bluuebunny/crossref_metadata_2025 huggingface dataset:
A Queueing Problem in Which the Arrival Times of the Customers are Scheduled
Authors: Mercer A.
Published: December 2018

The queueing problem considered is that in which (i)the customers are scheduled to arrive at equal time intervals but a customer may arrive at any time after the start of the interval during which he was scheduled to arrive, or may even not arrive at all; the lateness distribution is perfectly general.(ii)the total service-time of a customer is supposed to consist of a finite number of stages, such that the times spent in each of the stages are independent and identically distributed, and the probability of leaving a stage at any time depends on the time since the current scheduling interval began.

A method is discussed which enables the non-equilibrium distribution of the queue length at any time to be derived, and results for the equilibrium distribution are given. Most of the results relate to the case in which there is a single server but extensions of the argument for more than one server are outlined.
On the Theory of Classical Regression and Double Sampling Estimation
Authors: Tikkiwal B. D.
Published: December 2018

This paper examines the various classical results in the theory of regression and double sampling estimation and extends them to the study of a finite population.
An Exact Distribution of the Fisher–Behrens–Welch Statistic for Testing the Difference between the Means of Two Normal Populations with Unknown Variances
Authors: Ray W. D. , Pitman A. E. N. T.
Published: December 2018

This paper obtains the distributions of two statistics u and v (Welch, 1937) which have in the past been suggested for testing the equality of two normal means when the population variances are unknown.

It is shown that these distributions are weighted finite sums of t-distributions for the case when the sample sizes are odd.
An Analysis of Transformations
Authors: Box G. E. P. , Cox D. R.
Published: December 2018

In the analysis of data it is often assumed that observations y  1, y  2, …, yn are independently normally distributed with constant variance and with expectations specified by a model linear in a set of parameters θ. In this paper we make the less restrictive assumption that such a normal, homoscedastic, linear model is appropriate after some suitable transformation has been applied to the y's. Inferences about the transformation and about the parameters of the linear model are made by computing the likelihood function and the relevant posterior distribution. The contributions of normality, homoscedasticity and additivity to the transformation are separated. The relation of the present methods to earlier procedures for finding transformations is discussed. The methods are illustrated with examples.
The Robbins–Monro Method for Estimating the Median Lethal Dose
Authors: Cochran W. G. , Davis M.
Published: December 2018

The Robbins–Monro method provides a sequential plan that gives an attractively simple estimate of the LD50 in bioassay and is practicable for agents in which the response (death or survival) is known within an hour. By machine computations, its performance is examined for experiments using 50 or less animals. If the experiment's initial guess at the LD50 is within 2σ of the true LD50, a slight variant of the plan (the delayed version) can be recommended. For new agents in which the experimenter's initial knowledge of the LD50 and of σ may be poor, a two-stage plan is recommended, the first stage using single animals at equally spaced doses, the second stage being an ordinary Robbins–Monro plan. In a preliminary comparison with a standard 4-level non-sequential experiment, the sequential plan gave mean-square errors about 20 per cent lower if σ and the LD50 are guessed accurately, and much larger gains in accuracy if the LD50 is guessed poorly. The problem of attaching a standard error to the Robbins–Monro estimate of the LD50 is discussed.
Analysis of Factorial Experiments by Estimating Monotone Transformations of the Data
Authors: Kruskal J. B.
Published: December 2018

Data may sometimes be described by a linear model with fewer terms if a transformation is applied. For example, in a factorial design the need for certain interaction terms may be eliminated by transformation. If attention is restricted to all monotone transformations, it is possible and perhaps useful to find the monotone transformation which minimizes the residual sum of squares after removing the effects explained by the model. Several sets of data from the statistical literature are analysed this way.
A Bayesian Approach to Classification
Authors: Dunsmore I. R.
Published: December 2018

In this paper a branch of Bayesian statistical decision theory is investigated. A wide range of prediction problems in regression situations is considered within one statistical framework. A model is derived and applied to problems of classification.
A Derivation of the Probabilistic Explication of Information
Authors: Good I. J.
Published: December 2018

The quantitative explication of I(H: E | G), the amount of information concerning H provided by E given G, is obtained by assuming that I(H:E.F | G) is some function of I(H: E G|) and I(H:F|E. G). This assumption is less restrictive than the more customary assumption of strict additivity.
On the Distribution of Products of Random Variables
Authors: Lomnicki Z. A.
Published: December 2018

The problem of finding the probability density function of the product of n identically distributed independent normal variables was solved by Springer and Thompson (1966). Their formulae for n ≤ 7 are simplified in this paper and generalized to an arbitrary number of factors. Similar formulae for the corresponding probability distribution functions are derived. The applicability of these results to the cases of the negative exponential, Weibull and gamma distributions is discussed.
A Generalization of Bayesian Inference
Authors: Dempster A. P.
Published: December 2018

Procedures of statistical inference are described which generalize Bayesian inference in specific ways. Probability is used in such a way that in general only bounds may be placed on the probabilities of given events, and probability systems of this kind are suggested both for sample information and for prior information. These systems are then combined using a specified rule. Illustrations are given for inferences about trinomial probabilities, and for inferences about a monotone sequence of binomial pi. Finally, some comments are made on the general class of models which produce upper and lower probabilities, and on the specific models which underlie the suggested inference procedures.
A General Definition of Residuals
Authors: Cox D. R. , Snell E. J.
Published: December 2018

Residuals are usually defined in connection with linear models. Here a more general definition is given and some asymptotic properties found. Some illustrative examples are discussed, including a regression problem involving exponentially distributed errors and some problems concerning Poisson and binomially distributed observations.
An Exact πPS Sampling Scheme—Generalization of a Method of Hanurav
Authors: Vijayan K.
Published: December 2018

In his recent paper Hanurav (1967) discussed the problem of optimum utilization of auxiliary information for the estimation of the total (or mean) of a finite population and gave some solutions to the problem for the case of samples of size 2. In this paper we extend one of his procedures (sampling scheme A“ in his paper) to cover general sample sizes and also prove some of its optimum properties. The method is illustrated on the data given in Hanurav's paper.
Linear Bayesian Methods
Authors: Hartigan J. A.
Published: December 2018

A method of linear prediction is proposed, which follows the Bayesian scheme in combining prior and present information, but which uses only the first two moments of the distribution of parameters and observations, rather than the complete probability model required of Bayesian techniques.
Comparison of Sequential Bioassays in Small Samples
Authors: Davis Miles
Published: December 2018

Five sequential designs for estimating the median in quantal bioassay are compared with a non-sequential one. Mean-square errors of the estimates are calculated exactly in a numerical experiment with the factors: design, first dose, step, number of trials and dose-response curve. Each experimental unit uses 12 animals. Sequential experiments are more accurate, especially for first doses distant from the median. Delayed designs and many trials are best when the median is not well known beforehand. The assumed dose–response curves have little effect on the accuracy of the estimated median.
Spatial Variability and the Theory of Sampling in Random Fibrous Networks
Authors: Dodson C. T. J.
Published: December 2018

The two-dimensional variability of areal density is of interest in the characterization of flat fibrous networks such as paper and non-woven textiles and the corresponding one-dimensional case is pertinent to the study of textile yarns. An idealization of such materials to the random case has proved useful in many studies. This paper gives an analytical description of the spatial variability of random networks made from uniform straight fibres. This is based on the derivation of the isotropic point autocorrelation function for the structure, and an analysis of the variance and covariance among finite inspection cells in complete sampling schemes.
The Choice between Alternative Ancillary Statistics
Authors: Cox D. R.
Published: December 2018

Basu (1964) has shown that there may be alternative ancillary statistics for the same problem. It is suggested in the present note that this non-uniqueness can be resolved by taking that ancillary statistic which separates the expected information into components that differ as widely as possible.
Interval Estimation from the Likelihood Function
Authors: Hudson D. J.
Published: December 2018

During the last few years, several authors have devoted attention to both old and new methods of making inferences from likelihood functions. In this paper we study the properties of interval estimates which are obtained by drawing a horizontal line across the graph of the likelihood function. An exact evaluation is reported for one case of positive and one of negative binomial sampling, with parameter θ. The attained confidence coefficient α(θ) is graphed over 0 ⩽ θ ⩽ 1 for these two cases. A brief look is taken at intervals obtained when the random variable is continuous.
Comments and Queries Comment on “An Estimation Procedure for Mixtures of Distributions” by Choi and Bulgren
Authors: Macdonald P. D. M.
Published: December 2018

Choi and Bulgren's (1968) estimator for the mixing measure of a mixture of known distributions is biased in small samples; a variant of their estimator has a much smaller bias, and a smaller mean squared error, for mixtures of normal distributions differing in mean. The maximum-likelihood estimator is shown to be more computable than Choi and Bulgren suggest. Estimation is much more difficult when the component distributions are unknown; for example, a mixture of two normal components has five parameters, but no more than four may be estimated when the components are close together.
Permanent Expressions for Order Statistic Densities
Authors: Vaughan R. J. , Venables W. N.
Published: December 2018

Of late there has been a need to extend the traditional concept of an order statistic. Either the ordered statistics are obtained from statistics which are assumed to be correlated but with identical marginal densities (Young, 1967; Takahasi, 1969) or they are obtained from statistics which are sampled independently from different populations (Loynes, 1966; Tong, 1970). This note demonstrates that the marginal densities of the order statistics obtained by the latter extension can be expressed neatly by the use of permanents. The results appear to be new and one of the authors (Vaughan, 1970) has used these results in traffic research.
Outliers in Time Series
Authors: Fox A. J.
Published: December 2018

Two models are considered for outliers and their effects in time series. Likelihood ratio and approximate likelihood ratio criteria are derived for these models and the power functions are compared with that of the approach generally applied in the past.
Queues with Scheduled Arrivals: A Correction, Simplification and Extension
Authors: Mercer A.
Published: December 2018

Customers are scheduled to arrive at a queue during equal time intervals but they may be late; the lateness distribution is perfectly general. Bulk arrivals with an exponential service time distribution, single arrivals with staged services and single arrivals with a general service time distribution are considered when customers must arrive in the interval for which they were scheduled or not at all. Results given by the author in a previous paper, for single arrivals who may come in a later interval than the one for which they were scheduled and have an exponential service time distribution, are corrected. It is concluded that when customers are scheduled then the equilibrium distribution of queue length is a truncated sum of weighted geometric distributions, irrespective of the number of arrivals per interval, the lateness distribution, the service time distribution and the number of servers.
Spatial Interaction and the Statistical Analysis of Lattice Systems
Authors: Besag Julian
Published: December 2018

The formulation of conditional probability models for finite systems of spatially interacting random variables is examined. A simple alternative proof of the Hammersley–Clifford theorem is presented and the theorem is then used to construct specific spatial schemes on and off the lattice. Particular emphasis is placed upon practical applications of the models in plant ecology when the variates are binary or Gaussian. Some aspects of infinite lattice Gaussian processes are discussed. Methods of statistical analysis for lattice schemes are proposed, including a very flexible coding technique. The methods are illustrated by two numerical examples. It is maintained throughout that the conditional probability approach to the specification and analysis of spatial interaction is more attractive than the alternative joint probability approach.
An Asymptotic Equivalence of Choice of Model by Cross-Validation and Akaike's Criterion
Authors: Stone M.
Published: December 2018

A logarithmic assessment of the performance of a predicting density is found to lead to asymptotic equivalence of choice of model by cross-validation and Akaike's criterion, when maximum likelihood estimation is used within each model.
Spatial Contact Models for Ecological and Epidemic Spread
Authors: Mollison Denis
Published: December 2018

A wide variety of phenomena of geographical spread can be described in terms of a mechanism of “growth” (e.g. birth, infection) and a “contact distribution” which describes how the locations of the individual(s) involved in a migratory move, or infection at a distance, are spatially related. I shall survey work on such models, beginning with an examination of the relations between stochastic and deterministic models; it emerges that both linear and nonlinear deterministic models have close connections with the less interesting “linear” (exponential growth) stochastic models.

More realistic models must be nonlinear as well as stochastic; some results are now available for such models. As in the linear case, these deal mainly with asymptotic behaviour. Simulations reveal that nonlinear stochastic processes have a richer spectrum of non-asymptotic behaviour than linear models, though in some circumstances the simpler models may provide an adequate approximation.

Thus theoretical study of the short-term behaviour of such processes may be difficult, but should prove rewarding. The other main outstanding problems are those of inference for such models, especially the estimation of contact distributions.
Collapsibility of Multidimensional Contingency Tables
Authors: Whittemore Alice S.
Published: December 2018

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

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

Maximum likelihood inference for the coefficients of a multiple regression with missing values is studied by simulation, using artificially generated multivariate normal observations with randomly deleted missing values. The method is compared with least squares on the complete observations by mean squared error. Two methods of estimating the covariance matrix of the m.l. estimates are compared, and the applicability of large sample theory to obtain tests and confidence intervals for the regression coefficients is considered for moderate size samples.
Tests of 'Randomness' for Spatial Point Patterns
Authors: Ripley B. D.
Published: December 2018

Tests of “randomness” and methods of edge-correction for spatial point patterns are surveyed. The asymptotic distribution theory and power of tests based on the nearest-neighbour distances and estimates of the variance function are investigated.
On the Structural Representation for Polynomial-Projecting Predictor Models Based on the Kalman Filter
Authors: Godolphin E. J. , Stone J. M.
Published: December 2018

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

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

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

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

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

This article investigates the family {I  λ;λ ϵ ℝ} of power divergence statistics for testing the fit of observed frequencies {Xi; i = 1, …, k} to expected frequencies {Ei; i = 1, …, k}. From the definition 2nIλ=2λ(λ+1)∑i=1kXi{(XiEi)λ−1};λ∈ℝ

it can easily be seen that Pearson's X  2 (λ = 1), the log likelihood ratio statistic (λ = 0), the Freeman-Tukey statistic (λ = –½) the modified log likelihood ratio statistic (λ = –1) and the Neyman modified X  2 (λ = –2), are all special cases. Most of the work presented is devoted to an analytic study of the asymptotic difference between different I  λ however finite sample results have been presented as a check and a supplement to our conclusions. A new goodness-of-fit statistic, where λ = ⅔, emerges as an excellent and compromising alternative to the old warriors, I  0 and I  1.
Estimation and Hypothesis Testing in Finite Mixture Models
Authors: Aitkin Murray , Rubin Donald B.
Published: December 2018

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

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

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

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

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

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

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

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

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

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

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

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

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

We suggest refinements of the box counting method which address the obvious problems caused by the incomplete information and inaccessibility of the limit. A method for the statistical analysis of these corrected data is developed and tested on simulated and real data.
On the Use of Nonparametric Regression for Checking Linear Relationships
Authors: Azzalini Adelchi , Bowman Adrian
Published: December 2018

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

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

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

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

The extremal index is an important parameter measuring the degree of clustering of extremes in a stationary process. If we consider the point process of exceedance times over a high threshold, then this can be shown to converge asymptotically to a clustered Poisson process. The extremal index, a parameter in the interval [0, 1], is the reciprocal of the mean cluster size. Apart from being of interest in its own right, it is a crucial parameter for determining the limiting distribution of extreme values from the process. In this paper we review current work on statistical estimation of the extremal index and consider an optimality criterion based on a bias-variance trade-off. Theoretical results are developed for a simple doubly stochastic process, and it is argued that the main formula obtained is valid for a much wider class of processes. The practical implications are examined through simulations and a real data example.
A Gradient Algorithm Locally Equivalent to the Em Algorithm
Authors: Lange Kenneth
Published: December 2018

In many problems of maximum likelihood estimation, it is impossible to carry out either the E-step or the M-step of the EM algorithm. The present paper introduces a gradient algorithm that is closely related to the EM algorithm. This EM gradient algorithm approximately solves the M-step of the EM algorithm by one iteration of Newton's method. Since Newton's method converges quickly, the local properties of the EM gradient algorithm are almost identical with those of the EM algorithm. Any strict local maximum point of the observed likelihood locally attracts the EM and EM gradient algorithm at the same rate of convergence, and near the maximum point the EM gradient algorithm always produces an increase in the likelihood. With proper modification the EM gradient algorithm also exhibits global convergence properties that are similar to those of the EM algorithm. Our proof of global convergence applies and improves existing theory for the EM algorithm. These theoretical points are reinforced by a discussion of three realistic examples illustrating how the EM gradient algorithm can succeed where the EM algorithm is intractable.
Experimental Design and Observation for Large Systems
Authors: Bates R. A. , Buck R. J. , Riccomagno E. , Wynn H. P.
Published: December 2018

Large systems require new methods of experimental designs suitable for the highly adaptive models which are employed to cope with complex non-linear responses and high dimensionality of input spaces. The area of computer experiments has started to provide such designs especially Latin hypercube and lattice designs. System decomposition, prevalent in several branches of engineering, can be employed to decrease complexity. A combination of system decomposition using a sparse matrix method, experimental design and modelling is applied to one example of an electrical circuit simulator producing a usable emulator of the circuit for use in optimization and sensitivity analysis.
Predictive Updating Methods with Application to Bayesian Classification
Authors: Chen Rong , Liu Jun S.
Published: December 2018

We propose algorithms based on random draws from predictive distributions of unknown quantities (missing values, for instance). This procedure can either be iterative, which is a special variation of the Gibbs sampler, or be sequential, which is a variation of sequential imputation. In the latter case one can update the posterior distribution with new observations easily. The methods proposed have intuitive statistical implications and can be generalized to accommodate other Bayesian-like procedures. We display some applications of the method in connection with the Bayesian bootstrap, classification, hierarchical models and selection of variables. In particular, as an application of the method, we present a unified treatment of switching regression models driven by a general binary process, and we develop a Bayesian testing procedure. Some simulations and a real example are used to illustrate the methods proposed.
Design, development, and evaluation of locust bean seed dehuller
Authors: Okonkwo Clinton Emeka , Olaniran Abiola , Ojediran John Olusegun , Olayanju Tajudeen Adeniyi , Ajao Faith , Alake Adewumi Samuel
Published: December 2018

Locust beans dehulling machine was design, develop, and evaluated. The machine was evaluated at different speed and boiling time for its performance efficiency. The results showed that with increase in the boiling time from the first to second hr the throughput capacity, qualitative, and quantitative dehulling efficiency increased but from the second to the fourth hr of boiling, it decreased. Whereas as the dehulling speed increase the throughput capacity increased but the quantitative and qualitative dehulling efficiency decreased. Highest throughput capacity and the least labor requirement were recorded at 1 hr boiling, whereas highest quantitative and qualitative dehulling efficiency was recorded at 2 hr of boiling. The boiling time and dehulling speed significantly affects the throughput capacity, quantitative and qualitative dehulling efficiencies of the dehuller, but does not affect labor requirement. The economic analysis reveals that developed dehuller can be useful for small to medium scale locust bean processing industries.

Practical applications

The developed dehuller is relevant in the dehulling of boiled locust bean seed. This would, therefore, combat the challenges surrounding locust bean processing especially with the rural women dwellers and commercial producers. The dehuller would, therefore, reduce the time consumption and drudgery associated with the processing of locust bean.
Validity and reliability of a freehand 3D ultrasound system for the determination of triceps surae muscle volume in children with cerebral palsy
Authors: Barber L. , Alexander C. , Shipman P. , Boyd R. , Reid S. , Elliott C.
Published: December 2018

This study assessed the validity, intra‐rater and inter‐rater reliability of segmentation of in vivo medial gastrocnemius (MG), lateral gastrocnemius (LG) and soleus (SOL) muscle volume measurement using a single sweep freehand 3D ultrasound (3DUS) in children with cerebral palsy (CP). The MG, LG and SOL of both limbs of 18 children with CP (age 8 years 4 months ± 1 year 10 months, 11 males, unilateral CP = 9, bilateral CP = 9, Gross Motor Functional Classification System I = 11, II = 7) were scanned using freehand 3DUS and magnetic resonance imaging (MRI). All freehand 3DUS and MRI images were segmented and volumes rendered by two raters. Validity was assessed using limits of agreement method. Intra‐rater and inter‐rater reliability was assessed using intra‐class correlation (ICC), coefficient of variance (CV) and minimal detectable change (MDC). Freehand 3DUS overestimated muscle volume of the MG and LG by < 0.3 mL (1%) and underestimated SOL by < 1.3 mL (1.5%) compared with MRI. ICCs for intra‐rater reliability of the segmentation process for the freehand 3DUS system and MRI for muscle volume were > 0.98 and 0.99, respectively, for all muscles. ICCs for inter‐rater reliability of the segmentation process for freehand 3DUS and MRI volumes were > 0.96 and 0.98, respectively, for all muscles. MDCs for single rater freehand 3DUS and MRI were < 4.0 mL (14%) and 3.2 mL (11%), respectively, in all muscles. Freehand 3DUS is a valid and reliable method for the measurement of lower leg muscle volume that can be measured with a single sweep in children with CP in vivo. It can be used as an alternative to MRI for the detection of clinically relevant changes in calf muscle volume as the result of growth and interventions.
Latino/a Citizen Children of Undocumented Parents Negotiating Illegality
Authors: Rodriguez Cassaundra
Published: December 2018

Objective: The objective of this study is to examine how citizen young adults with undocumented parents manage parental illegality.

Background: These citizen young adults are part of mixed‐status families, which consist of members with different immigration statuses and often include U.S. citizen and undocumented immigrant family members. With 16 million people in mixed‐status families, scholars are beginning to capture their unique experiences, but little is known about the adult‐age citizen children in these families.

Method: Data for this study include interviews with 34 Latino/a citizen young adults ages 18 to 28. Interviews were analyzed by using the sociological concepts of legal violence and multigenerational punishment.

Results: The findings demonstrate that young adults are somewhat shielded from parental deportation concerns because of less sustained contact with parents and because of the perception that parents are cautious. Young adults also manage illegality when they apply for federal college financial aid and navigate the possibility of sponsoring their immigrant parents for legalization. Young adults' legal access to wage labor also entails distinct responsibilities to participate in family breadwinning.

Conclusion: This research demonstrates how parental undocumented status shapes family negotiations and state‐produced punishments for adult citizen children previously unaccounted for in immigration and family scholarship. These findings point to the distinct challenges of citizen young adults—experiences that differ from undocumented peers, the children of lawfully present parents, and minor children in mixed‐status families.