bluuebunny/crossref_metadata_2025_split huggingface dataset:
Structural Probability and Prediction for the Multivariate Model
Authors: Fraser D. A. S. , Haq M. Safiul 
Published: December 2018

Summary
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

Summary
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

Summary
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

Summary
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

Summary
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.
Asymptotic Properties of Conditional Maximum-Likelihood Estimators
Authors: Andersen Erling Bernhard 
Published: December 2018

Summary
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

Summary
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

Summary
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.
Transformation of a Birth Process into a Poisson Process
Authors: Waugh W. A. O'N. 
Published: December 2018

Summary
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

Summary
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.
The Numerical Solution of a Set of Conditional Estimation Equations
Authors: Andersen E. B. 
Published: December 2018

Summary
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

Summary
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

Summary
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).
Two-Factor Experiments in Non-Orthogonal Designs
Authors: John J. A. , Smith T. M. F. 
Published: December 2018

Summary
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

Summary
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

Summary
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

Summary
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

Summary
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.
Goodness-of-fit Test Using Sample Quantiles
Authors: Bofinger Eve 
Published: December 2018

Summary
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.
On the First Emptiness of Dams with Markovian Inputs
Authors: Shanbhag D. N. 
Published: December 2018

Summary
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

Summary
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

Summary
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&gt;σ12+σ22, (ii) σ32&lt;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

Summary
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.
On Interval Estimation of a Ranked Parameter
Authors: Alam K. , Saxena K. M. Lal 
Published: December 2018

Summary
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

Summary
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

Summary
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

Summary
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

Summary
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

Summary
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 &lt; 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

Summary
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

Summary
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

Summary
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

Summary
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.