bluuebunny/crossref_metadata_2025_split huggingface dataset:
A Generalization of the Bayesian Steady Forecasting Model
Authors: Smith J. Q. 
Published: December 2018

Summary
The Bayesian Steady Forecasting model is generalized to a very wide class of processes other than the normal by defining the time series on the decision space. Examples of such processes are presented including a Beta-Binomial process, a Poisson-Gamma process and a Student-t sample distribution steady model. Simple updating relations are given for most of the processes discussed.
Some Prior and Posterior Distributions in Survival Analysis: A Critical Insight on Relationships Derived from Cross-Sectional Data
Authors: Elandt-Johnson Regina C. 
Published: December 2018

Summary
Many physiological characteristics such as, for example, blood pressure, level of serum cholesterol, vital capacity, may be considered as ageing factors contributing to the overall hazard rate function in an additive fashion (formula (3.2)). If so, the regression function of the characteristic on time, in a population of survivors to time t, depends on t even if the characteristic, itself, does not vary with t, for any one individual. Also, if there is a relationship between a characteristic and age for an individual, it cannot be uniquely estimated from population cross-sectional data, unless its functional contribution to the hazard rate is determined. Special consideration is given to the analysis, when the prior (i.e. at t = 0) distribution of each characteristic is normal, and the characteristics are independent.
Multi-Armed Bandits and the Gittins Index
Authors: Whittle P. 
Published: December 2018

Summary
A plausible conjecture (C) has the implication that a relationship (12) holds between the maximal expected rewards for a multi-project process and for a one-project process (F and φi respectively), if the option of retirement with reward M is available. The validity of this relation and optimality of Gittins' index rule are verified simultaneously by dynamic programming methods. These results are partially extended to the case of so-called “bandit superprocesses”.
On the E-Optimality of Some Block Designs
Authors: Cheng Ching-Shui 
Published: December 2018

Summary
This paper is concerned with the investigation of E-optimal block designs. Some conditions are given under which there is a regular graph design which is E-optimal. Immediate applications of these results demonstrate that a great majority of the designs obtained by John and Mitchell (1977) are indeed E-optimal. It can also be shown that a group-divisible design with λ1 = λ2 + 1 &gt; 1 and group size 2 is E-optimal. The same result also holds for a PBIB design with a cyclic scheme, λ2 = λ1 ± 1, and v = 5. Another application shows that if d is a BIBD, a group-divisible design with λ2 = λ1 + 1, a group-divisible design with λ1 = λ2 + 1 &gt; 1 and group size 2, or a PBIB design with a cyclic scheme, λ2 = λ1 ± 1 and v = 5, then the dual design of d is also E-optimal.
On the E-Optimality of Regular Graph Designs
Authors: Jacroux Mike 
Published: December 2018

Summary
This paper is an investigation into the E-optimality of regular graph designs within various classes of proper block designs. Several sufficient conditions are given for the existence of an E-optimal regular graph design within the classes considered. It is shown that when a regular graph design exists whose minimum non-zero eigenvalue is large enough, then an E-optimal regular graph design exists. Several examples are given to show how the derived sufficient conditions can be applied.
Moments of the Least Squares Estimators in a Non-Linear Regression Model
Authors: Clarke G. P. Y. 
Published: December 2018

Summary
The least squares estimates of the parameters of a non-linear regression model with normal and independent errors are expanded as a power series in independent standardized normal variables. From this expansion, expressions are derived for the variances and covariances which include one term beyond the usual approximation by the inverse of the information matrix. Similarly, expressions for the biases are found and overall relationships between the biases, variances and Beale's measures of non-linearity. Data following the Richards' Function are used in an example.
On Randomized Dynamic Allocation Indices for the Sequential Design of Experiments
Authors: Glazebrook K. D. 
Published: December 2018

Summary
In response to a suggestion by Bather, Gittins proposed the adoption of rules for sampling one at a time from several Bernoulli populations which were based on randomized versions of his dynamic allocation indices. Such rules, Gittins conjectured, might sometimes be both asymptotically optimal and also (almost) Bayes with respect to the usual discounted reward criterion. This conjecture is investigated and verified.
The Geometry of Robust Procedures in Linear Models
Authors: McKean Joseph W. , Schrader Ronald M. 
Published: December 2018

Summary
A geometry similar to the “co-ordinate-free” approach to least squares estimation in linear models is developed for R- and M-estimation. This is done by replacing Euclidean distance with appropriate distance measures. This approach allows development of a theory of estimable functions even in cases where expectations of errors do not exist, as well as a simple treatment of general linear hypotheses.
An Estimation Procedure of Parameters of a Certain Spectral Density Model
Authors: Taniguchi Masanobu 
Published: December 2018

Summary
Let {X(t)} be a Gaussian stationary process with mean zero and true spectral density g(x). We shall fit a certain spectral model f θ (x) for this process, and propose an estimate of θ, say θ^n, by minimizing a criterion D{f θ , g), which measures the nearness of f θ (x) to g(x). Also we shall derive the asymptotic distribution of θ^n. For the case of some appropriate spectral parametrization of f θ (x) we show that θ^n can be expressed in an explicit form. Furthermore, we shall investigate the asymptotic efficiency of θ^n.
An Asymptotically Bayes Sequential Test for Comparing Two Normal Means
Authors: Havre L. S. 
Published: December 2018

Summary
We consider sequential tests to decide whether the difference between the means of two normal populations is negative or positive. A Bayesian formulation is adopted, with costs of sampling which differ for the two populations and depend on the difference between the means. The asymptotic “shape”, in the sense of Schwarz (1962), of the Bayes continuation region is found, and this is used to derive an asymptotically Bayes test. A number of asymptotic optimality properties of this test are proved, and it is compared by computer simulation with a two-population SPRT and a truncated generalized two-population SPRT.
Revising Previsions: A Geometric Interpretation
Authors: Goldstein Michael 
Published: December 2018

SUMMARY
This paper considers the way in which an individual's previsions are changed by new information. Firstly, reasons are discussed for preferring prevision to probability as the fundamental element in the subjective formulation of statistical procedures. Then, following de Finetti, an inner product space is constructed, such that the vectors are random quantities of interest and the inner product corresponds to the previsions of the individual. The expected effect of new data is expressed by a bounded self-adjoint operator on this space. The information expected from the data is represented in terms of the eigenstructure of the operator. If the operator is compact, this representation has particularly simple form. New data impose orthogonal co-ordinate axes on the original inner-product space. The information expected about any random quantity is represented by a specified shrinkage along each axis. to any order of accuracy, all the information may be represented by a finite dimensional subspace. Finally, the geometric representation is related to more conventional, totally specified models.
A First Passage Problem in a Random Walk with a Quality Control Application
Authors: Munford A. G. 
Published: December 2018

SUMMARY
This paper is concerned with a first passage problem for a discrete time random walk which arises in a quality control scheme proposed by the author. There are two barriers, one of which is absorbing and the other such that the random walk particle is immediately returned to the origin upon reaching it. An explicit expression is derived for the probability distribution of the time to absorption when the barriers are symmetrically placed on either side of the origin.
Robust Sequential Approximate Bayesian Estimation
Authors: West M. 
Published: December 2018

SUMMARY
An approximation to the sequential updating of the distribution of location parameters of a linear time series model is developed for non-normal observations. The behaviour of the resulting non-linear recursive filtering algorithm is examined and shown to have certain desirable properties for a variety of non-normal error distributions. Illustrative examples are given and relationships with previous work on robustness and sequential estimation are mentioned.
A Hierarchical System of Interaction Measures for Multidimensional Contingency Tables
Authors: Agresti Alan 
Published: December 2018

Summary
Two summary measures are proposed of the amount of rth degree (r + 1 factor) and higher interaction displayed in a (d + 1)-dimensional contingency table, 1 ≤ r ≤ d. The measures are based on a comparison of the “partially-raked” table having the r-factor interactions and lower-order effects removed to the “fully-raked” table in which all effects are removed. The measures have a proportional reduction in error construction with reference to using d of the variables to predict the remaining one within the partially-raked and fully-raked tables, and they are generalizations of the lambda and tau measures of association for cross-classifications of two nominal variables.
Prediction Models and Unequal Probability Sampling
Authors: Cumberland William G. , Royall Richard M. 
Published: December 2018

Summary
Prediction models are used to study the Horvitz–Thompson estimator in probability–proportional-to-size sampling and six estimators of its variance. The variance estimators include the Horvitz–Thompson, Yates–Grundy, and jackknife statistics, as well as two bias-robust estimators from prediction theory. An empirical study confirms prediction theory's implications about these estimators.
A Credibility Interval for the Probability that a New Observation Belongs to One of Two Multivariate Normal Populations
Authors: Rigby R. A. 
Published: December 2018

Summary
The moments of the logarithm of the likelihood ratio of a new observation, drawn from one of two multivariate normal populations, are obtained from the posterior moment generating function. The distribution of the logarithm of the likelihood ratio is approximated using Pearson curves. The distribution of the probability p that a new observation belongs to one of the two populations can be obtained by transformation. The relationship between the expected value of this distribution and the “predictive” estimate of p is shown.
Conjectures for Optimal Block Designs
Authors: John J. A. , Williams E. R. 
Published: December 2018

Summary
In the study and construction of optimal block designs over the past 20 years a number of conjectures have been repeatedly stated and used. The purpose of this note is to bring together some of these conjectures. Although known to those actively engaged in research in design, it is hoped that this note will stimulate other statisticians and mathematicians to give their attention to these unsolved problems.
Likelihood Based Inference Using Signed Ranks for Matched Pairs
Authors: Pettitt A. N. 
Published: December 2018

SUMMARY
Exact and approximate inference based on the marginal likelihood which results from the signed ranks of the within pair differences of independent matched pairs is considered. Inference is made using Bayesian ideas. A quickly computed approximate analysis is introduced and this is shown to be extremely good when the within pair differences are assumed to have a normal distribution. Numerical comparisons are also made when the differences have a logistic distribution, but for this case the approximation is not as good. The approximations involve the Wilcoxon signed rank statistic and the half-normal scores signed rank statistic. The approximation is extended to consider regression models for matched pairs data. An application is given illustrating the ideas.
On the Hypergeometric Birth Process and Some Implications About the Gamma Distribution Representation
Authors: Ferreri Carlo 
Published: December 2018

SUMMARY
A stochastic birth process {X H(t), t ≥ 0} is derived from a special parametric form of the probability generating function (p.g.f.) of the four-parameter hypergeometric series distribution (HSD). In such context the generalized Waring distribution is obtained as a special equilibrium distribution. The distribution of XH(t) is expressed as a compound distribution whose compounder is a generally time-dependent hyper-gamma distribution (HGD). This compounder is, in turn, regarded as a convolution of a gamma distribution (GD) and a generalized HSD distribution whose generalizer is an exponential distribution (ED). This allows, for example, a separation of the effects of proneness and liability when the negative binomial process is assumed in accident theory. The result is extended by showing that the gamma distribution can be represented as an infinite convolution of generalized negative binomial distributions having ED's as generalizers. The HGD is similarly expressed.
Inequalities on Rank Correlation with Missing Data
Authors: Papaioannou Takis , Loukas Sotiris 
Published: December 2018

SUMMARY
New inequalities are obtained for Spearman's footrule, its associated sum of the absolute values of rank differences, the number of discordant pairs associated with Kendall's tau and the coefficient of concordance of several rankings when one or more individuals are missing or added to the data.
A Note on Conditional Prediction in the Multivariate Linear Model
Authors: Reinsel Gregory 
Published: December 2018

SUMMARY
In this paper we investigate the effects of errors in the estimation of the covariance structure of a multivariate random vector on the prediction of unobserved components of a further vector conditional on the values of the remaining observed components of the vector. We derive an exact expression for the increase in the mean square error of the usual least squares predictor due to these estimation errors which shows that the increase is substantial for small samples.
An Optimal Property of Kernel Estimators of a Probability Density
Authors: Hall Peter 
Published: December 2018

SUMMARY
Let f̂(x) be an asymptotically unbiased, nonparametric estimator of the density f(x) based on observations falling within the interval (x – ∈, x + ∈), where ∈ → 0 as the sample size diverges. We derive a lower bound to the variance of f(x), and prove that the bound is attained by a kernel estimator. This result is extended to estimates of f (r)(x), and to estimates of derivatives whose bias is improved by taking out the effects of unwanted terms.
On Extensions of the Gauss-Markov Theorem to the Case of Stochastic Regression Coefficients
Authors: Pfeffermann D. 
Published: December 2018

SUMMARY
Several theorems which extend the Gauss-Markov theorem to the case of stochastic vectors of coefficients are presented in the literature. Some of these theorems, although differently formulated and proved, are based on the same assumptions and arrive at similar results. Some theorems are special cases of theorems, already existing in the literature. In other cases, theorems, which appear to be similar in their underlying assumptions and conclusions, differ in ways that are not immediately apparent. A new extension, optimal prediction of coefficients of unobserved relations, is considered.
Stochastic Models for Rock Instability in Tunnels
Authors: McCullagh Peter , Lang Peter 
Published: December 2018

SUMMARY
We consider a tunnel of rectangular cross-section driven in hard rock containing three joint sets (series of parallel discontinuity planes that traverse the rock mass). If three planes intersect at a point just above the tunnel, a tetrahedron is formed whose base appears as a triangle in the tunnel roof. If the base triangle is contained entirely between the tunnel walls, the tetrahedral block is said to be kinematically unstable and may require support. Overlapping tetrahedra may also occur. In this paper we begin with the simplifying assumption that the spacings within each joint set are exponentially distributed, a model previously considered by Lang (1979), Warburton (1980), Pahl (1981), and consistent with the empirical findings of Priest and Hudson (1976). The principal results concern the total volume and base area of the overbreak (kinematically unstable rock), the distribution of apex height and the number of apexes, together with the number of simple blocks, composite blocks and key blocks. A similar model based on three independent gamma processes is developed and shows that increased regularity of the spacings leads to an increase in the volume of overbreak. Finally, it is shown how some of the results may be applied to circular and semi-circular tunnels.
Poisson Convergence for Dissociated Statistics
Authors: Barbour A. D. , Eagleson G. K. 
Published: December 2018

SUMMARY
A Poisson limit theorem is derived for the number of “large” values observed among comparisons of independent, but not necessarily identically distributed random variables. The comparisons made need not be the same and may depend on the two variables being compared. An application to the assessment of large numbers of correlation coefficients is given.
Asymptotic Behaviour of Conditional Maximum Likelihood Estimators in a Certain Exponential Model
Authors: Bar-Lev Shaul K. 
Published: December 2018

SUMMARY
In this paper we investigate the asymptotic behaviour of the conditional maximum likelihood estimator in an exponential model of order 2 introduced in Bar-Lev and Reiser (1982). This model, with natural parameters θ1 and θ2 (the latter a nuisance parameter), is characterized by expressing θ2 as a particular function of the mixed parameters. A direct proof is given for the asymptotic equivalence of the conditional maximum likelihood estimator and the maximum likelihood estimator for θ1. Some exact results concerning the relationships between these estimators are also presented.
Sequential Treatment Allocation Using Biased Coin Designs
Authors: Smith Richard L. 
Published: December 2018

SUMMARY
Biased coin designs are used in clinical trials as a means of achieving approximate balance within a randomized design. In this paper, detailed results are obtained for a class of biased coin designs from the point of view of the degree of balance achieved, selection bias, accidental bias and inference following the randomized trial. These results are developed in detail for the simple situation with two treatments and no prognostic factors. They are then extended to cover (i) more than two treatments with no prognostic factors, (ii) two treatments with prognostic factors.
Variance Estimation for the Combined Ratio and Combined Regression Estimators
Authors: Wu C. F. Jeff 
Published: December 2018

SUMMARY
A class of variance estimators including the standard ones, for the combined ratio estimator and for the combined regression estimator, is proposed. Optimal variance estimators in terms of minimizing the mean square error are obtained. Both model-free and model-dependent comparison of some standard variance estimators is made. For the combined ratio estimator, a new formula for the second order expansion of its mean square error is derived; the jackknife variance estimator is shown to be closely approximated by a (computationally) simpler estimator in the proposed class; and both model-free and model-dependent comparison of the biases of the variance estimators in the proposed class is made.
A Note on the Analysis of Resolvable Block Designs
Authors: Speed T. P. , Williams E. R. , Patterson H. D. 
Published: December 2018

SUMMARY
Yates (1939, 1940) pointed out that ordinary randomized block methods can be used, if necessary, to analyse lattice designs. This useful property is shown to extend to any resolvable incomplete block design including designs with blocks of unequal size.
Testing for Serial Correlation in Regression with Missing Observations
Authors: Robinson P. M. 
Published: December 2018

SUMMARY
In order to test for serial correlation in residuals for static time series regression in the presence of missing data, the score principle is applied both to the likelihood conditional on the observation times, and to an unconditional form of likelihood. Asymptotic distributions of the test statistics are established, under both the null hypothesis of no serial correlation, and sequences of local, correlated, alternatives, enabling analytic comparison of efficiency.
The Minimax Risk for Two-Stage Procedures in Clinical Trials
Authors: Bather John , Simons Gordon 
Published: December 2018

SUMMARY
The risk involved in a trial to compare two medical treatments is shared by patients who receive the inferior treatment during the experimental phase and those remaining after the experiment who might all receive the inferior treatment if the results are misleading. We consider the maximum of this risk with respect to the unknown probabilities of success and seek allocation rules that minimize this quantity, for a given total of patients. It needs extensive computations to find such minimax procedures, but there are simple and almost equally effective allocation rules based on a truncated sequential probability ratio test.
A Non-Gaussian State Space Model and Application to Prediction of Records
Authors: Smith R. L. , Miller J. E. 
Published: December 2018

SUMMARY
We develop a class of state space models for censored data. The basic model assumes an exponential distribution for the observations, conditionally on unobserved state variables. The model may be generalised by allowing transformations. We develop an application to the prediction of records. This is illustrated with some athletics data, though we also discuss briefly the possibility of more general applications connected with extreme values.
Design Effects of Two-Stage Sampling
Authors: Skinner C. J. 
Published: December 2018

SUMMARY
The effect of a two-stage sampling design on statistical inference is discussed. A definition of a design effect is given. The structure of design effects for a class of statistics is investigated. Results have both a design-based and a model-based interpretation. The relation between design effects for multivariate statistics and design effects for univariate statistics is considered.
Estimates for a Regression Parameter Using Ranks
Authors: Pettitt A. N. 
Published: December 2018

SUMMARY
In this paper we consider the estimation of a regression parameter in a partially specified model where, after an unknown monotone increasing transformation, the response is normally distributed and related to an explanatory variable by a linear model. We consider a Monte Carlo resampling technique due to Doksum and various modifications of it. In addition a simple estimate based on a modification of Fisher and Yates' normal scores method and an estimate using the means of ranks are considered. The estimates are compared using simulation.
Corrected Maximum Likelihood in Non-Regular Problems
Authors: Cheng R. C. H. , Iles T. C. 
Published: December 2018

SUMMARY
Maximum likelihood (ML) estimation can break down for distributions like the three-parameter Weibull or gamma where one of the parameters is a limit of the range of the distribution. It is suggested that use of the product of densities for the likelihood function is a misapplication of the ML method in such non-regular cases, and that this is the reason for its failure. It is shown that ML works quite satisfactorily if the likelihood is corrected in an appropriate way.