bluuebunny/crossref_metadata_2025_split huggingface dataset:
Optimal Programmes for Varietal Selection
Authors: Curnow R. N. 
Published: December 2018

SUMMARY
The statistical theory of the sequences of selections that occur in plant breeding programmes is discussed. The emphasis is on numerical results rather than the underlying mathematical theory. The effects of non-normality in the initial distribution of yield on the optimal schemes already proposed for one and two successive selections from a normal distribution are investigated. Other topics considered are the optimal number of varieties to include in a programme involving two successive selections from a normal distribution, the effect of varieties × years interactions, the use of information from the first selection stage in the second-stage selection criterion, three successive selections from a normal distribution, the external economy of two successive selections from a normal distribution and the optimal number of selection stages.
Estimation from Quantiles in Destructive Testing
Authors: Stout H. P. , Stern F. 
Published: December 2018

SUMMARY
The estimation of mean and standard deviation from the values of two quantiles dividing the specimens into three groups has, by previous authors, been made the basis of a quality control system of gauging specimens at two levels. When a specimen may be gauged once only, single gauging, different specimens must be gauged at each level, and the efficiency of the method is reduced.
For a variate normally distributed with mean, μ, and standard deviation, σ, the efficiency of estimation by single gauging of a quantity μ + ασ is calculated, and contour maps drawn to show the variation of this efficiency with the gauge levels, expressed as normal deviate values, for α → 0, α = – 1, α = – 2, α = – 3 and α → – ∞. Maximum efficiency is attained when the gauge levels are set symmetrically about the mean.
Contour maps calculated for a strongly asymmetric case of the gamma distribution show the maximum efficiency of estimation of μ to be 20·6 per cent, and of σ to be 20·0 per cent, while the positioning of the gauge levels for maximum efficiency is now rather critical and the optimum levels are no longer symmetrical about the mean.
Inequalities for First Emptiness Probabilities of a Dam with Ordered Inputs
Authors: Gani J. , Pyke R. 
Published: December 2018

SUMMARY
This paper considers the probabilities of first emptiness times for a dam fed by certain ordered inputs α 1, …, αp, and subject to a steady-release rule. Simple inequalities are derived, which prove more tractable in practice than the exact probabilities. These are applied to the particular case of two ordered Poisson inputs α 1, α 2. The paper concludes with conditions for the probability that the dam will eventually become empty.
The Estimation of Spectral Densities
Authors: Daniels H. E. 
Published: December 2018

SUMMARY
A method of estimating spectral densities is developed which uses the data explicitly to help determine the best smoothing procedure. Two techniques are discussed. The first involves polynomial approximations, the second is an interpolation technique which is useful when a limited number of autocorrelations is available. The Gaussian and Laplacian weight functions play important roles in the first and second technique respectively.
On Sufficiency and the Exponential Family
Authors: Fraser D. A. S. 
Published: December 2018

SUMMARY
The use of the likelihood function as the minimal sufficient statistic provides a simple and direct proof of results by Barankin and Katz (1959) and Barankin (1961) concerning minimal sufficient statistics. In Section 2 the likelihood function is used to analyse the effect of sampling on the dimensionality of the sufficient statistic and it provides a simple and transparent proof that fixed dimension for the sufficient statistic is restricted to the exponential family. In Section 3 a class of selected exponential distributions is shown to be complete.
Simultaneous Confidence Limits for Cross-Product Ratios in Contingency Tables
Authors: Goodman Leo A. 
Published: December 2018

Summary
Fisher (1962) has proposed a method for obtaining confidence limits for the cross-product ratio in a 2 × 2 table which requires that the user solve a quartic equation. Based on a different mathematical derivation, Cornfield (1956) had proposed a similar method. In the present article, we shall present simpler methods for obtaining confidence limits for the cross-product ratio in a 2 × 2 table, and we shall extend these methods to obtain simultaneous confidence intervals for the r(r - 1) c(c - l)/4 cross-product ratios in an r × c table (or for a subset of them) and also for the relative differences between the corresponding cross-product ratios in K different r × c tables. In addition, we shall present a modification of a method suggested by Gart (1962a) for the 2 × 2 table, and we shall extend the modified method to the r × c table. The methods presented herein are easier to apply than those given in the earlier literature. For the 2 × 2 table, the confidence limits presented herein are asymptotically equivalent to the limits given earlier. When max (r, c, K) &gt; 2, the simultaneous confidence intervals presented herein for the cross-product ratios and for the relative differences between cross-product ratios are asymptotically shorter than the corresponding intervals given by Cornfield (1956), for the usual probability levels. The method proposed herein for studying the relative differences between cross-product ratios in K r × c tables can also be used to supplement the earlier methods of analysis given by Plackett (1962) and Goodman (1963b) for testing the null hypothesis that these differences are all nil.
A Note on the Bartlett Decomposition of a Wishart Matrix
Authors: Kabe D. G. 
Published: December 2018

Summary
By suitably factorizing the generalized variance, a concise derivation of the Bartlett decomposition of a central Wishart matrix is given. The method is extended to give a decomposition of a p-dimensional non-central Wishart matrix of rank t (≤ p), in terms of a t-dimensional non-central Wishart matrix of rank t, (p - t) independent χ2 variates and 1/2(p - t)(p + t - 1) independent unit normal variates.
Using the Observations to Estimate the Prior Distribution
Authors: Clutton-Brock M. 
Published: December 2018

Summary
A parameter μ is to be estimated from an unbiased, unit-variance measurement x. The prior distribution is symmetrical about zero with unknown scale parameter σ. It is claimed that the observation x gives information about σ which is contained in the likelihood distribution p(dx|σ). An estimator μ̂ = γx is found, based on the posterior distribution of μ conditional on the most probable value of σ. For a prior distribution of arbitrary shape, γ is zero when x2 ≤ 1 and approaches 1 – x–2 when x2 ≥ 1. A minimum mean-square estimator is found based on an estimate of the prior variance. This gives the same result, independently of the shape of the prior distribution, as the previous estimator for a normal prior.
Some General Results in Sequential Design
Authors: Whittle P. 
Published: December 2018

Summary
We consider a sequential decision problem in which one has a choice of several different types of observation (or “experiment”) of differing costs and degrees of informativeness. In the most general case considered it is assumed that the cost of an observation of type s is crs if the last observation used was of type r, so allowance is made for transition cost (the cost of a change in type of experiment). The equations governing the loss function are discussed in Sections 2 and 3. In Theorem 4 the optimal choice of observation type is completely determined for the case of sequential discrimination between two simple hypotheses in the absence of transition costs, overshoot being neglected. The optimal switching values for the case when there are positive transition costs are determined in Theorem 5. In Section 7 partial results, embodied in Theorem 6, are obtained for the determination of the optimal number of observations to take at a time in the case when sampling costs are not simply proportional to the number of observations.
Application of Stochastic Approximation to Process Control
Authors: Comer J. P. 
Published: December 2018

Summary
The objective of process control may be to hold a response Y as close to some specified target Y0 as possible by adjusting an independent variable X. In the simplest cases, this objective may be met by choosing a suitable fixed value of X as quickly as possible after the process is started up or after an unusual disturbance occurs during operation. In more complicated cases, it may be advantageous to continue the adjustment of X during normal operation. Two stochastic approximation procedures are presented for handling these two different control requirements. The advantage of the stochastic approximation procedures over more conventional procedures is that relatively little prior knowledge of the process is required to achieve reasonably good results.
Note on the Confidence-Prior of Welch and Peers
Authors: Hartigan J. A. 
Published: December 2018

Summary
Welch and Peers have shown that it is possible to determine a prior distribution for a one-dimensional parameter by requiring that the associated one-sided Bayes intervals are asymptotically confidence intervals. It is shown in this note that their procedure does not apply if certain natural two-sided Bayes intervals are used.
A Test for “Intrinsic Correlation” in the Theory of Accident Proneness
Authors: Subrahmaniam K. 
Published: December 2018

Summary
We consider a model in accident theory which is a modified version of the one proposed and studied by Bates and Neyman (1952a). The model envisages a correlation between the two kinds of accident in the model of Bates and Neyman. We set up a test of significance that this correlation is zero. Some properties of the distribution arising from the modified approach are presented.
The Decision Theory Approach to Sampling Inspection
Authors: Wetherill G. B. , Campling G. E. G. 
Published: December 2018

Summary
Some decision theory models are outlined for acceptance inspection of large batches of items. Firstly, the effects of errors in the algebraic formulation of the models and of errors in parameters used in the models are studied. Secondly, the amount of improvement in utility through use of double and sequential plans is investigated.
Inferences Concerning a Population Correlation Coefficient from One or Possibly Two Samples Subsequent to a Preliminary Test of Significance
Authors: Srivastava S. R. , Bancroft T. A. 
Published: December 2018

Summary
It is shown in this paper that under certain restrictions on population parameters, estimates formulated on the basis of a preliminary test of significance concerning inferences for a population correlation coefficient are better than the usual unbiased estimators.
A General Approach to Some Screening and Classification Problems
Authors: Marshall Albert W. , Olkin Ingram 
Published: December 2018

Summary
This paper is concerned with the problem of classifying items which belong to one of several classes. Each item is characterized by a variable Y which may lie in one of several sets; the actual class to which the item belongs is determined by the set which contains Y. We suppose that Y is costly, inconvenient, or impossible to observe, but that an observation X=(X1,⋯,XK) is available which is correlated with Y. The problem considered is the optimal use of screening variables in the classification problem. We assume that the conditional distribution of Y given x is known, and that optimality is to be judged in terms of a given loss function.
A simple characterization of minimum risk procedures is given which suggests useful computational methods. These are illustrated by a number of examples for which specific procedures are obtained. The possibility of observing X1,…, Xk sequentially is also considered.
Least-Squares Efficiency for Vector Time Series
Authors: Hannan E. J. 
Published: December 2018

Summary
A theorem due to Rosenblatt (1959) concerning the circumstances under which least squares is asymptotically efficient for the estimation of the matrix of regression parameters in a system of regressions is re-formulated in a simpler form and is extended. A theorem is proved relating to the efficiency of least squares under linear constraints which is not specifically of a time series nature.
Confidence Properties of Bayesian Interval Estimates
Authors: Peers H. W. 
Published: December 2018

Summary
Coverage probabilities, in the confidence theory sense, of Bayes interval estimates constructed according to different criteria are examined. Suggestions are made for the choice of a prior density in the case of complete ignorance concerning the parameter under estimation. These densities are members of the family of relatively invariant densities discussed by Hartigan (1964). Confidence properties of a related family are also discussed.
On the Superposition of Point Processes
Authors: Çinlar E. , Agnew R. A. 
Published: December 2018

Summary
Given point processes N1, …, Nm their superposition is the point process N defined by N(t) = N1(t) + … + Nm(t), t ≥ 0. An equivalent description of the system (N1, …, Nm) is by the process (Xn, Tn) where the Tn are the points of N, and Xn = k if and only if Tn is a point of Nk. The use of (X, T) process enables one to study the dependence of N1, …, Nm. Necessary and sufficient conditions are obtained for N, …, Nm to be independent, and for the superposition N to be a renewal process. For example, if N1 and N2 are renewal processes and X is independent of N, then N is a renewal process only if X is a homogeneous Markov chain.
A Simplified Monte Carlo Significance Test Procedure
Authors: Hope Adery C. A. 
Published: December 2018

Summary
The use of Monte Carlo test procedures for significance testing, with smaller reference sets than are now generally used, is advocated. It is shown that, for given α = 1/n, n a positive integer, the power of the Monte Carlo test procedure is a monotone increasing function of the size of the reference set, the limit of which is the power of the corresponding uniformly most powerful test. The power functions and efficiency of the Monte Carlo test to the uniformly most powerful test are discussed in detail for the case where the test criterion is N(γ, 1). The cases when the test criterion is Student's t-statistic and when the test statistic is exponentially distributed are considered also.
On the Asymptotic Behaviour of Posterior Distributions
Authors: Walker A. M. 
Published: December 2018

Summary
Let a random sample of size n be taken from a distribution having a density depending on a real parameter θ, and let θ have an absolutely continuous prior distribution with density π(θ). We give a rigorous proof that, under suitable regularity conditions, the posterior distribution of θ will, when n tends to infinity, be asymptotically normal with mean equal to the maximum-likelihood estimator and variance equal to the reciprocal of the second derivative of the logarithm of the likelihood function evaluated at the maximum-likelihood estimator, independently of the form of π(θ).
On Cox and Snell's General Definition of Residuals
Authors: Loynes R. M. 
Published: December 2018

Summary
Cox and Snell have introduced a definition of residuals, in a situation more general than the usual linear hypothesis. They have also discussed briefly the distribution of these residuals, and the complementary aspect of transforming them so that they have (approximately) the same distribution as the random variables which they are effectively estimating. Here it is shown how a complete discussion can be given.
Constrained Discrimination between K Populations
Authors: Anderson J. A. 
Published: December 2018

Summary
The Bayes rule approach to discrimination, assigning a sample point to the population whose posterior probability is largest, can lead to large misallocation probabilities. There have been several empirical attempts to overcome this difficulty but an objective method is suggested here. This is to find the allocation rule that maximizes the probability of correct allocation subject to the misallocation probabilities satisfying individual upper bounds. Necessary and sufficient conditions for the optimal rule are given and it is shown that a similar approach enables the Neyman–Pearson lemma to be generalized. Analytic methods of finding the optimal rule are discussed but these are of limited application so an approximate, iterative solution is suggested which can be used quite generally.
Subjective Bayesian Models in Sampling Finite Populations
Authors: Ericson W. A. 
Published: December 2018

Summary
A general and basic model for inference about characteristics of a finite population of distinguishable elements is presented from a subjectivistic–Bayesian point of view. A subjectivist analogue to simple random sampling, based on the notion of exchangeable random variables, is discussed and the inputs and assumptions underlying the model are shown to involve nothing more than is required for inference under Bayesian models for infinite populations. The model is illustrated by a number of particular examples including one based on the multinomial distribution which incorporates a prior distribution representing an extreme position of initial ignorance. Inferences under this particular model are shown to agree closely in several respects with usual “classical” results. Finally, an extension of the results is presented involving the use of concomitant measurements, and under this Bayesian model several common ratio and regression estimators are shown to arise as means of posterior distributions.
Beta-Optimal Tests and an Application to the Summary Evaluation of Experiments
Authors: Davies Robert B. 
Published: December 2018

Summary
A concept of optimality of a test, based on the speed with which its power function reaches a pre-assigned value, is introduced and conditions for a test to have this property are considered. The concept is applied to the weighted combination of independent normal test statistics; tests for the presence of effects and for the equality of effects are deduced.
The Measurement of Association of Rows and Columns for an r × s Contingency Table
Authors: Altham Patricia M. E. 
Published: December 2018

Summary
The generalization of Edwards's argument for the measure of association of the rows and columns of 2 × 2 table, to that of an r × s table whose rows and columns are assumed unordered, shows, not surprisingly, that association ought to be measured by some function of the (r − 1)(s − 1) cross-ratios. Such a function is suggested by the introduction of a metric on certain equivalence classes. The properties of such metrics are examined, and in particular comparisons are made with Good's suggestion of the use of the algebraic rank of the contingency table, and with Lindley's significance test for association in the r × s table.
A Probability Plotting Procedure for General Analysis of Variance
Authors: Gnanadesikan R. , Wilk M. B. 
Published: December 2018

Summary
This paper describes a generalization of probability plotting to supplement general analysis of variance procedures. The mean squares in a general orthogonal analysis of variance are ordered and plotted against the corresponding expected values of standardized ordered mean squares. Since the mean squares may have differing degrees of freedom, alternate conceptions are possible with respect to association of the ordered mean squares with their parent distributions.
In considering the statistical distribution of the ith standardized ordered mean square, the view adopted here is that of complete conditioning, that is, repeated sampling so constrained that the order relationships of the sample mean squares is such that the ith ordered mean square comes from a χ2(vi)/vi distribution, for i = 1, …, K, where K denotes the total number of mean squares in the collection and v1, v2, …, vK are the respective degrees of freedom of the ordered mean squares as observed. Using this completely conditioned distribution, methods are described for computing the required plotting positions, viz. the expected values of the standardized ordered mean squares.
Some illustrative examples of use of the proposed procedure are given.
On Bounds Useful in the Theory of Symmetrical Factorial Designs
Authors: Gulati B. R. , Kounias E. G. 
Published: December 2018

Summary
Consider a finite n-dimensional projective space PG(n, s) over a Galois field of order s = ph (where p, h are positive integers and p is a prime characteristic of the field). A set of k distinct points in PG(n, s), no four coplanar, is said to be complete if there exists no other set with kx points with k1 &gt; k. The number of points in a maximal complete set is denoted by m4(n + 1, s). The exact value of m4(n + 1, 2) is known for n ≤ 7. When n ≥ 8, the best upper bound on m4(n + 1, 2) is due to Seiden (1964). It is the purpose of this paper to show that m4(4, s) = s + 1 for s &gt; 4 and to obtain bounds for m4(n + 1, s), n &gt; 3.
Some Problems of Fitting for Contingency-Type Bivariate Distributions
Authors: Mardia K. V. 
Published: December 2018

Summary
Plackett (1965) has given a family of contingency-type (C-type) bivariate distributions. He has studied the median regressions for the C-type distributions and we obtain the scedastic curves for these distributions based on the semi-interquartile range and derive various regressions and scedastic curves for the uniform C-type distribution. We use these results to construct general methods of fitting C-type distributions. One of the methods is illustrated by using Johannsen's data of beans and our results are compared with the fit given by some other distributions.
The Saddle Point of the Likelihood Surface for a Linear Functional Relationship
Authors: Sprent P. 
Published: December 2018

Summary
In a recent paper Solari has shown that there is no maximum-likelihood solution to the problem of estimating a linear functional relationship when both variates are subject to errors that have an unspecified bivariate normal distribution. The estimators purporting to be maximum-likelihood estimators were shown by Solari to determine a saddle point. This discovery clears up some anomalies that have been noted in the past.
Some Tests of Independence for Stationary Multivariate Time Series
Authors: Wahba Grace 
Published: December 2018

Summary
Let X(t)=(X1(t)X2(t)⋮XP(t)),t=⋯−1,0,1…, be a p-dimensional zero-mean stationary Gaussian time series possessing a spectral density matrix F(ω) = {fij(ω)}, i, j = 1, 2, …, p, satisfying some mild regularity conditions. Let F^(ωl), l=1, 2, … ,M, F^(ωl)={f^ij(ωl)} be suitably defined sample spectral density matrices for M values of ω, based on a record of length T ≫ M. We consider the following (null) hypotheses: H1: Xi(t), Xi(s) independent if i ≠ j, all s, t, H2: X1(t) independent of Xi(s), j = 2, …, p, all s, t, H3: X1(t), X1(t + τ) independent, all τ ≠ 0 (“white noise”).
Approximate likelihood-ratio tests are found and the test statistics λi, i = 1, 2, 3, are found to be functions of the {F^(ωl), l=1, 2, … ,M}. The {F^(ωl)} converge in mean square to a family of independent complex Wishart matrices. As a consequence of this fact, log λ1 and log λ2 converge in first mean to random variables whose null densities can be given explicitly, being distributed as the logarithms of products of independent beta random variables with integer indices. Under the null hypothesis λ3 is distributed as λ˜3 where λ˜3 is Bartlett's statistic for homogeneity of variances. The asymptotic distributions of log λi, i = 1, 2, 3, under the alternative are discussed. Under the alternative, log λ3 tends in first mean to log λ˜3. A power series expansion for the characteristic function of log λ˜3 under the alternative is given.