bluuebunny/crossref_metadata_2025_split huggingface dataset:
Bias in Nonlinear Estimation
Authors: Box M. J. 
Published: December 2018

Summary
Although it is widely recognized that maximum-likelihood estimates of the parameters in non-linear models are generally biased, little work appears to have been done on quantitatively assessing these biases. In this paper the difficulties of exact calculation of the bias for a simple example are first illustrated, after which a general method of calculating the biases in a class of nonlinear least-squares problems is presented. The bias in Bayesian estimation is also considered, although the illustrative examples are all for the case of a uniform prior, i.e. the estimation is maximum likelihood. In the most important of the subsidiary results, a generalized ratio of the bias to the variance–covariance matrix of the parameter estimates is defined, and shown to be closely related to Beale's (1960) measures of nonlinearity. Finally the philosophy is applied to a somewhat different problem, namely determining the biases in the maximum-likelihood estimates of the parameters of the gamma distribution.
Arbitrary Event Initial Conditions for Branching Poisson Processes
Authors: Lawrance A. J. 
Published: December 2018

Summary
Arbitrary event initial conditions for the branching Poisson process (the Bartlett–Lewis cluster process) are obtained. These correspond to the process starting at an arbitrary event, where an arbitrary event is defined in the Khintchine fashion. The conditions give the joint distribution of the number and structure of the initial subsidiary processes; in particular, the marginal distribution of the number of initial subsidiary processes is shown to be the mixture of a Poisson variable and a Poisson variable plus one. It is shown that these conditions marginally repeat themselves at each subsequent event, and thus that the sequence of intervals between events forms a stationary sequence of random variables.
The Moments of the Maximum of Correlated Normal and t-Variates
Authors: Afonja Biyi 
Published: December 2018

Summary
For a k-dimensional random variable x, the moments of max (x1, …, xk) = max(x) are expressed in terms of the moments of the corresponding truncated standardized distributions. The normal and t-distributions are treated as special cases. When the variables xi have equal means, the moments of max (x) for the t-distribution are expressed in terms of the moments of the truncated normal distribution. In the normal case, explicit expressions are given for the mean and the second moments of max (x), corresponding ones being given for the case of equal means in the t-distribution. The results are applied to the selection and estimation of the maximum of a set of parameters.
The Likelihood Surface in the Linear Functional Relationship Problem
Authors: Copas J. B. 
Published: December 2018

Summary
In a recent paper, Solari has shown that no maximum likelihood solution exists in the linear functional relationship problem. When account is taken of the rounding-off errors in the observations, however, the appropriate likelihood function is bounded and a solution can be found which is approximately maximum likelihood, in the sense that the value of the likelihood at that solution is close to the global supremum. The novel form of this solution is shown and the likelihood surface in a numerical example is discussed.
Comparison of Some Two-Sample Location Tests for Non-Normal Alternatives
Authors: Afifi A. A. , Kim P. J. 
Published: December 2018

Summary
Small to moderate sample size performance of the two-sample χ2, Kolmogorov–Smirnov, Wilcoxon and F-tests of location is investigated in a class of non-normal distributions through Monte Carlo sampling. The class of distributions is that of mixtures of two normal distributions with different means and/or variances. The cases of mixtures considered represent part of the regions for types I, II, IV, VI and VII of the Pearson system of continuous distributions. The mixture distributions from which the samples are drawn differ only in means, and possess varying degrees of skewness and kurtosis. Based on the Monte Carlo results, the Wilcoxon and Kolmogorov–Smirnov tests generally have higher power than the F-test, except for near normal underlying distributions where the F-test is optimal. The power of the χ2 test is less than optimal except when the sample size is large.
The Performance of a Sequential Procedure for a Slippage Problem
Authors: Srivastava M. S. 
Published: December 2018

Summary
The basic problem known as a “Slippage problem” is to decide that none of the k experimental categories is better than the control or decide that a certain category is better. In this paper, a class of asymptotically efficient sequential procedures is proposed when both the error probabilities are controlled at a specified level (see also Srivastava, 1966). Assuming that these populations are normal with unknown variance σ2, the performance of the sequential procedure is studied for moderate sample sizes. The results of the calculation show that these error probabilities are controlled at the specified level for all values of the parameters and d &gt; 0, where d is the amount of slippage. A similar study for the ranking problem has been done by Srivastava and Ogilvie (1968).
On the Analysis of Bivariate Non-Stationary Processes
Authors: Priestley M. B. , Tong H. 
Published: December 2018

Summary
In this paper, we propose a general definition of the evolutionary (time-dependent) cross-spectrum between two non-stationary processes and describe its physical interpretation. We also study the estimation of the evolutionary cross-spectrum at each time instant t from a single realization of a bivariate process. Further, we propose a definition (and a method of estimation) for the coherency (spectrum) between the two components of the bivariate process and show that the notion of residual variance bound first introduced in the analysis of bivariate stationary processes can be extended to that of non-stationary processes. As an application of the evolutionary cross-spectral analysis of bivariate non-stationary stochastic processes, we consider the estimation of the transfer function of a linear open-loop time-dependent system. Numerical illustrations of the estimation of a time-dependent transfer function are included.
Simultaneous Confidence Intervals for Product-Type Interaction Contrasts
Authors: Gabriel K. R. , Putter J. , Wax Y. 
Published: December 2018

Summary
The set of product-type interaction contrasts, which contains the subsets of interaction residuals, tetrad contrasts, double-dichotomy contrasts and pooled-tetrad contrasts, is discussed. In the Normal case with equal and known variances, simultaneous confidence intervals for a given set of such contrasts can be constructed in several ways. Five such methods (the Scheffé method, the Tukey method, the Dunn method, a method based on Roy's maximum-root statistic and a modification of Tukey's method) are presented and compared in terms of the widths of the resulting 95 and 99 per cent confidence intervals. The Dunn method is found to yield the shortest intervals for interaction residuals, for tetrad contrasts and for double-dichotomy contrasts. On the other hand, for the set of pooled-tetrad contrasts, and therefore also for any larger set of product-type interaction contrasts, the maximum-root method yields the shortest intervals. A table of the half-widths of the intervals given by the recommended methods is provided.
Two-Sample Tests with Unordered Pairs
Authors: Hinkley D. V. 
Published: December 2018

Summary
Pairs of observations, x and y, are taken on n individuals such that all observations are independent normal with a common variance, and x and y have possibly different means. The ordering of each pair (x, y) is unknown, so that only min (x, y) and max (x, y) are available. Some simple tests of equality of means are discussed for known and unknown variance.
Minimax Designs for Fourier Series and Spherical Harmonics Regressions : A Characterization of Rotatable Arrangements
Authors: Kupper Lawrence L. 
Published: December 2018

Summary
In the framework of the approximate theory of the optimal design of experiments, Hoel (1965) represented minimax designs for Fourier series and spherical harmonics regressions of order r in terms of certain normalizing coefficients which are difficult to interpret. In this paper it is shown that these designs are intimately related to rotatable arrangements of points of order r in two and three dimensions, respectively. This result is used to construct exact minimax designs for Fourier series regression of all orders and for spherical harmonics regression of orders one and two. Sequential designs and infinite classes of designs depending on only one parameter are given.
Some Discrete Approximations to Continuous Time Stochastic Models
Authors: Sargan J. D. 
Published: December 2018

Summary
The paper considers the asymptotic biases in various econometric estimators when data generated by a stochastic differential equation system of the form
d y d t − A y ( t ) = B z ( t ) + a ( t )
are estimated by approximating these equations in the form
{ y ( t + δ ) − y ( t ) } / δ = 1 2 A { y ( t + δ ) + y ( t ) } + 1 2 B { z ( t + δ ) + z ( t ) } + v ( t ) ,
where y(t) is a vector of endogenous variables, z(t) is a vector of exogenous variables and A and B are matrices of fixed coefficients, assumed estimated subject to certain a priori restrictions. It is shown that the asymptotic biases are O(δ2) as δ→0, on reasonable assumptions.
Generalizations of Mean Square Error Applied to Ridge Regression
Authors: Theobald C. M. 
Published: December 2018

Summary
Hoerl and Kennard (1970) have proposed a method of estimation for multiple regression problems which involves adding small positive quantities to the diagonal of XT X. They use a type of mean square error to justify the procedure. This paper considers some generalizations of mean square error and provides a stronger defence of the method.
Allocation to Strata and Relative Efficiencies of Stratified and Unstratified πPs Sampling Schemes
Authors: Ramachandran Geetha , Rao T. J. 
Published: December 2018

Summary
The problem of optimum allocation to strata has been earlier examined in the light of a priori distributions. In this context, under the criterion of minimum expected variance, the sampling strategy consisting of an unstratified πPS sampling scheme together with the Horvitz–Thompson (HT) estimator was shown to be inferior to the strategy consisting of a stratified πPS sampling scheme with the corresponding HT estimator with this optimum allocation. In this paper, when stratification is based on the auxiliary information, we study whether a stratified πPS sampling strategy with various non-optimal allocations is likely to be worth while and whether it should be attempted at all. For populations commonly met in practice, we derive sufficient conditions for unstratified πPS sampling to be preferable to non-optimal stratified πPS sampling. An illustrative example is provided towards the end of the paper.
Projectors, Generalized Inverses and the Blue'S
Authors: Rao C. Radhakrishna 
Published: December 2018

Summary
It is well known that in the Gauss–Markov model (Y, Xβ, σ2 V) with | V | ≠ 0, the BLUE (best linear unbiased estimator) of Xβ is Y1, the orthogonal projection of Y on M(X), the space spanned by the columns of X, with inner product defined as (x, y) = x'V-1 y. A quadratic function of Y2, the projection of Y on the orthogonal complement of M(X), provides an estimate of σ2. It may be seen that Y = Y1 + Y2. When V is singular, the inner product definition as in non-singular case is not possible. In this paper a suitable theory of projection operators is developed for the case | V | = 0, and a decomposition Y = Y1 + Y2 is obtained such that Y1 is the BLUE of Xβ and a quadratic function of Y2 is the MINQUE (Minimum Norm Quadratic Unbiased Estimator) of σ2 in the sense of Rao (1972).
Components of Cramér-Von Mises Statistics. Ii
Authors: Durbin J. , Knott M. , Taylor C. C. 
Published: December 2018

Summary
Let θ^ be an asymptotically efficient estimator of parameter vector θ based on an ordered sample of n independent observations y 1, ..., y n from a distribution with distribution function F(y, θ) and let x^j=F(yj,θ^), j = 1, ..., n. Let Ŵn 2 be the Cramér–von Mises statistic calculated from ◯ 1, ..., ◯ n. This paper shows how to construct components ẑ n1, ẑ n2, ... such that Ŵ n 2 = ∑j=1 ∞ μj ẑ nj 2 where ẑ n1, ẑ n2, ... are asymptotically independent N(0, 1) variables and considers the use of these components for testing goodness of fit in the presence of unknown parameters. Asymptotic significance points are given for tests of normality and exponentiality for Ŵn 2, Anderson and Darling's Â n 2 and Watson's Û n 2. The asymptotic powers of these statistics and of the components are studied against alternatives of interest.
Synchronous and Asynchronous Distributions for Poisson Cluster Processes
Authors: Oakes David 
Published: December 2018

Summary
A simple relation between the synchronous and asynchronous distributions of a Poisson cluster process is proved. This is used in conjunction with the Palm–Khintchine equations to derive an expression for the counting distribution of such a process. It is shown that the synchronous inter-event intervals have coefficient of variation greater than or equal to one, and that the forward recurrence time has a non-increasing hazard function. An expression is derived for the joint survivor function for two consecutive synchronous intervals of a Bartlett–Lewis cluster process.
Joint Probability Distributions in the Meixner Classes
Authors: Lancaster H. O. 
Published: December 2018

Summary
The classes of statistical distributions, for which exp [xu(t)]/E(exp [xu(t)]) generates a system of orthogonal polynomials, have been characterized by Meixner (1934). His proof is now simplified. The theory is applied to obtain joint distributions in the normal, binomial, gamma and Poisson Meixner classes. The pre-eminent importance of those joint distributions with the polynomial biorthogonal property is established. Their simple regression properties are demonstrated. Some general theorems on convolutions of the biorthogonal distributions are proved.
Maximum Likelihood Estimation in the Three-Parameter Lognormal Distribution
Authors: Giesbrecht F. , Kempthorne O. 
Published: December 2018

Summary
Several authors (Hill, 1963; Box and Cox, 1964; Harter and Moore, 1966) have discussed the problem of estimating α, μ and σ2 where observations xi, i = 1, 2, ..., n, are available such that y = log (x + α) has a normal distribution with mean μ and variance σ2. In this paper it is shown that the difficulties encountered because the “likelihood” becomes unbounded are avoided if one takes into account the grouping error inherent in the data and uses the “correct” likelihood (Kempthorne and Folks, 1971; Copas, 1972). The behaviour of the maximum likelihood estimators is investigated using asymptotic theory and Monte Carlo simulations.
Optimal Incomplete Block Designs
Authors: John J. A. , Mitchell Toby J. 
Published: December 2018

Summary
The class of regular graph (RG) designs, conjectured to be optimal among all incomplete block designs, is defined. The results of a systematic search of the class of RG designs are given for all cases in which v ≤ 12, r ≤ 10 and v ≤ b. In nearly every case, the optimum design is determined for each of the three optimality criteria: A, D and E. For v &gt; b, we present the duals of the optimal designs for v &lt; b. Many of the designs are new and these are tabulated in a back-up report.
Exponential Families and Conditioning on Statistics Which are Not Minimal Sufficient
Authors: Berman Mark 
Published: December 2018

Summary
The likelihood function for each of k independent sets of data is assumed to belong to the two-parameter exponential family, the two parameters for the ith data set being φi, which is a nuisance parameter, and θ, which is common to all the data sets and is the parameter of interest. The theory of similar tests suggests that the appropriate method for testing θ is to condition on the statistic which is minimal sufficient for Ψ = (φ1 …, φk) when θ is known. This minimal sufficient statistic will be different depending on whether or not the φi‘s are known to be equal. The effect of assuming that the φi‘s are not equal when in fact they are (and vice versa) is investigated and some examples are given. The broad conclusion is that, provided the k samples are balanced in a certain sense, no great harm is done by conditioning on the incorrect statistic.
Finding the Outliers that Matter
Authors: Andrews David F. , Pregibon Daryl 
Published: December 2018

Summary
A method is proposed for examining a linear model for the presence of one or more important outliers—deviant observations which have a potentially large influence on the resulting parameter estimates. For this purpose, a new statistic is proposed and its distributional properties are discussed. The method itself is exploratory in nature, but exact significance tests are available. Several examples illustrate the method. Computational aspects are discussed.
Non-Parametric Bayesian Analysis of Survival Time Data
Authors: Kalbfleisch John D. 
Published: December 2018

Summary
A Bayesian analysis of the semi-parametric regression and life model of Cox (1972) is given. The cumulative hazard function is modelled as a gamma process. Both estimation of the regression parameters and of the underlying survival distribution are considered. The results are compared to the results obtained by other approaches.
Some Tests of Randomness Based Upon the Variance-Time Curve of the Poisson Process
Authors: Liebetrau Albert M. 
Published: December 2018

Summary
In an earlier paper, the author shows that a suitably normalized estimator η^0 of the variance-time curve of a Poisson process is asymptotically normal as the time of observation of the process increases. In this paper, the distributions of the functionals ζ^1c=∫01η^c(t) and ζ^2c=∫01[η^c(t)]2 are obtained, and computing formulae for the sample analogues are provided. The first is normally distributed. For the second, which is reminiscent of the Cramer-von Mises statistic, the characteristic function, the first two moments and approximations to the upper tail of the distribution function are given. These approximations are compared with the results of a Monte Carlo study.
Inference About the Intraclass Correlation Coefficient in the Beta-Binomial Anova for Proportions
Authors: Crowder Martin J. 
Published: December 2018

Summary
The paper is concerned with the analysis of sets of proportions where there is strong variation within sets. In one parameterization (Crowder, 1978) the underlying mean proportions are π1,…, πk in the k sets, and variation within sets is associated with a parameter σ2. The last of these is the intraclass correlation coefficient for the basic binary data and is of independent interest, rather than just a nuisance parameter. We propose a technique for inference about σ2.
Finitely Additive Priors, Coherence and the Marginalization Paradox
Authors: Sudderth William D. 
Published: December 2018

Summary
The marginalization paradox, which arises in a Bayesian theory of inference based on improper, countable additive prior distributions, is resolved when proper, finitely additive distributions are used instead. The resolution is related to the equivalence of coherent inferences to inferences from proper, finitely additive priors under a certain definition of “coherence”.
A Trimmed Jackknife
Authors: Hinkley David , Wang Hai-Li 
Published: December 2018

Summary
The jackknifed version of a regular estimate is the average of the sample pseudo-values, which in general are not independent and often have long-tailed distributions. We examine the simple alternative of the trimmed average of the pseudo-values, which is a naive type of robust estimate. The asymptotic theory is developed and two simple examples are discussed.
A Note on Maximum Likelihood Estimation for Regression Models Using Grouped Data
Authors: Burridge J. 
Published: December 2018

Summary
The estimation of parameters for a class of regression models using grouped or censored data is considered. It is shown that with a simple reparameterization some commonly used distributions, such as the normal and extreme value, result in a log-likelihood which is concave with respect to the transformed parameters. Apart from its theoretical implications for the existence and uniqueness of maximum likelihood estimates, this result suggests minor changes to some commonly used algorithms for maximum likelihood estimation from grouped data. Two simple examples are given.
On the Non-Parametric Estimation of Mixture Proportions
Authors: Hall Peter 
Published: December 2018

SUMMARY
Non-parametric estimates of mixing proportions based on kernel-type density estimators are badly suited to several types of data. They suffer from aberrations due to rounding or truncation of the measurements, and their construction involves the crucial choice of the “window size”, or smoothing parameter. In many circumstances estimators based on the empiric distribution function would be more suitable, and in this paper we investigate their properties. The estimators we introduce lead in a natural way to non-parametric forms of well-known parametric estimators. Their efficiency approaches 100 per cent as the distances between the component distributions increase.
Invariant Distributions Associated with Matrix Laws Under Structural Symmetry
Authors: Jensen D. R. , Good I. J. 
Published: December 2018

Summary
Let Y(n x m) be a random matrix in the space F n x m of real matrices having location-scale parameters (θ, Ω) such that (i) θ belongs to a linear subspace M of F n x m; (ii) the distribution L(Y) exhibits a type of structural symmetry; and (iii) a certain transformation T(Y) is translation-invariant with respect to M and is invariant under changes of scale. Then the distribution L{T(Y)} is invariant for all underlying symmetric distributions L(Y). The types of symmetry are spherical symmetry and symmetry under multiplication on the left by orthogonal and similar matrices; the scale changes are multiplication by a scalar and multiplication on the right by a non-singular matrix. Applications yield the invariance under structural symmetry of distributions usually associated with normal-theory inferences in multivariate regression analysis and in testing equality of dispersion matrices.
Exact and Approximate Distributions of the Maximum Likelihood Estimator of a Slope Coefficient
Authors: Anderson T. W. , Sawa Takamitsu 
Published: December 2018

Summary
When the errors are normally independently distributed with equal variance, the maximum likelihood estimator of the slope of a linear functional relationship is the slope of the line minimizing the sum of squared deviations orthogonal to the line. The exact density and distribution of this estimator are obtained. Approximate distributions are obtained, and their accuracies are discussed.
The Decomposition of Treatment Degrees of Freedom in Quantitative Factorial Experiments
Authors: Bailey R. A. 
Published: December 2018

Summary
In an experiment in which every treatment factor has the same number, p, of levels, where p is prime, there is a classical breakdown of the treatment degrees of freedom into components such as AB, AB 2, AB 2 C,…, each of (p - 1) degrees of freedom. The disadvantages of this system are (i) the lack of canonical single degrees of freedom and (ii) the fact that the breakdown bears no relation to the contrasts typically of interest if all treatment factors are quantitative. In this note we decompose the treatment degrees of freedom into single degrees of freedom, and use these to show how appropriate choice of levels of quantitative factors enables quantitative contrasts to be completely unconfounded in classical designs.