bluuebunny/crossref_metadata_2025 huggingface dataset:
Eliminating Singularities of Stein-Type Estimators of Location Vectors
Authors: Berger James O. , Bock M. E.
Published: December 2018

In estimating a multivariate location vector in three or more dimensions, it is well known that Stein-type estimators can offer considerable improvement in risk over the best invariant estimator. A common problem arising in the use of such estimators is that simple versions often have a singularity at zero. Methods of eliminating such singularities are discussed in this paper. The resulting estimators are usually considerably better than the uncorrected versions, and yet are still quite simple.
The Aliasing Problem in Differential Equation Estimation
Authors: Robinson P. M.
Published: December 2018

This paper is concerned with the estimation of the parameters in a simple open-loop differential equation model. We suggest first some frequency-domain “narrow-band” and “broad-band” estimators that are based on the assumption that the observable input variable has no spectral mass beyond Nyquist frequency. We study the asymptotic biases of these estimators under the contradictory hypothesis that the spectral density of the input is a rational function of frequency. On considering the limiting situation of the sampling interval converging to zero, we derive relatively simple multiplicative correction factors that can be applied to the original estimates, with the objective of reducing the bias.
Bayesian Forecasting
Authors: Harrison P. J. , Stevens C. F.
Published: December 2018

This paper describes a Bayesian approach to forecasting. The principles of Bayesian forecasting are discussed and the formal inclusion of “the forecaster” in the forecasting system is emphasized as a major feature. The basic model, the dynamic linear model, is defined together with the Kalman filter recurrence relations and a number of model formulations are given. Multi-process models introduce uncertainty as to the underlying model itself, and this approach is described in a more general fashion than in our 1971 paper. Applications to four series are described in a sister paper. Although the results are far from exhaustive, the authors are convinced of the great benefits which the Bayesian approach offers to forecasters.
On a Test for Normality Based on Sample Entropy
Authors: Prescott P.
Published: December 2018

Sensitivity contours are used to examine the effect of outliers on a test of normality based on sample entropy. The contours are compared with those of the Shapiro–Wilk W-test and it is shown that the entropy test is considerably less sensitive to outliers than the W-test. This is illustrated using the results of a confounded 25 factorial experiment.
Parameter Estimation for the Carrier-Borne Epidemic Model
Authors: Saunders Roy , Kryscio Richard J.
Published: December 2018

We derive the maximum likelihood estimates (m.l.e.) of the infection and removal rates of the carrier-borne epidemic model when the process has been observed continuously for a fixed or random period of time. For both sampling schemes we derive the distribution of the m.l.e. of the inverse of the removal rate. We also consider the problem of estimating the relative removal rate of the model when the process has been observed continuously for a period of time, but the exact times between events is unknown. In this case, we propose an estimator which is appropriate for populations having a large initial number of susceptibles.
Oscillations in the Finite Random Sequence
Authors: Imhof J. P.
Published: December 2018

Oscillations are defined for a random sequence of finite length. The oscillation of maximal amplitude is preceded by oscillations of increasing amplitudes and followed by oscillations of decreasing amplitudes. The joint law of their numbers is determined. There is analogy with known results for upper and lower records. A sampling experiment gives some idea of the behaviour of oscillations in the presence of a trend in mean or in standard deviation.
Errors-In-Variables Estimation for Gaussian Lattice Schemes
Authors: Besag Julian
Published: December 2018

It can happen that the variates of primary interest in a simple Gaussian lattice scheme are not directly observable. An errors-in-variables formulation may then be appropriate. This note describes the corresponding maximum-likelihood estimation of unknown parameter values. An example is given.
Bayesian Life Table Analysis
Authors: Cornfield Jerome , Detre Katherine
Published: December 2018

The moments of the posterior p.d.f. of the probability of surviving to time t, P(t), are obtained, assuming a time-dependent Poisson process for failures and i.i.d. gamma prior densities for the hazard function. For improper densities the results reduce to the Kaplan–Meier estimate of p(t) and to the Cox result for the comparison of two survival curves, which, because of the use of improper priors, may be inadmissible with respect to mean square error loss. A way of estimating the priors from the data, and hence of obtaining estimates that may be uniformly superior to those of Kaplan–Meier and Cox, is given. The use of a class of more realistic, but still non-parametric, priors is discussed.
Exact and Approximate Maximum Likelihood Estimators for Vector Moving Average Processes
Authors: Osborn Denise R.
Published: December 2018

This paper derives the exact likelihood function for the vector moving average process; the method used is a generalization of that adopted by Box and Jenkins (1970, Appendix A7.4) for the univariate process. Tunnicliffe Wilson (1973) has previously considered the estimation of parameters in multivariate time series models, and his procedure for moving averages is shown to be an approximation to maximum likelihood. A procedure for the computation of the exact likelihood function is also suggested.
On Resolving the Controversy in Statistical Inference
Authors: Wilkinson G. N.
Published: December 2018

The controversy concerning the fundamental principles of statistics still remains unresolved. It is suggested that one key to resolving the conflict lies in recognizing that inferential probability derived from observational data is inherently noncoherent, in the sense that their inferential implications cannot be represented by a single probability distribution on the parameter space (except in the Objective Bayesian case). More precisely, for a parameter space R  1, the class of all functions of the parameter comprise equivalence classes of invertibly related functions, and to each such class a logically distinct inferential probability distribution pertains. (There is an additional cross-coherence requirement for simultaneous inference.) The non-coherence of these distributions flows from the nonequivalence of the relevant components of the data for each.

Noncoherence is mathematically inherent in confidence and fiducial theory, and provides a basis for reconciling the Fisherian and Neyman–Pearsonian viewpoints. A unified theory of confidence-based inferential probability is presented, and the fundamental incompatibility of this with Subjective Bayesian theory is discussed.
The Distribution of Quadratic Forms in Non-Normal Variables and an Application to the Variance Ratio
Authors: Knuri A. I. , Good I. J.
Published: December 2018

Good (1968a, b) using non-rigorous arguments, gave an expression for the characteristic function C.F. (x‘A  x, t) of a quadratic form in a non-normal random column vector x whose characteristic function is known, where A is positive semi-definite. A general formula for C.F. (x‘A  x, t) is proved here, which coincides with Good's expression when x has a real stable characteristic function. In the general formula, A need not be positive semi-definite and this greater generality is of value for finding the distribution of the ratio of two quadratic forms in non-normal variables. The theory is used for finding approximately the distribution of a ratio of quadratic forms in a three-dimensional random vector x having an even stable distribution with exponent 3/2. The procedure of regarding x as normal, combined with the Cornish–Fisher expansion, would have been far from robust in this example.
Spectral Analysis of Intervals between Events in Stationary Bivariate Point Processes
Authors: Charnock D. M.
Published: December 2018

A method is developed for analysing stationary bivariate point processes through their interval properties. The technique is based on representing the intervals as processes in continuous time. Expressions for a cross-covariance function and the corresponding cross-spectrum are given and some examples are considered. We note that use of this technique together with the device of smoothing makes computation of spectral estimates for point processes more efficient.
A Procedure for Estimating Seasonal Moving Average Models Based on Large-Sample Estimation of the Correlogram
Authors: Godolphin E. J.
Published: December 2018

In recent years considerable interest has centred on a family of moving average models proposed by Box and Jenkins (1970) for the description of time series which contain a seasonal component. A method is given in the paper for estimating the parameters of the seasonal models based on a principle due to Walker (1961) for the estimation of non-zero members of the autocorrelation function. An illustration of the method is given.
A General Family of Discrete Distributions with Hypergeometric Probabilities
Authors: Tripathi Ram C. , Gurland John
Published: December 2018

A three-parameter family of distributions which belongs to Kemp's wide class, and which extends a two-parameter family of Katz, is investigated. Relations involving moments and probabilities are utilized in obtaining minimum χ2 estimators of the parameters. The asymptotic relative efficiency of various estimators is compared and a numerical example given.
Variable Selection in Multivariate Regression : An Application of Simultaneous Test Procedures
Authors: McKay R. J.
Published: December 2018

Simultaneous procedures for variable selection in multiple linear regression have recently been given by Aitkin. One of these procedures, proposed for the case when the regression equation is to be used for descriptive purposes, is an application of each of a number of simultaneous procedures concerned with the multivariate general linear model and given by Gabriel with applications in the manova context. The applications of Gabriel's procedures to multivariate linear regression are presented here and illustrated as generalizations of Aitkin's technique.
Conservative Statistical Inference
Authors: Robinson G. K.
Published: December 2018

It is argued that statistical problems can usefully be divided into two classes: one-person problems for which Bayesian techniques are appropriate, and many-person problems, for which Bayesian techniques are not appropriate. Two conditions are presented which it is felt that statistical procedures for many-person problems should satisfy. Some of the consequences of these conditions are then investigated and discussed.
The Inverse Gaussian Distribution and its Statistical Application—A Review
Authors: Folks J. L. , Chhikara R. S.
Published: December 2018

This paper reviews the development of the inverse Gaussian distribution and of statistical methods based upon it from the paper of Schrödinger (1915) to the present (1978). After summarizing the properties of the distribution, the paper presents tests of hypotheses, estimation, confidence intervals, regression and “analysis of variance” based upon the inverse Gaussian. its potential role in reliability work is discussed and work on Bayesian statistics is reviewed briefly. An extensive set of references to the distribution is given.
On the Distribution of Residual Autocorrelations in Box–Jenkins Models
Authors: McLeod A. I.
Published: December 2018

The large sample distribution of the residual autocorrelations in the arma model is derived. The main advantage of this derivation over that of Box and Pierce (1970) is that it extends directly to more general situations. Generalizations of the derived distribution are presented for the residual autocorrelations in the multiplicative seasonal arma model and for the autocorrelations of a subseries of the residuals.
Improper Priors, Spline Smoothing and the Problem of Guarding Against Model Errors in Regression
Authors: Wahba Grace
Published: December 2018

Spline and generalized spline smoothing is shown to be equivalent to Bayesian estimation with a partially improper prior. This result supports the idea that spline smoothing is a natural solution to the regression problem when one is given a set of regression functions but one also wants to hedge against the possibility that the true model is not exactly in the span of the given regression functions. A natural measure of the deviation of the true model from the span of the regression functions comes out of the spline theory in a natural way. An appropriate value of this measure can be estimated from the data and used to constrain the estimated model to have the estimated deviation. Some convergence results and computational tricks are also discussed.
A Class of Shrinkage Estimators
Authors: Farebrother R. W.
Published: December 2018

In this paper we define a class of shrinkage estimators, all of whose members have a mean square error matrix which is less than that of the ordinary least squares estimator by a positive semidefinite matrix if (β-b  *)T  X  T  X (β-b  *) ≤ σ2. The ridge regression, principal component and minimum conditional mean square error estimators are members of this class.
Two-Way Elimination of Heterogeneity
Authors: Singh M. , Dey A.
Published: December 2018

A general method of analysis of non-orthogonal three-way designs (designs eliminating heterogeneity in two directions) is proposed. Analogous to the efficiency-balanced block designs, efficiency-balanced three-way designs are defined. The utility of the proposed method of analysis is demonstrated by giving simplified analyses of known three-way designs.
A Quasi-Bayes Sequential Procedure for Mixtures
Authors: Smith A. F. M. , Makov U. E.
Published: December 2018

Coherent Bayes sequential learning and classification procedures are often useless in practice because of ever-increasing computational requirements. On the other hand, computationally feasible procedures may not resemble the coherent solution, nor guarantee consistent learning and classification. In this paper, a particular form of classification problem is considered and a “quasi-Bayes” approximate solution requiring minimal computation is motivated and defined. Convergence properties are established and a numerical illustration provided.
Nearest Neighbour Models in the Analysis of Field Experiments
Authors: Bartlett M. S.
Published: December 2018

The method of adjusting plot values by covariance on neighbouring plots in randomized field experiments, suggested by Papadakis in 1937, is re-examined theoretically for both one-dimensional and two-dimensional layouts, making use of Markovian and autonormal models.

The gain in efficiency over orthodox randomized block analysis can be appreciable when the number of treatments is fairly large, and can be increased by iterating the analysis; this also reduces the discrepancy between the apparent accuracy from the residual sum of squares, and the true accuracy of the treatment comparisons after adjustment. Some illustrative examples are included.
A Note About the Multipliers in Latent Root Regression
Authors: Eplett W. J. R.
Published: December 2018

A recent treatment of multiple regression involves the use of Lagrange multipliers. These multipliers are explicitly characterized in this note as partial covariances.
Least Squares Approximation of Matrices by Additive and Multiplicative Models
Authors: Gabriel K. R.
Published: December 2018

Reduced rank approximation of matrices by Householder–Young methods is shown to be equivalent to fitting of a bilinear (multiplicative) model and to projection onto an optimally chosen subspace. The relation to linear approximation is made evident. Least squares fitting of a mixed linear (additive) and bilinear (multiplicative) model is proved to be a two-stage process: (1) fit the linear part of the model, then take residuals, and (2) fit the bilinear part to the residuals. Extensions of this result are given as well as some results on distributions of residuals and tests against alternatives of given rank. Statistical applications are shown in principal component analysis, in biplot graphical display and in fitting additive or Mandel-type models to two-way tables.
Discrete Time Series Generated by Mixtures Ii: Asymptotic Properties
Authors: Jacobs Patricia A. , Lewis Peter A. W.
Published: December 2018

The darma (discrete mixed autoregressive-moving average) processes are a broad but parametrically simple class of models for a stationary sequence of dependent discrete random variables. A darma process is formed as a random linear combination of independent identically distributed discrete random variables. The process is specified by the distribution of the independent variables, which is also the marginal distribution of the random process, and several other chosen parameters which independently determine the covariance structure of the process. In this paper the asymptotic properties of the darma process are studied. Limiting results for estimates of moments, percentiles and quantiles are obtained. Asymptotic properties of the χ2 test for goodness-of-fit for the marginal distribution of the process are also studied.
A Non-Parametric Test for Comparing Two Non-Independent Distributions
Authors: Raviv Alona
Published: December 2018

Using a sample from an unknown bivariate distribution, we propose a test for the hypothesis that one marginal distribution is stochastically larger than the other. We show that the test statistic has an asymptotic normal distribution, and that the proposed test is asymptotically non-parametric. This test is compared to the paired t-test for large samples in terms of asymptotic relative efficiency and for samples of size 20 by simulation estimates of size and power. There are important cases in which the power of the proposed test exceeds that of the paired t-test; whereas even under normality its power is near that of the paired t-test.
Some Two-Dimensional Designs Balanced for Nearest Neighbours
Authors: Freeman G. H.
Published: December 2018

The construction of row and column designs balanced for nearest neighbours is given, the commonest practical application being to polycross designs for seed production. In some designs all plants may be used either as seed parents or as pollinators, but for others only the interior plants can be seed parents, the outside plants being pollinators only. Some small designs are given, but the construction of others could well require long computer searches. Latin squares of a special type known as complete Latin squares are particularly suitable.
The Variance Modified Linear Bayes Estimator
Authors: Goldstein Michael
Published: December 2018

A modification of the linear Bayes estimator of the mean of a distribution of unknown form is proposed, involving a linear estimate for the variance of the distribution. The risk properties of the estimator are discussed and an example is given.
On the Use of Conditional Asymptotic Normality
Authors: Fligner Michael A. , Hettmansperger Thomas P.
Published: December 2018

Methods for obtaining the limiting distribution of a complicated statistic which depends on another auxiliary statistic are discussed. Examples are given in which a general conditional approach due to Sethuraman is found to be extremely fruitful in solving this type of problem.
The Determination of the Order of an Autoregression
Authors: Hannan E. J. , Quinn B. G.
Published: December 2018

It is shown that a strongly consistent estimation procedure for the order of an autoregression can be based on the law of the iterated logarithm for the partial autocorrelations. As compared to other strongly consistent procedures this procedure will underestimate the order to a lesser degree.
Algorithms to Search for Optimal Row-And-Column Designs
Authors: Jones Byron
Published: December 2018

An algorithm is described that searches for the row and column components to form an optimal row-and-column design. It is based on one given previously (Jones, 1976) for block designs. A second algorithm is described for combining the components to form a row-and-column design. Both algorithms are suitable for use on a computer. The optimality criterion used allows treatment contrasts to be weighted. Examples of the use of the algorithms are given and their performance is discussed.
Some Misleading Arguments Involving Conditional Independence
Authors: Dawid A. P.
Published: December 2018

Some misleading arguments in probability theory and statistics are examined, and shown to have a common structure, expressible in terms of conditional independence. Using an informal approach (which can be rigorized) the arguments are corrected by finding what conclusions are justified in general, and thus showing what further condition is needed to make the original arguments valid.
Inference on Symmetric Functions of Exchangeable Populations
Authors: Sugden R. A.
Published: December 2018

A model is proposed for inference on symmetric functions of a finite population where the only prior information available is exchangeability of the unknown unit values. It is shown through sufficiency that the labels convey no information.

When the sample size is fixed, the order statistic is complete as well as sufficient so that optimal estimators are symmetric. In particular, the sample mean is the minimum variance unbiased estimator of the population mean, averaging under the model being equivalent to averaging firstly over the sample design and then over all permutations of the units.

A new subjective justification is therefore found for the use in practice of classical formulae based on simple random sampling, but now for any sample design.
On Log-Linear Hazards
Authors: Oakes David
Published: December 2018

A simply computed estimator of the information matrix for the coefficients of log-linear hazard functions with right censored data is shown to be exactly unbiased.
Comments on Model Selection Criteria of Akaike and Schwarz
Authors: Stone M.
Published: December 2018

It is demonstrated that the comparison of the model selection criteria of Akaike and Schwarz is sensitive to the type of asymptotic analysis adopted.
Selecting the Better Bernoulli Treatment Using a Matched Samples Design
Authors: Tamhane Ajit C.
Published: December 2018

The problem of selecting the better Bernoulli treatment using a matched samples design is considered in the framework of the indifference-zone approach. A single-stage procedure is proposed and its properties are studied. Tables of sample sizes for implementing the proposed procedure are given. A comparison is made with an independent samples design and the associated Sobel-Huyett selection procedure.
The Interpretation of Improper Prior Distributions as Limits of Data Dependent Proper Prior Distributions
Authors: Akaike Hirotugu
Published: December 2018

By using examples the difficulty of interpreting an improper prior distribution as a limit of some proper prior distributions is demonstrated. It is shown that an improper prior distribution can often be more adequately described as a limit of some data adaptive proper prior distributions.
The Variance Function of the Difference between Two Estimated Responses
Authors: Box G. E. P. , Draper N. R.
Published: December 2018

The work of Herzberg (1967) is reviewed and some additional features of the variance function of the difference between two estimated responses, for first, second and third order rotatable designs are given.
Characterization of the Normal Distribution Among the Continuous Symmetric Spherical Class
Authors: Ali Mir M.
Published: December 2018

When component random variables are identically and independently distributed the independence of X and S implies normality of the components. In the present note this classical result is extended to the case when the components have a joint distribution which belong to the class of spherically symmetric distributions. Furthermore, the classic result that independence of components arising from the class of spherically symmetric distributions implies normality of components is derived in an elegant manner.
Factor Analysis for Categorical Data
Authors: Bartholomew D. J.
Published: December 2018

The method of factor analysis is widely used as an exploratory tool to reduce the dimensionality of multivariate data. The fact that the standard model is strictly applicable only when the manifest variables are scaled is a serious limitation in social science where the variables are often categorical. In this paper we aim to provide a theoretical framework within which methods for the factor analysis of categorical data can be devised and compared. Discussion is restricted to the case of ordered categories where the latent variables are continuous. It is argued that the choice of model should be made from a restricted set which includes two existing models as special cases. A new method is proposed together with a simple approximate technique of fitting for the one-factor model. The paper concludes with an evaluation of existing methods and makes some suggestions about the direction which future research should take.
Partially Balanced Change-Over Designs Based on M-Associate Class PBIB Designs
Authors: Blaisdell E. A. , Raghavarao D.
Published: December 2018

The authors systematically investigate the class of change-over designs that are partially balanced for the estimation of the elementary direct and residual effects contrasts, and whose constructions are based on m-associate PBIB designs. In light of the complicated mathematical structure of the analysis, there is a need to introduce restrictions on the various incidence relations. By means of these assumed constraints the concept of partially balanced change-over designs based on m-associate class PBIB designs [PBCOD(m)] is defined. Four new series of these designs are constructed and illustrated.
Variance of the Sample Space-Time Autocorrelation Function
Authors: Pfeifer Phillip E. , Deutsch Stuart Jay
Published: December 2018

An important part of the diagnostic checking of space-time autoregressive moving average (starma) models is testing the temporal independence of the residuals. In the context of the three-stage modelling procedure, such a test is based on the sample space-time autocorrelation function. This paper developes approximate variances of the sample space-time autocorrelation function when the underlying process is white noise, which are needed to test significance of the observed autocorrelations.
Efficient Cyclic Designs
Authors: John J. A.
Published: December 2018

The paper lists efficient and robust cyclic designs for 6 ≤ v ≤ 30, r ≤ 10 and r = ik (i ≥ 1).
A Further Note on the Use of Neighbouring Plot Values in the Analysis of Field Experiments
Authors: Bartlett M. S.
Published: December 2018

Some further remarks on the iterated covariance method of adjusting plot values by neighbouring values refer (i) to its comparable efficiency with maximum likelihood; (ii) to the complications arising from the “two-sided” nature of the regression adjustment.
Transformations and the Jackknife
Authors: Cressie Noel
Published: December 2018

Whether to jackknife a parameter estimate or some function of it has in the past relied on recommendations based on folklore rather than statistical analyses. This paper puts the jackknifed estimator into the context of finding a least squares estimator from a model involving a location parameter with additive “pseudo” errors. Obtaining and interpreting confidence intervals from the partitioning of the “total” sum of squares into “residual” sum of squares, plus a sum of squares due to a hypothesized value of the parameter, requires the error variance to be constant. This in turn can equally be interpreted as requiring the variance of the original estimator to be constant. Therefore, using this criterion of jackknifing “pivotal quantities”, it is possible in principle to find a prejackknifing transformation for any general problem.
A Note on Testing for Gaps in Seasonal Moving Average Models
Authors: Harvey A. C. , Tomenson J.
Published: December 2018

A Lagrange multiplier test is suggested as an alternative to the procedure proposed by Godolphin for testing for gaps in a moving average model. It is shown to have more desirable statistical properties.
A Note on the Comparison of Certain Sampling Strategies
Authors: Padmawar V. R.
Published: December 2018

In this note we compare strategies H  1, H  2 and H  3 under a commonly used superpopulation model, where H1 consists of a πPS scheme and the Horvitz–Thompson (HT) estimator; H  2 consists of the Midzuno–Sen scheme and the corresponding HT estimator and H  3 is the Rao–Hartley–Cochran strategy. We first show that the sufficient condition for H  1 to be superior to H  2, due to Chaudhuri (1976), can never hold. We then suggest an alternative sufficient condition which is an improvement over the condition due to Rao (1967). Further, we disprove the claim that H  3 is superior to H  2 for g > 1 (Ajgaonkar and Pedgaonkar) and then give a sufficient condition for H  3 to be superior to H  2. We conclude the note with a remark on the result due to Pedgaonkar and Ajgaonkar (1978).
On Some Simple Estimates of an Exponent of Regular Variation
Authors: Hall Peter
Published: December 2018

We present a class of simple estimates of an exponent of regular variation. Unlike those proposed recently by de Haan and Resnick (1980), ours converge at an algebraic rather than a logarithmic rate, and unlike those considered by Teugels (1980), their form does not depend on the unknown exponent.
Minimum Distance Estimation and Components of Goodness-Of-Fit Statistics
Authors: Parr William C. , Schucany William R.
Published: December 2018

The relationship of minimum distance (MD) estimation to components of goodness-of-fit statistics is considered. M-estimation is viewed as a special case, with interesting interpretations in terms of the defining Ψ-function as related to linear combinations of the components and modified Fourier approximations to the efficient score. The essence of the competition between efficiency and robustness is the determination of the magnitudes of the coefficients of the high frequency components. Applications to the composite and simple goodness-of-fit problems are indicated.
Multivariate Calibration
Authors: Brown P. J.
Published: December 2018

A set of q responses Y = (Y  1  ,…, Yq)T are determined by a set of p explanatory variables x = (X  1,…, Xp)T. A set of l observed vectors Y are available at a single unknown x and it is desired to draw inferences about this unknown vector X. In order to do this calibrating data is available jointly on (Y, X) where two situations are distinguished (i), x is controlled, (ii) x is random.

Using orthodox sampling theory on the one hand and Bayesian methods on the other hand point estimators and confidence regions are derived and contrasted. A procedure for selection of a subset of responses is given. Finally a comparison is made of the methods on data from (a) a random calibration experiment of wheat quality using an infrared spectrometer and (b) a controlled experiment of point finish.
Characterizations and Goodness of Fit Tests
Authors: O'Reilly Federico J. , Stephens Michael A.
Published: December 2018

In this article a systematic approach to providing goodness of fit tests is discussed, for the composite goodness of fit problem of testing that the distribution F of a random sample comes from a parametric family F  o. Characterization procedures are emphasized, and it is shown that, at least for the exponential case, invariant characterizations appear to be better than those which are not invariant. A general technique is developed for producing invariant characterizations and for the exponential case it is shown how these are related to characterizations already in the literature. Power studies are given to examine the tests based on both invariant and non-invariant characterizations.
Minimum Distance Non-Parametric Estimation of Mixture Proportions
Authors: Titterington D. M.
Published: December 2018

Hall (1981a) develops a method of estimating mixture proportions using empirical distribution functions and a distance measure. A similar approach is suggested here based on density estimates. The method is applicable to general discrete data and multivariate data as well as to univariate continuous data and to ordered categorical data. For convenient quadratic distance measures the asymptotic theory is developed and remarks are made about practical implementation. Cases treated in detail are un-smoothed and smoothed multinomial data and univariate continuous data smoothed by the kernel method.
Estimation in Contingency Tables Using Prior Information
Authors: Albert James H. , Gupta Arjun K.
Published: December 2018

Prior beliefs of association and independence in a two-way contingency table are discussed, and estimators of the cell probabilities are proposed which can incorporate this prior information. In the 2 × 2 table where the cell counts are assumed to have a multinomial distribution, estimators are developed which can incorporate prior beliefs about the correlation coefficient and the cross-product ratio. In the I × 2 table in which one set of marginal totals is fixed, estimators are developed which reflect prior information about the similarity of a set of cell probabilities. Numerical examples are given to illustrate the use of these estimators.
Some New Methods for Constructing Block Designs Having Orthogonal Factorial Structure
Authors: Gupta S. C.
Published: December 2018

Block designs having orthogonal factorial structure are considered and some useful methods of constructing such designs are described. These methods can be used to construct designs for a wide range of parameter specifications. They also produce designs which are smaller than those obtainable through some of the existing methods.
A General Completeness Theorem in Sampling Theory
Authors: Liu Tzen-Ping
Published: December 2018

Generalized symmetry of designs and estimators is defined to be invariance under a subgroup of the group of label permutations. A simple sufficient condition in terms of the design is given for the generalized order statistic, of which each generalized symmetric estimator is a function, to be complete. This condition is shown also to be necessary when the range of possible values for each characteristic is sufficiently large.
A Remark on Censoring and Surrogate Response Variables
Authors: Cox D. R.
Published: December 2018

Survival data are often subject to right censoring and to a consequent loss of information about the effect of explanatory variables. Sometimes it is possible to recover some of this lost information via a surrogate response variable measured on censored individuals and intended to predict the remaining life-time. This possibility is studied theoretically under idealized assumptions.
On Cumulative Sum Procedures and the Sprt with Applications
Authors: Khan Rasul A.
Published: December 2018

Both one-sided and two-sided cumulative sum procedures of Page (1954) are shown to be closely related to a sequential probability ratio test (SPRT). The generating functions (Laplace transforms) of cumulative sum procedures are found in terms of the generating functions of a certain SPRT. An example is discussed and some applications are given.
Correcting a Proof of a Characterization of the Exponential Distribution
Authors: Dufour Robert , Maag Urs R. , Van Eeden Constance
Published: December 2018

This article points out and corrects an error in the proof of Theorem 2 of Seshadri, Csörgö and Stephens (1969).
On the Elimination of Nuisance Parameters in the Proportional Odds Model
Authors: McCullagh Peter
Published: December 2018

The problem of eliminating nuisance parameters in the context of the proportional odds model is considered. The technique used involves a form of sequential conditioning but it is not equivalent to a conditional or partial likelihood. Applications to ordered responses in the context of a matched pairs design are considered but the method can also be used where the responses are continuous.
Two New Tests Associated with Analysis of Variance
Authors: Azzalini A. , Cox D. R.
Published: December 2018

Two new tests are described in connexion with analysis of variance. The first is for the presence of qualitative interaction between a treatment and an intrinsic factor, both with qualitatively defined levels. Such an interaction is said to be present if there are two levels of the treatment factor and two levels of the intrinsic factor such that the treatment difference has opposite signs at the two levels of the intrinsic factor. The second test is for the presence of a treatment effect which can be tested via any of a hierarchical sequence U  1, U  1 + U  2, …, U  1 + … + Ur of sums of squares. An allowance for selection is calculated.
Asymptotic Expansions for Distributions and Quantiles with Power Series Cumulants
Authors: Withers C. S.
Published: December 2018

Cornish and Fisher (1937) gave the first few terms of the formal expansions for the distribution and percentiles of an asymptotically normal random variable (r.v.) in terms of its cumulants. They also showed that these expansions can sometimes produce extremely accurate approximations. In practice the cumulants are first expanded as a power series in a known parameter n (such as the sample size or degrees of freedom), and these expansions are substituted into the Edgeworth and Cornish-Fisher expansions, which are then rearranged in powers of 1/√n and truncated. This paper gives explicit formulae for the general terms both for the Cornish-Fisher expansions and for the derived expansions.
A New Bayesian Analysis of a Random Effects Model
Authors: Ghosh Malay , Meeden Glen
Published: December 2018

For a typical random effects model in the one way analysis of variance a new Bayesian analysis is offered. An exchangeable prior distribution is defined over the parameters. It is suggested that rather than use the usual “F” test one should consider this as an estimation problem. The posterior distribution of a function of the parameters which measures the amount of variation present is found.
Bartlett Adjustments to the Likelihood Ratio Statistic and the Distribution of the Maximum Likelihood Estimator
Authors: Barndorff-Nielsen O. E. , Cox D. R.
Published: December 2018

For rather general parametric models, a simple connection is established between the Bartlett adjustment factor of the log-likelihood ratio statistic and the normalizing constant c of the formula c | ĵ |½ L̄ for the conditional distribution of a maximum likelihood estimator as applied to the full model and the model of the hypothesis tested. This leads to a relatively simple demonstration that division of the likelihood ratio statistic by a suitable constant or estimated factor improves the chi-squared approximation to its distribution. Various expressions for these quantities are discussed. In particular, for the case of a one-dimensional parameter an approximation to the constants involved is derived, which does not require integration over the sample space.
A Different Empirical Bayes Interpretation of Ridge and Stein Estimators
Authors: Oman Samuel D.
Published: December 2018

Ridge and Stein-like estimators have been motivated as being empirical Bayes estimates with respect to the prior β ~ N(0, τ2  V-  1) for the vector of regression coefficients β in the usual model y = Xβ + ϵ, where the hyperparameter τ2 is estimated from the data. V = I results in a ridge pattern of shrinkage while V = Xt X gives a Stein-like pattern. In this article an alternative formulation is considered, according to which the data represent a sample from a multivariate normal random vector (Y, X  1, …,Xp) and β gives the regression of Y on the Xi in the population. Ridge estimators are shown to arise as empirical Bayes estimators when one believes a priori that the independent variables are uncorrelated, while Stein-like estimators are shown to obtain under an indifference prior for the population dispersion matrix of the Xi.
Locally Best Invariant Tests of the Error Covariance Matrix of the Linear Regression Model
Authors: King Maxwell L. , Hillier Grant H.
Published: December 2018

This paper considers a class of hypothesis testing problems concerning the covariance matrix of the disturbances in the classical linear regression model. A test that is locally best invariant against one-sided alternative hypotheses is constructed and shown to be identical to a one-sided version of the Lagrange Multiplier test.
Tailor-Made Tests of Goodness of Fit
Authors: Hall Peter
Published: December 2018

We examine a large class of distributional tests equivalent to tests based on degenerate U-statistics. The factors which influence the performance of these tests are isolated. An analysis of the factors leads us to suggest tests with improved power properties against certain types of alternatives. One such test is based on a chi squared statistic which employs overlapping cells, rather than disjoint cells. It is shown that this test has power superior to that of the classical chi squared statistic.
The Use of Uncategorized Data to Improve the Performance of a Nonparametric Estimator of a Mixture Density
Authors: Hall Peter , Titterington D. M.
Published: December 2018

We present a very simple, utilitarian technique for combining categorized and uncategorized data to construct a nonparametric estimator of a component mixture density. The method can be used for a wide class of estimators, and provides a reduction in the variance compared with the estimator based solely on categorized data.
Analysis of Field Experiments by Least Squares Smoothing
Authors: Green Peter , Jennison Christopher , Seheult Allan
Published: December 2018

Assuming a smooth trend plus independent error model for the environmental effects in the yields of a field plot experiment, least squares smoothing methods are developed to estimate both the treatment effects and the unknown trend. Treatment estimates are closely related to those resulting from a generalized least squares analysis in which the covariance structure for the environmental effects has a particular form. However, the main emphases are on the accuracy of treatment estimates under a fixed smooth trend plus error model and the exploratory power of the basic method to isolate trend effects of unknown form.

Although the detailed development is for the one-dimensional case, generalizations of the smoothness concept and extensions to two dimensions are also discussed.

Application of the basic method is illustrated on three data sets and the results compared with other analyses.
A Distributional Model for Repeated Failure Time Measurements
Authors: Crowder Martin
Published: December 2018

A standard model for repeated measurements is based on the multivariate Normal distribution with equicorrelated variables. A corresponding analysis is developed for Weibull failure times. The resulting distribution has some attractive properties for practical application to multivariate failure times.
Balance, Orthogonality and Efficiency Factors in Factorial Design
Authors: Bailey R. A.
Published: December 2018

It is shown that (i) general balance with respect to the factorial structure and (ii) orthogonal factorial structure are essentially the same for factorial designs with a single system of blocks. Upper bounds for efficiency factors in generally balanced factorial designs are found which are tighter and more widely applicable than those previously available.
The Effect of Positive Dependence on Chi-Squared Tests for Categorical Data
Authors: Gleser Leon J. , Moore David S.
Published: December 2018

We introduce a general definition of positive dependence for finite-state processes, and show that if successive observations are positively dependent, all tests that are asymptotically equivalent to standard Pearson chi-squared tests have asymptotic null distributions stochastically larger than those obtained under the usual independence assumptions. Ignoring positive dependence therefore leads to too frequent rejection of null hypotheses. This qualitative conclusion applies in particular to certain cases of Markov dependence, and of dependence induced by cluster sampling, that have been studied by previous authors.
Bayesian Estimation of Finite Population Parameters in Categorical Data Models Incorporating Order Restrictions
Authors: Sedransk J. , Monahan J. , Chiu H. Y.
Published: December 2018

This note describes a Bayesian method for estimation of finite population parameters in general population surveys where acceptable regression-type models are typically unavailable. A categorical data model is adopted as in Ericson (1969, Section 4). However, specifications of smoothness are incorporated into the prior distribution. These smoothness conditions are expressed as unimodal or, possibly, multi-modal order relations among the category probabilities. Emphasis is placed on posterior inference about the finite population mean. Of independent interest is the methodology for evaluating the posterior moments and probabilities using Monte Carlo integration with importance sampling.
Predictive Likelihood Inference with Applications
Authors: Butler Ronald W.
Published: December 2018

Conditional and marginal predictive likelihood are defined and used in predicting unobserved or missing data. A distinction is made between predictive and estimative goals of a data analysis. Such methodology and distinctions are illustrated in the context of outlier theory and mixed model ANOVA.
Distinguishing Outlier Types in Time Series
Authors: Muirhead C. R.
Published: December 2018

Distinguishing an outlier in a time series arising through measurement error from one arising through a perturbation of the underlying system can be of use in data validation. In this paper a method of testing for the presence of an outlier of unknown type is proposed. Then the properties of a rule based on the likelihood ratio which attempts to distinguish the two types of outlier are examined and compared with those of the corresponding Bayes rules. An example involving data from an industrial production process is studied.
Screening in a Normal Model
Authors: Boys R. J. , Dunsmore I. R.
Published: December 2018

An individual is deemed ‘successful’ if the value of a certain measurement of interest Y lies in some given specification region. In situations in which Y is difficult to measure, the individuals may be screened using a correlated variable X which is easier to measure. The motivation behind screening is to try to increase the proportion of 'successes' by eliminating those individuals who are unlikely to be successful. Most approaches, except for very large sample situations, have incorporated the involved notions of tolerance regions. We present here a predictive approach to find the critical values of X for which the success probability for a retained future individual reaches a satisfactory level. A simple loss structure is also introduced to provide an alternative criterion for finding the critical values of the screening variable X. The methods are exemplified within the context of a bivariate normal model.
Existence of Maximum Likelihood Estimates in Regression Models for Grouped and Ungrouped Data
Authors: Silvapulle M. J. , Burridge J.
Published: December 2018

In general, concavity of the log likelihood alone does not imply that the MLE exists always. For a class of linear regression models for grouped and ungrouped data, a necessary and sufficient condition is obtained for the existence of the maximum likelihood estimator. This condition has an intuitively simple interpretation. Further, it turns out that there are similar necessary and sufficient conditions for the existence of maximum likelihood estimates for a number of other non-linear models such as Cox's Regression Model. For a given set of data, these conditions may be verified by Linear Programming Methods.