bluuebunny/crossref_metadata_2025 huggingface dataset:
A Relatively Simple Form of the Distribution of the Multiple Correlation Coefficient
Authors: Gurland John
Published: December 2018

A series is obtained for the cumulative distribution function of the multiple correlation coefficient in which the coefficients are interpretable as binomial probabilities. When N−p is even (N is the sample size and p is the number of components in the underlying multivariate normal distribution) the series is finite with 12(n−p)+1 terms. Other series are also considered. A comparatively simple approximation to the general distribution of the multiple correlation coefficient is presented which, in particular for p = 2, is more accurate than Fisher's z-transform over a large set of values of the parameters involved.
A Bayesian Approach to Calibration
Authors: Dunsmore I. R.
Published: December 2018

A Bayesian statistical decision theory model for a wide range of prediction problems in regression situations was derived in a previous paper (Dunsmore, 1966). In this paper the model is applied to problems of calibration.
Rank-Order Tests of Linear Hypotheses
Authors: Bennett B. M.
Published: December 2018

This paper considers tests for linear hypotheses using the ranks of independent observations from an unspecified distribution. By means of results on non-linear estimation of the regression vector (3 it is shown that the decomposition of, and tests for the sum of squares of ranks proceeds analogously to the usual analysis of variance model. These results are then applied to the Wilcoxon and Kruskal–Wallis tests and a multiple rank correlation coefficient.
Random Permutations
Authors: Plackett R. L.
Published: December 2018

The problem of generating random permutations of the integers 1, 2, …, n arises, for example, when sampling a randomization distribution and when tables of permutations are required for application to experimental design. An algorithm is described which minimizes the amount of randomization necessary to generate a random permutation, although in practice longer but simpler procedures are likely to be preferable. We discuss the probability distributions for the number of digits required by standard methods of generation from a sequence of random digits. Particular attention is given to the asymptotically efficient multistage randomization procedure. We obtain approximate formulae for the mean and variance of the number of digits and compare them with the exact results. An argument of a partly conjectural nature is put forward for the asymptotic normality of this number. The possibility that the permutations have unequal probabilities is briefly considered.
A Central Tolerance Region for the Multivariate Normal Distribution
Authors: John S.
Published: December 2018

In a multivariate normal distribution the probability density takes any particular value at all points on the surface of an ellipsoid whose centre is the mean of the distribution. Among such ellipsoids there is one, R, say, that contains 100α per cent of the individuals in the population. The paper deals with the problem of determining from a random sample a region which contains R with prescribed probability β. In the univariate case, R reduces to an interval with the mean as midpoint. Any linear function of variables whose joint distribution is normal has again a normal distribution. Let Ta denote the interval corresponding to R in the case of the linear combination with coefficients vector a. A method of determining from the sample intervals which simultaneously include Ta for all a with probability β is indicated.
Missing Data in Regression Analysis
Authors: Haitovsky Yoel
Published: December 2018

Two alternative methods for dealing with the problem of missing observations in regression analysis are investigated. One is to discard all incomplete observations and to apply the ordinary least-squares technique only to the complete observations. The alternative is to compute the covariances between all pairs of variables, each time using only the observations having values of both variables, and to apply these covariances in constructing the system of normal equations. The former is shown to be equivalent to the Fisher–Yates method of assigning “neutral” values to missing entries in experimental design.

The investigation is carried out by means of simulation. Eight sets of regression data were generated, differing from each other with respect to important factors. Various deletion patterns are applied to these regression data. The estimates resulting from applying the two alternative methods to the data with missing entries are compared with the known regression equations. In almost all the cases which were investigated the former method (ordinary least squares applied only to the complete observations) is judged superior. However, when the proportion of incomplete observations is high or when the pattern of the missing entries is highly non-random, it seems plausible that one of the many methods of assigning values to the missing entries should be applied.
Plant Competition: Three Species Per Pot
Authors: McGilchrist C. A.
Published: December 2018

An experiment is considered in which several species are grown two per pot and three per pot in equal proportions. It is of interest to consider differences between three species per pot yields and what might be predicted for them from the two species per pot yields. An analysis of variance is suggested for these differences and this analysis is derived using relationship algebra.
Some Problems of Optimal Stopping
Authors: DeGroot Morris H.
Published: December 2018

An experimenter can take observations sequentially from a normal distribution with unknown mean. When he stops sampling, he receives a net gain that depends on the values that have been observed and on the cost of sampling. Optimal stopping rules are developed for problems of sampling with and without recall, and for problems involving forced stopping.
Experiments with Mixtures: A Generalization of the Simplex-Lattice Design
Authors: Lambrakis D. P.
Published: December 2018

A theory is developed for experiments with mixtures of n “major” components with proportions ci (i = 1,2,..., n), where each component is itself a mixture of several other components with proportions xij(i=1,2,…,n;j=1,2,…,ni). The purpose of this theory is the empirical prediction of the response to any mixture of the n “major” components when the response depends only on the proportions ci and xij, but not on the total amount of the mixture.
Experiments with p-Component Mixtures
Authors: Lambrakis D. P.
Published: December 2018

A design for experiments with mixtures of p components is developed in which the prediction of the response to any p-component mixture is based on responses to mixtures containing all p components with non-zero proportions.
On the Distributions of the Times between Events in a Stationary Stream of Events
Authors: Leadbetter M. R.
Published: December 2018

In this paper, series expressions are obtained for the distributions of times between events in a stationary stream of events. The terms in the series involve factorial moments of the number of events in the interval (0, t). Similar results are obtained for a “mixture” of two stationary streams.
Majorants of the Chromatic Number of a Random Graph
Authors: Holgate P.
Published: December 2018

The probabilistic behaviour of several upper bounds for the chromatic number of a graph is investigated, when the graph is constructed at random.
Structural Probability and Prediction for the Multivariate Model
Authors: Fraser D. A. S. , Haq M. Safiul
Published: December 2018

The multivariate normal distribution can be used to describe the response variable of a system. A more comprehensive multivariate model is described in this paper: it has a distribution describing an error variable internal to a system, with a known multivariate distribution; and it has a positive affine transformation, the physical quantity, which generates a response vector from an error vector. This more comprehensive model is a structural model and it provides structural probability statements concerning the physical quantity.

Error and structural distributions are derived for the multivariate model. The structural distribution for a quantity can be used to generate structural prediction distributions : various prediction distributions are obtained for the multivariate model. The results are specialized to cover the case of the multivariate normal structural model.

The classical multivariate normal has been analysed by Bayesian methods (Geisser and Cornfield, 1963). The more comprehensive multivariate structural model does not need the use of subjective methods.
The “Maximum Likelihood Solution” of the Problem of Estimating a Linear Functional Relationship
Authors: Solari Mary E.
Published: December 2018

The problem considered is that of estimating a functional relationship (assumed linear) between two unobservable mathematical quantities ξ and η from pairs of observations on these quantities when both sets of observations are subject to normal independent errors. The problem has attracted much interest over a long period and one reads repeatedly that the method of maximum likelihood yields unsatisfactory estimators in this case. In this note we show that in fact no maximum-likelihood solution exists for this problem, which ceases then to provide an example of unsatisfactory maximum-likelihood estimators and merely joins the queue of problems in which the likelihood approach fails to produce estimators. The distinction, although academic, is worth making.
A Note on Sequential Estimation
Authors: Solomon Daniel L.
Published: December 2018

Moran (1951) infers that for some stationary stochastic processes, problems of parameter estimation may be simplified by employing sequential estimation procedures. He considers for example, estimation of the birth rate in the (stationary) Furry–Yule process. The purpose of this note is to indicate that Moran's suggestion may be useful for non-stationary processes as well. In particular, we consider maximum likelihood estimation of the parameter of a non-homogeneous, pure birth process.
Stochastic Models for Earthquake Occurrence
Authors: Vere-Jones D.
Published: December 2018

This paper attempts to survey some of the stochastic models which have been proposed for the sequence of energies and origin times of earthquakes from a given region, and to describe some examples of their application. to a good approximation in a regional study, each earthquake may be regarded as a point event, and consequently the main emphasis is on stochastic point processes. The theory of such processes is developed in a form suitable for this context, with particular emphasis being given to the clustering models of Neymann–Scott and Bartlett–Lewis. The use of these models is illustrated with reference to earthquake data from New Zealand. A final Section is concerned with stochastic models for aftershock sequences—the trains of smaller shocks which frequently follow the occurrence of large shallow earthquakes.
Use of Generalized Inverse Matrices in Manova
Authors: John J. A.
Published: December 2018

The concept of a generalized inverse matrix is used to derive the likelihood ratio statistic for testing a general estimable hypothesis in the multivariable linear model. The results, which are analogous to those in Searle (1965), are illustrated by considering the one-way model and the two-way model with one observation per cell.
On the Representation of Ignorance in Poisson Processes
Authors: Hasofer A. M.
Published: December 2018

The only prior density function of the intensity parameter m in a homogeneous Poisson process with complete prior ignorance which satisfies simple consistency conditions on predictors is f(m) ∞ m-1.
Asymptotic Properties of Conditional Maximum-Likelihood Estimators
Authors: Andersen Erling Bernhard
Published: December 2018

The problem of obtaining consistent estimates for structural parameters in the presence of infinitely many incidental parameters was discussed first by Neyman and Scott (1948). In this paper a maximum-likelihood method based on the conditional distribution given minimal sufficient statistics for the incidental parameters is suggested. It is proved that conditional maximum-likelihood estimates in the regular case are consistent and asymptotically normally distributed with a simple asymptotic variance. The efficiency problem of this new estimator is discussed in particular with respect to some situations with ancillary information.
The Fitting of Non-Stationary Time-Series Models with Time-Dependent Parameters
Authors: Rao T. Subba
Published: December 2018

We use the method of weighted least squares to estimate the time-dependent parameters of non-stationary time-series models. Approximate expressions for the bias and variance of the estimates, which could be used to assess the merits of various weight functions on the basis of “mean square error” criterion, are obtained. In Section 5, it is shown that the estimates obtained by weighted least-squares method are the same as estimates obtained by weighted maximum-likelihood estimation procedure. The procedures are numerically illustrated in the last section.
Estimating the Parameters of a Linear Function of a Random Variable
Authors: Sclove Stanley L. , Van Ryzin John
Published: December 2018

Let W be a random variable and X be a linear function of W: X = αW + β. Given a sample of independent observations distributed as X, we wish to find maximum-likelihood estimators for the parameters α and β of the linear function. If the support of W is the whole real axis, the maximum-likelihood estimators can be found by the usual methods; in other cases restricted maximization techniques must be used. Here we restrict attention to cases in which the support is the interval [a, + ∞) or the lattice {a + kh, k = 0, 1, 2, …} and the density of W is decreasing over the support. Special attention is given to the exponential and geometric distributions. If the parameter of the distribution is also unknown, its maximum-likelihood estimator can also be obtained when the support of W is the lattice.
Spectral Analysis with Randomly Missing Observations
Authors: Bloomfield P.
Published: December 2018

Spectral analysis of data with randomly missing observations is considered. Conditions are found under which consistent estimation of the spectral density function of the observed process is possible. An estimate is proposed and the results of a simulation study of its first two moments are presented.
Transformation of a Birth Process into a Poisson Process
Authors: Waugh W. A. O'N.
Published: December 2018

The pure birth process with linear birth rates is considered. The sum of sojourn times is shown to have a functional relationship with an asymptotic estimate of the population size that is known from the theory of branching processes. A theorem concerning this estimate, due to Kendall (1966), is proved by means of this relationship, in a way which brings out the connection between Kendall's theorem and an important property of non-time-homogeneous Poisson processes. Further developments are then studied. An alternative way to generate the birth process is described. This brings in certain conditioned processes, the condition being the value of the asymptotic estimate just mentioned. Rates of convergence to the asymptotic value are also considered.
On the Asymptotic Properties of the Maximum-Likelihood Estimate Obtained from Dependent Observations
Authors: Bar-Shalom Yaakov
Published: December 2018

The problem of weak consistency and asymptotic efficiency of the maximum-likelihood estimate in the case of dependent random variables (observations) is considered. A set of readily applicable conditions that ensure these properties of the maximum-likelihood estimate is presented. The conditions are expressed in terms of the probability density distribution of individual observations, conditioned upon all past observations. The connection between these conditions and the Fisher information measure is also discussed.
Bayes Estimates for the Linear Model
Authors: Lindley D. V. , Smith A. F. M.
Published: December 2018

The usual linear statistical model is reanalyzed using Bayesian methods and the concept of exchangeability. The general method is illustrated by applications to two-factor experimental designs and multiple regression.
The Numerical Solution of a Set of Conditional Estimation Equations
Authors: Andersen E. B.
Published: December 2018

In this paper we discuss the numerical solution of a set of conditional likelihood equations essential for the statistical analysis of psychological questionnaires. The model underlying this type of statistical analysis is described in detail and the conditional maximum-likelihood method that is used for estimating item parameters is discussed in relation to the chosen model. The conditional likelihood equations contain a generalized version of the elementary symmetric functions. The main problem in solving the estimation equations consists in finding a rapid recursive way to compute these functions. Such a procedure is described in the paper. In the final section of the paper the developed method is illustrated by a numerical example.
Experimental Designs with Many Classifications
Authors: Freeman G. H.
Published: December 2018

A general method of analysis is given for a design with a set of treatments added to a p-way orthogonal classification. If there is any grouping within the treatments, the treatment sum of squares may be partitioned; the partitioning is assisted by expressing this sum of squares as a quadratic form in the estimated treatment parameters. When the treatments fall into two groups, possibly with unequal replication, the complete partition of the treatment sum of squares is derived. Designs on three-way classifications are considered in some detail. The more useful ones are mostly on single Latin squares, and new ways of adding various numbers of treatments to 5 times 5 and 6times6 Latin squares are described, examples of possible designs being given. Lack of balance of the treatments with respect to one of the orthogonal classifications may be compensated for in another classification so that some designs are better balanced with three classifications than with one or two.
On Lehmann's Test for Homogeneity of Variances
Authors: Ghosh B. K.
Published: December 2018

For testing the equality of variances in k ≥ 2 normal populations Lehmann (1959) proposed a test procedure based on the logarithms of the sample variances. This paper investigates certain properties of that procedure, such as how to determine its critical region for small sample sizes, and whether or not the procedure is unbiased and robust. An asymptotic comparison is also made between Lehmann's test and the more well-known test due to Bartlett (1937).
Analysis of Log-Linear Models
Authors: Gokhale D. V.
Published: December 2018

Log-linear models are extensively used to analyse categorical and “stimulus-response” data. This paper gives an iterative procedure for obtaining maximum likelihood estimates of cell frequencies and of the parameters of a log-linear model in a multinomial experiment.
Two-Factor Experiments in Non-Orthogonal Designs
Authors: John J. A. , Smith T. M. F.
Published: December 2018

Some of the problems of asymmetrical factorial experiments using incomplete block designs of equal block size are considered. A set of conditions is established under which a non-orthogonal design for an m × n factorial experiment will give an orthogonal analysis of the main effects and interaction. These conditions are based upon the variances and covariances of the estimated treatment effects in the basic design, and cover all known classes of designs that give an orthogonal analysis. Simple expressions for the adjusted main effects and interaction sums of squares are obtained.
Some Approximations for the Distribution of a Multivariate Likelihood Ratio Criterion
Authors: Korin B. P. , Stevens E. H.
Published: December 2018

Some approximations, using χ  2 and F, are given for the distribution of the likelihood ratio statistic used for simultaneous testing of the mean and covariance of a multivariate normal distribution. Consideration is given to the accuracy of the proposed approximations.
The Estimation of Parameters in Multivariate Time Series Models
Authors: Wilson G. Tunnicliffe
Published: December 2018

We shall present a practical iterative method for estimating parameters in mixed autoregressive moving-average models for multivariate stationary time series. This method essentially generalizes that of Marquardt (1963) as applied by Box and Jenkins (1970) to univariate time series. We shall investigate the statistical properties of the method in order to demonstrate desirable convergence behaviour.
On the Estimation of the Parameters in the Bivariate Negative Binomial Distribution
Authors: Subrahmaniam Kocherlakota , Subrahmaniam Kathleen
Published: December 2018

Edwards and Gurland (1961) and Subrahmaniam (1966) have considered a correlated model as an alternative to the Bates and Neyman (1952) model, appropriate in the theory of accident proneness. The latter has presented a test for suitability of Bates–Neyman model against the alternative of the correlated model. Edwards and Gurland, on the other hand, are mainly concerned with the estimation of the parameters. Unfortunately, they are restricted to moments estimators under some constraints on the parameters. In the present paper, the problem of estimation is tackled, with a view to assessing the different methods available.
Marginalization Paradoxes in Bayesian and Structural Inference
Authors: Dawid A. P. , Stone M. , Zidek J. V.
Published: December 2018

We describe a range of routine statistical problems in which marginal posterior distributions derived from improper prior measures are found to have an unBayesian property—one that could not occur if proper prior measures were employed. This paradoxical possibility is shown to have several facets that can be successfully analysed in the framework of a general group structure. The results cast a shadow on the uncritical use of improper prior measures.

A separate examination of a particular application of Fraser's structural theory shows that it is intrinsically paradoxical under marginalization.
Some Designs for Extrapolation Outside a Sphere
Authors: Draper Norman R. , Herzberg Agnes M.
Published: December 2018

Methods for selecting a first-order response surface design when, as is usually the case, both variance and bias error exist, are applied to a situation in which it is desired to extrapolate the fitted model in a specified direction outside of a sphere within which all the runs are to be made.
Goodness-of-fit Test Using Sample Quantiles
Authors: Bofinger Eve
Published: December 2018

A goodness-of-fit test is constructed using sample quantiles for a p.d.f. F(x, θ) (where θ is to be estimated) which is continuous and strictly increasing at the quantiles of interest. It is shown to be asymptotically equivalent, under alternatives “close” to the null, to the usual goodness-of-fit test based on grouped observations, the advantage being that we may avoid the difficulties of choosing cell boundaries for grouping.
Testing Transformations to Normality
Authors: Atkinson A. C.
Published: December 2018

Andrews's exact test for the value of the parameter in the Box and Cox parameteric family of transformations is compared with two tests derived from the likelihood function. These two tests are shown, for a numerical example, to be uniformly more powerful than the exact test.
On the First Emptiness of Dams with Markovian Inputs
Authors: Shanbhag D. N.
Published: December 2018

In the present paper some well-known results on random walk have been used to arrive at the results of Ali Khan and Gani (1968), Gani (1969), Brockwell and Gani (1970) and Matthews (1972) concerning the first emptiness problems of dams with Markovian inputs.
Some Exact Tests for Normality in the Presence of Unknown Parameters
Authors: Csorgo M. , Seshadri V. , Yalovsky M.
Published: December 2018

The scale and location parameters in the normal and some exponential families are eliminated by means of suitable transformations on the original observations and the transformed random variables are then shown to possess certain known distributions with known parameters on the null hypothesis. Exact tests using Kolmogorov-type statistics can then be performed on the transformed variables for testing the null hypothesis.
On Some Procedures for Testing a Linear Relation Among Variances
Authors: Naik Umesh D.
Published: December 2018

In this paper, procedures are given for testing the hypothesis that the relation σ32=σ12+σ22 holds among the three variances σ12,σ22 and α32. This hypothesis is tested against the alternatives (i) σ32>σ12+σ22, (ii) σ32<σ12+σ22 and (iii) σ32≠σ12+σ22. The test procedures satisfy the property that the size or the Type I error does not exceed the preassigned level α. Optimum properties of the tests and their size and power functions are also investigated. The generalization of the procedures to the case involving more than three variances is also discussed.
The Conditioned Diffusion Equation and its Use in Population Genetics
Authors: Narain P.
Published: December 2018

The forward and backward conditioned diffusion equations relative to the event of the process attaining absorption in one of the boundaries have been derived from the corresponding Kolmogorov differential equations. The backward conditioned diffusion equation has been used to derive the mean and variance of the length of time until absorption in one of the boundaries. The general results so obtained have been applied to the problem of random drift in population genetics, giving the means and variances of the distributions of time until fixation as well as of time until extinction of a particular gene in a finite population.
A General Method of Confounding for Symmetrical Factorial Experiments
Authors: Cotter Sarah C.
Published: December 2018

This paper considers the problem of conducting an mn factorial experiment in blocks size ml. Designs can be constructed for all values of m, although for certain values better confounding patterns are available. Analysis of these designs is given, showing which components of the sum of squares are confounded with blocks.
On Interval Estimation of a Ranked Parameter
Authors: Alam K. , Saxena K. M. Lal
Published: December 2018

Let F(x; θ) denote a family of distributions on the real line, indexed by the real-valued parameter θ. It is assumed that the given family is stochastically increasing in θ, that is, F(x; θ) is non-increasing in θ for each x. Let θ  l …, θk represent k unknown values of the parameter θ, and let X  l …, Xk represent k independent observations from the distributions

F(x; θ  l), …, F(x; θk),

respectively. Let X* and θ* denote the ith smallest values among the observations and the parameters, respectively. For a given confidence level we obtain an interval estimate of θ*, based on X*. We consider special cases where θ is a location parameter, a scale parameter or a binomial parameter.
A Restricted Sequential Test
Authors: Brown B. M.
Published: December 2018

A restricted sequential procedure is presented for testing the hypothesis θ = θ0, about an unknown parameter θ, against compound alternatives. It is based upon a corresponding procedure for testing Brownian motion drift, and approximations to OC and ASN functions, and confidence intervals, are obtainable from the Brownian motion case. The procedure is applicable to many common families of distributions indexed by θ.
Estimation of Weibull Parameters from Two-Order Statistics
Authors: Murthy V. K. , Swartz G. B.
Published: December 2018

The use of a computationally simple statistic for estimating, from small samples, the important reciprocal-shape parameter, γ, of the Weibull distribution is described. The estimator uses two suitably selected order statistics from a sample of N failure times. The choice of the two has been made to minimize the variance of the estimator; however, concise formulae are given to permit the use of any two order statistics in the case of censored samples. The statistic is unbiased, its efficiency relative to the Cramér–Rao bound appears to approach 70 per cent and its exact distribution function is given. The statistic is applied to hypothesis tests of the reciprocal-shape parameter when the location parameter is unknown. The relationship between this test and other tests for Weibull parameters are discussed in the Introduction.
Missing Values in Multivariate Analysis
Authors: Beale E. M. L. , Little R. J. A.
Published: December 2018

This paper presents computational results for some alternative methods of analysing multivariate data with missing values. We recommend an algorithm due to Orchard and Woodbury (1972), which gives an estimator that is maximum likelihood when the data come from a multivariate normal population. We include a derivation of the estimator that does not assume a multivariate normal population, as an iterated form of Buck's (1960) method.

We derive an approximate method of assigning standard errors to regression coefficients estimated from incomplete observations, and quote supporting evidence from simulation studies.

A brief account is given of the application of these methods to some school examinations data.
Bayes Equivariant Estimators in High Order Hierarchical Random Effects Models
Authors: Sahai Hardeo
Published: December 2018

The Bayes equivariant estimators of the variance components (Zacks, 1970, 1971) are characterized in the case of r-stage hierarchical random effects models when the random effects are normally distributed and are mutually and completely independent. Non-trivial Bayes equivariant estimators are derived using a special prior distribution for the three-stage hierarchical model. It is observed that for the squared error loss function every Bayes equivariant estimator of the residual variance component is inadmissible.
Error Probabilities and Average Sample Number of the Sequential Probability Ratio Test
Authors: Siegmund D.
Published: December 2018

Let x  1,  x  2, ... be independent random variables which under p  θ have probability density function of the form exp (θx – Ψ(θ)} relative to some measure v, where Ψ is normalized so that Ψ(0) = Ψ‘(0) = 0. Let a ≤ 0 < b, sn = ∑1  n  x  k, and T=inf{n:sn∉(a,b)}. Approximations are given for p  θ{sT ≥; b} and E  θ(T) based on asymptotic considerations arising in renewal theory. The accuracy of these approximations is discussed for normally distributed x‘s. It is shown that for θ = 0 these approximations give complete asymptotic expansions as b → ∞ in powers of b  −1 with exponentially small remainder.
Calculation of Confidence Intervals for Noncentrality Parameters
Authors: Venables W.
Published: December 2018

The end points of a confidence interval for the noncentrality parameter of noncentral χ2 or F are identified as upper and lower percentage points of a distribution. It is shown how these can be calculated by applying the inverse Cornish–Fisher expansion.

The same procedure can be used to find the value of the noncentrality needed to give a fixed size χ2 or F test some specified power; however, in this situation the results may be only approximate.
Maximum Likelihood Estimation for Dependent Observations
Authors: Crowder Martin J.
Published: December 2018

The asymptotic properties of m.l.e. are discussed for generally dependent observations. Conditions are derived for weak consistency and asymptotic Normality of the estimates. We further consider the case where some of the parameters are “transient” in the sense that the accumulated information on them from the sample does not increase indefinitely; then the interest lies in estimating the other parameters consistently. Examples are given, and the work is related to that of Neyman and Scott (1948).
An Investigation of the F-Test Procedure as an Estimation Short-Cut
Authors: Leonard Tom , Ord Keith
Published: December 2018

When estimating fixed effects in the one-way anova model the F-test for the equality of the group means is sometimes used as a preliminary test of significance. This paper provides alternatives to the percentage points in the F-test by re-formulating the problem under estimation, as opposed to hypothesis testing, criteria. The new procedure possesses strikingly different properties, and it is argued that fixed-size tests are not obviously relevant within an estimation framework.
Some Considerations in the Optimal Design of Experiments in Non-Optimal Situations
Authors: Herzberg Agnes M. , Andrews David F.
Published: December 2018

Designs which satisfy optimal design criteria will usually not be optimal when some observations are missing, when outliers are present or when, contrary to the assumptions, the error of the observations arises from a non-Gaussian distribution. Designs robust against such short-comings will be introduced. They are slightly less than optimal under ideal conditions but will be more efficient under more realistic conditions. The probability of breakdown of a design is defined. Measures of robustness of a design are introduced in the cases of the generalized variance and the minimization of the maximum variance criteria. These measures and the probability of breakdown should be taken into account when the decision for a particular type of design is made. Some examples are given.
Sequential Tests for Composite Hypotheses with Two Binomial Populations
Authors: Hoel D. G. , Weiss G. H. , Simon R.
Published: December 2018

Sequential procedures for testing composite hypotheses about the parameters of two binomial distributions are developed. The testing of a null hypothesis against a onesided alternative is studied. It is shown that SPRT tests of simple hypotheses can be used for the composite situation with the desired error probabilities being preserved. Computer simulations indicate that when discrimination is based upon the difference in success probabilities, a procedure based on a likelihood ratio with nuisance parameters replaced by sequential maximum-likelihood estimates is shown to result in the smallest expected sample size.
Properties of the Exponential Scores Test for the K-Sample Problem Under the Lehmann Model
Authors: Burr P. , Young D. H.
Published: December 2018

Properties of an exponential scores statistic which provides a non-parametric test of the homogeneity of k continuous populations are considered. Tables of exact critical values are given for the case k = 3 and some small sample sizes and approximations to the critical values are developed and evaluated. Small sample power comparisons are made with the Kruskal–Wallis rank test under the Lehmann model and some asymptotic efficiency results are developed under a limiting form of this model. Finally, a modified form of the test to allow for censoring is presented.
Identification of Parameters by the Distribution of a Maximum Random Variable
Authors: Anderson T. W. , Ghurye S. G.
Published: December 2018

Under what conditions does the distribution of the maximum of a set of independent random variables uniquely determine the distributions of the component random variables? In the univariate case, a sufficient condition is that for every pair of distinct densities in the family of possible densities, one density converges to zero infinitely faster than the other, as x → ∞. Hence, the distribution of max {X  i, i = 1, ..., n} when X  i has the distribution N(μi, σ2  i), uniquely determines μi, σ2  i, i = 1, ..., n (except for indexing). The identifiability property is proved for bivariate normal distributions for every n when all correlations are positive; each component of the vector of maxima consists of the maximum of that component of the n constituent vectors.
A Cramér–Von Mises Type Goodness of Fit Statistic Related to √B
1 and B
2
Authors: Pettitt A. N.
Published: December 2018

We investigate a statistic introduced by de Wet and Venter to test for normality and a Cramér–von Mises statistic asymptotically equivalent to this statistic.

It is shown that the Cramér–von Mises statistic can be written as a sum of components which are polynomial functions of the original standardized observations, the most important of which are Pearson's moment ratio statistics, √b  1 and b  2. Approximate small sample percentage points are given for the de Wet and Venter statistic. The asymptotic power of this statistic is investigated and the results of a small sample power study reported, confirming these results.
Bayes Factors from Mixed Probabilities
Authors: Dickey J. M. , Gunel E.
Published: December 2018

A new expression for a Bayes factor as a weighted average of conditional Bayes factors is given, resembling the familiar relation for a marginal probability as a weighted average of conditional probabilities. Interpretations are given for the three contexts of (i) the use of a non-sufficient statistic, (ii) inference for a simple hypothesis versus a vague alternative in terms of inference for a dichotomy and (iii) opinion pooling before sampling.
Bayesian Analysis of a Two-Sample Problem Based on the Rank Order Statistic
Authors: Brooks R. J.
Published: December 2018

A Bayesian analysis of the two-sample, location-shift problem based on the rank order statistic is described. It is assumed that the data available can only at best be considered as being on the ordinal scale. Exact and simplified approximate procedures are suggested. These are not distribution-free since the underlying population distributions need to be specified.
The Analysis of Interactions in Single Replicate Generalized Cyclic Designs
Authors: Dean A. M.
Published: December 2018

Interactions of a confounded single replicate factorial experiment arranged as a generalized cyclic design are partitioned, where possible, into linear, quadratic, cubic and higher degree components each based on a single degree of freedom. The information available on each component is obtained.
Density Estimation, Stochastic Processes and Prior Information
Authors: Leonard Tom
Published: December 2018

A method is proposed for the non-parametric estimation of a probability density, based upon a finite number of observations and prior information about the smoothness of the density. A logistic density transform and a reproducing inner product from the first-order autoregressive stochastic process are employed to represent prior information that the derivative of the transform is unlikely to change radically within small intervals. The posterior estimate of the density possesses a continuous second derivative; it typically satisfies the frequentist property of asymptotic consistency. A direct analogy is demonstrated with a smoothing method for the time-dependent Poisson process; this is similar in spirit to the normal theory Kalman filter. A procedure for grouped observations in a histogram provides an alternative to the histospline method of Boneva, Kendall and Stefanov. Five practical examples are presented, including two investigations of normality, an analysis of pedestrian arrivals at a Pelican crossing and a histogram smoothing method for mine explosions data.
Two-Sample Cramér-Von Mises Type Rank Statistics
Authors: Pettitt A. N.
Published: December 2018

In this paper weighted Cramér-von Mises type two-sample rank statistics are considered. It is shown that the statistics can be written as sums of squares of linear rank statistics. The asymptotic equivalence of the statistics to an easily computed version is shown and the asymptotic distribution of the statistics investigated. Finally, some specific examples are considered relating the Cramér-von Mises statistics to the Wilcoxon, Mood, Normal Scores and Savage rank statistics.
Reference Posterior Distributions for Bayesian Inference
Authors: Bernardo Jose M.
Published: December 2018

A procedure is proposed to derive reference posterior distributions which approximately describe the inferential content of the data without incorporating any other information. More explicitly, operational priors, derived from information-theoretical considerations, are used to obtain reference posteriors which may be expected to approximate the posteriors which would have been obtained with the use of proper priors describing vague initial states of knowledge. The results obtained unify and generalize some previous work and seem to overcome criticisms to which this has been subject.
On Asymptotic Posterior Normality for Stochastic Processes
Authors: Heyde C. C. , Johnstone I. M.
Published: December 2018

Asymptotic normality of the posterior distribution of a parameter in a stochastic process is shown to hold under conditions which do little more than ensure consistency of a maximum likelihood estimator. Much more stringent conditions are required to ensure asymptotic normality of the MLE. This contrast, which has implications of considerable significance, does not emerge in the classical context of independent and identically distributed observations.
The Symmetric M-Dimensional Simple Epidemic Process
Authors: Billard L. , Lacayo H. , Langberg Naftali A.
Published: December 2018

In the classical simple epidemic process (Bailey, 1975), only one disease is involved. In this work, the model is generalized to the case in which susceptibles are simultaneously exposed to m, m ≥ 1, diseases. An individual once infected by a particular disease remains infected and is immune to further infection from another disease. The process is called an m-dimensional simple epidemic process. The limiting finite-dimensional joint state probabilities and the marginal probabilities associated with each disease are obtained.
On Outlier Rejection Phenomena in Bayes Inference
Authors: O'Hagan A.
Published: December 2018

Inference is considered for a location parameter given a random sample. Outliers are not explicitly modelled, but rejection of extreme observations occurs naturally in any Bayesian analysis of data from distributions with suitably thick tails. For other distributions outlier rejection behaviour can never occur. These phenomena motivate new definitions of outlier-proneness and outlier-resistance. The definitions and methodology are Bayesian but the conclusions also have meaning for non-Bayesians because they are proved for arbitrary prior distributions. Thus, for example, the t distribution is said to be outlier-prone because it is shown that any admissible inference procedure applied to a t sample will effectively ignore extreme outlying observations regardless of prior information. On the other hand, the normal distribution, for example, is said to be outlier-resistant because it never allows outlier rejection, regardless of prior information.
A Robust Method for Testing Transformations to Achieve Approximate Normality
Authors: Carroll Raymond J.
Published: December 2018

We propose a competitor to likelihood and significance methods for power transformations to achieve approximate normality in a linear model. The new method is shown in theory and a Monte Carlo experiment to produce more robust inferences than the likelihood method and more powerful (although possibly slightly less robust) inferences than the significance method.
A Simple Asymptotic Estimate for the Index of a Stable Distribution
Authors: Haan L. , Resnick S. I.
Published: December 2018

A simple asymptotic estimate is constructed for the index of a stable distribution based on order statistics from a distribution in its domain of attraction. The asymptotic distribution of the estimate is then found in case the order statistics are taken from the stable distribution itself.
On Exchangeable Priors in Lot Acceptance
Authors: Eaves D. M.
Published: December 2018

A two-stage exchangeable hierarchical model for the lot acceptance problem is described. This is naturally dictated by the need to allow for the possibility of variable quality among the sampling units.
The Exponential Autoregressive-Moving Average Earma(P,Q) Process
Authors: Lawrance A. J. , Lewis P. A. W.
Published: December 2018

A new model for pth-order autoregressive processes with exponential marginal distributions, ear(p), is developed and an earlier model for first-order moving average exponential processes is extended to qth-order, giving an ema(q) process. The correlation structures of both processes are obtained separately. A mixed process, earma(p,q), incorporating aspects of both ear(p) and ema(q) correlation structures is then developed. The earma(p, q) process is an analog of the standard arma(p, q) time series models for Gaussian processes and is generated from a single sequence of independent and identically distributed exponential varables.
Lagrange-Multiplier Tests of Time-Series Models
Authors: Hosking J. R. M.
Published: December 2018

The Lagrange-multiplier test procedure is applied to hypotheses concerning autoregressive moving-average time-series models. The portmanteau and Quenouille goodness-of fit tests are derived in this manner against specific alternative hypotheses and two other tests are obtained which have the nature of pure significance tests.
On the Relative Efficiency of Two Paired-Data Experiments
Authors: Brooks R. J.
Published: December 2018

The expected gain in information through obtaining data is used to help evaluate, for the two-sample, paired-data problem, the consequences of using only the signs of the differences of the pairs of observations for inference. Relative efficiencies are calculated under the assumption of normal population distributions. The Bayesian approach to inference is used.
On Mixtures from Exponential Families
Authors: Shared Moshe
Published: December 2018

A mixture from exponential family is compared with a natural approximation in the family. It is shown that the two resulting densities must cross each other exactly twice and in a prescribed manner. A deeper understanding of the behaviour of some well known sets of data is obtained. Applications in reliability theory and for symmetric random walks are described.
Invertibility and Generalized Invertibility of Time Series Models
Authors: Hallin Marc
Published: December 2018

A new invertibility concept was recently introduced by Granger and Andersen (1978), generalizing the classical one for time-independent models; we show that, in the case of time-dependent models, it cannot be considered any more as a generalization. We also give a modified definition, which provides a strict generalization and still preserves Granger and Andersen's results.
Best Linear Unbiased Estimators for Repeated Surveys
Authors: Jones Roger G.
Published: December 2018

Recent work on the problem of obtaining best linear unbiased estimators from a sample survey which is repeated on several occasions has centred on the effects of extending the model assumptions to allow for stochastic variation in the parameters being estimated.

In this paper a unified approach to the problem is given using least squares theory. The results of Blight and Scott (1973) are extended, and the relationships between their results, those of Scott and Smith (1974) and the classical approach of Patterson (1950), or its generalization by Gurney and Daly (1965), are clarified. The problems involved in putting the time series estimators into practice are examined, with particular reference to the role of stationarity.
Threshold Autoregression, Limit Cycles and Cyclical Data
Authors: Tong H. , Lim K. S.
Published: December 2018

The notion of a limit cycle, which can only exist in a non-linear system, plays the key role in the modelling of cyclical data. We have shown that the class of threshold autoregressive models is general enough to capture this notion, a definition of which in discrete time is proposed. The threshold value has an interesting interpretation. Simulation results are presented which demonstrate that this new class of models exhibits some well-known features of non-linear vibrations. Detailed analyses of several real data sets are discussed.