certain tensor sums and products of polynomial splines. This approach may not be natural when one or more of the 'variables' are geographic, in particular where nature does not know north from east. In this case splines of radial structure, such as thin plate splines, for the geographic component, are more natural. In this paper we extend this theory of polynomial smoothing spline ANOVA models to include variables which take values in Euclidean k-space, and fits which turn out to include sums and products of both polynomial and thin plate smoothing splines. The cases of most interest would be k = 2 and k = 3. The formulation, interpretation and calculation of the models are discussed, and an application of the technique is illustrated. This work can be used to build predictive ANOVA-like models which describe a response as a function of spatial, temporal and other variables and to explore their interactions. The models can be fitted by using the existing publicly available code RKPACK.
Bayesian Predictive Inference for a Finite Population Proportion: Two-Stage Cluster Sampling
Authors: Nandram B. , Sedransk J. 
Published: December 2018

SUMMARY
Given binary data from a two-stage cluster sample, we present a method to carry out Bayesian predictive inference for a finite population proportion. Our probabilistic specification should be useful for many surveys of this type and yields simple analytical expressions for the prior and posterior mean and variance. Within cluster k, we assume that the Yki are a random sample from the Bernoulli distribution with probability θk. Conditional on β and τ, θ1,..., θN are a random sample from a beta distribution. Finally, β has a discrete distribution with specified probabilities. We use data from the National Health Interview Survey to illustrate the methodology and to show how to choose values for the parameters in the prior distribution.
Tools for the Symbolic Computation of Asymptotic Expansions
Authors: Andrews David F. , Stafford James E. 
Published: December 2018

SUMMARY
This paper describes a collection of procedures for the systematic computation of asymptotic expansions that are common in statistical theory and practice: expansions of functions of sums of independent and identically distributed random variables. The procedures permit the expansion of maximum likelihood estimates, the associated deviance or drop in likelihood and more general functions of random variables with distributions involving one or more parameters. The procedures are illustrated with examples involving general and specific laws.
Improved Score Tests for Generalized Linear Models
Authors: Cordeiro Gauss M. , Ferrari Silvia L. de Paula , Paula Gilberto A. 
Published: December 2018

SUMMARY
We present, in matrix notation, an asymptotic expansion for the null distribution of the score statistic in generalized linear models, corrected up to order n −1 where n is the sample size. The expansion has advantages for numerical purposes because it requires only simple operations on matrices. It is also sufficiently simple to be used analytically to obtain several closed form expressions, analogous to Bartlett corrections, in a variety of important score tests. Improved score tests for these models are discussed and various applications to some special tests are given. We show by simulation that two asymptotically equivalent adjusted score tests seem to improve, at least for continuous data, on the usual score test.
Heteroscedastic G-Optimal Designs
Authors: Wong Weng Kee , Cook R. Dennis 
Published: December 2018

SUMMARY
This paper addresses the issue of constructing large sample G-optimal designs when the variability of the response varies across a compact design space. A useful characterization theorem is presented along with a computer algorithm for generating (heteroscedastic) G-optimal designs. to facilitate comparisons between D- and G-optimal designs, Atwood's inequality for comparing D- and G-efficiencies in homoscedastic models is generalized to heteroscedastic models. Some robustness properties of these designs are presented.
Estimation of Variance in Crossover Designs
Authors: Kunert J. , Utzig B. P. 
Published: December 2018

SUMMARY
There is concern that the usual analysis of crossover designs with more than two treatments is subject to bias due to correlations between the measurements on the same experimental units. It has been shown by Kunert in the special case of balanced Latin squares that this bias can be present but that it is limited. Extending the work of Kunert we show in the present paper that there is a constant X* which guarantees that the estimate for the variance of any treatment contrast from the usual model multiplied by X* has an expectation which is at least as big as the true variance. This result holds for any within-unit covariance structure and it is valid for a class of commonly applied designs, allowing for fewer periods than treatments. The constant X* depends on the number of units, periods and treatments but not on the data or the unknown covariance matrix. We also deal with the effect that our result can have on tests for hypotheses about treatment contrasts.
A Note on Nonparametric Estimation of the Distribution Function from Interval-Censored and Truncated Observations
Authors: Frydman Halina 
Published: December 2018

SUMMARY
This paper is concerned with the nonparametric estimation of the distribution function F from interval-censored and truncated data as discussed by Turnbull. It is observed that Turnbull's characterization of F̂, the maximum likelihood estimator of F, is not applicable in general when the data are interval censored and truncated. It is shown, however, that Turnbull's characterization can be easily modified to obtain the appropriate characterization of F̂.
Time Series Analysis of Circular Data
Authors: Fisher N. I. , Lee A. J. 
Published: December 2018

SUMMARY
The paper considers the problem of modelling and analysing a time series of measurements which take the form of unit two-dimensional vectors. Several general classes of existing and new models are studied in terms of feasibility and flexibility. An approach is recommended which uses two of these classes, and which takes advantage of several standard time series algorithms that are available in modern software packages. An application is given to the analysis of a series of data on wind directions.
Variances for Maximum Penalized Likelihood Estimates Obtained Via the Em Algorithm
Authors: Segal Mark R. , Bacchetti Peter , Jewell Nicholas P. 
Published: December 2018

SUMMARY
We address the problem of providing variances for parameter estimates obtained under a penalized likelihood formulation through use of the EM algorithm. The solution proposed represents a synthesis of two existent techniques. Firstly, we exploit the supplemented EM algorithm developed by Meng and Rubin that provides variance estimates for maximum likelihood estimates obtained via the EM algorithm. Their procedure relies on evaluating the Jacobian of the mapping induced by the EM algorithm. Secondly, we utilize results from Green that provide expressions for Jacobians of mappings induced by EM algorithms applied to a penalized likelihood. The resultant procedure requires no more code than that needed for the penalized EM algorithm itself. The technique is demonstrated with an illustrative example.
Automated Kernel Smoothing of Dependent Data by Using Time Series Cross-Validation
Authors: Hart Jeffrey D. 
Published: December 2018

SUMMARY
The problem of selecting the bandwidth of a kernel regression estimator when the observed data are serially correlated is considered. The bandwidth is selected by using a version of cross-validation that seeks a good one-step-ahead predictor of the data. This method, referred to as time series cross-validation (TSCV), simultaneously estimates an optimal bandwidth and, given a time series model for the errors, the autocorrelation function of the data. In addition, different time series models having the same number of parameters can be compared by using TSCV. Boundary kernels play a key role in the proposed methodology since one-step-ahead prediction entails extrapolating past the available data. Boundary kernels are used at the bandwidth selection stage, but ‘proper’ kernels are used to estimate the regression function. It is shown that smooth (i.e. at least continuous) boundary kernels have some robustness to misspecification of the error model. This means that a simple correlation model, such as the first-order autoregressive process, will often suffice for selecting a bandwidth. A simulation study and real data examples indicate the usefulness of TSCV for smoothing time series data.