Beer and statistics

Occasionally one meets a figure whose memories are of a different era. Stella Cunliffe was president of the Royal Statistical Society from 1975 to 1977. She was, as it happens, the first woman President—the Society has had just one other in the 30 years since then, which might seem on statistical grounds an under-representation. Julian Champkin interviewed her.     

Spatio-temporal modelling using B-spline for disease mapping: analysis of childhood cancer trends

To examine childhood cancer diagnoses in the province of Alberta, Canada during 1983–2004, we construct a generalized additive mixed model for the analysis of geographic and temporal variability of cancer ratios. In this model, spatially correlated random effects and temporal components are adopted. The interaction between space and time is also accommodated. Spatio-temporal models that use conditional autoregressive smoothing across the spatial dimension and B-spline over the temporal dimension are considered. We study the patterns of incidence ratios over time and identify areas with consistently high ratio estimates as areas for potential further investigation. We apply the method of penalized quasi-likelihood to estimate the model parameters. We illustrate this approach using a yearly data set of childhood cancer diagnoses in the province of Alberta, Canada during 1983–2004.     

Book review

W.G.Cochran: Sampling Techniques, 3rd. Ed. John Wiley & Sons, New York-Santa Barbara-London-Sydney-Toronto 1977. 428 S., £ 12.50; $21.50.

H.Toutenburg: Vorhersage in linearen Modellen. Akademie-Verlag, Berlin 1975, VIII, 176b S., 3 Tab., 28,– M.

O.Kallenberg: Random Measure. Akademie-Verlag, Berlin 1975; Academic Press, London 1976. 104 pp., 28,– M.     

RANDOMISATION AND THE 1975 SENATE BALLOT DRAW

“So the last shall be first, and the first last; for many be called, but few chosen.” Matthew 20:16 The “random” draw for positions on the Senate ballot papers in the 1975 election resulted in an apparently non-random ordering, to the possible advantage of one particular party. This paper assesses the statistical significance of the 1975 draw and looks at possible causes of the evident non-randomness. A simplified yet realistic mathematical model is used to describe conditions under which the so-called donkey vote can have an effect on the final outcome of the election, thereby confirming the widely-held belief that the order of parties on the Senate ballot paper is relevant. We examine other Senate elections between 1949 and 1983 for the existence of relevant non-randomness similar to the 1975 result. Finally, we report briefly on our submission to the 1983 Joint Select Committee on Electoral Reform, which led to an improvement in the randomisation procedure.     

A brief proof on the generalized variance bound of the relative efficiency in statistics

In this paper, we obtain a brief proof on the generalized varance bound of the relative efficiency that was simultaneously given by Bloomfield and Watson(1975) and by Knott (1975).     

Orthogonal arrays and designs for partial triallel crosses

Abstract

Some block designs for Partial triallel crosses (PTC) are constructed in this paper using (a) orthogonal arrays (p², r, p, 2), where p is prime or a power of prime and (b) semi - balanced arrays (p (p???1)/2, p, p, 2), where p is a prime or power of an odd prime. Designs constructed are optimal in the sense of Kiefer (1975 Kiefer, J. 1975. Construction and optimality of generalized Youden designs. In A survey of statistical design and linear models, ed. J. N. Srivastava, 333–353. Amsterdam: North Hollond. [Google Scholar]). Some new designs for PTC experiments are also obtained.     

Percentage points and power calculations for outlier tests in a regression situation

The usefulness of an extra sum of squares statistics Q_K for detecting K outliers has been discussed previously in the context of two-way tables. (See Gentleman and Wilk, 1975a, 1975b; John and Draper 1978; and Draper and John, 1980,) That work is extended here to straight line regression situations arising from, and motivated by, a specific set of research data. Percentage points for the appropriate test statistics are obtained by simulation, and approximations for these percentage points are suggested. Power calculations made for various designs and outlier situations are briefly summarized.     

The performance of the adaptive optimal estimator under the extended balanced loss function

The adaptive optimal estimator of Farebrother (1975) is discussed by many authors, but the goodness of fitted model criterion that is used to investigate the performance of estimators is quite often ignored. Shalabh, Toutenburg, and Heumann (2009) proposed the extended balanced loss function in which the mean squared error and the Zellner's balanced loss function are just special cases of it. In this paper, we discuss the performance of the adaptive optimal estimator of Farebrother (1975) under the extended balanced loss function. Moreover, a Monte Carlo simulation experiment is conducted to examine the performance of the estimator in finite samples.     

A note on the solution of sample size problems using the Odeh and Fox charts

The usefulness of the Odeh and Fox (1975) charts is much enhanced by having φ for v₂ = ∞, a value quickly found from a table of Haynam, Govindarajulu and Leone (1970).     

On the equivalence of conglomerability and disintegrability for unbounded random variables

Statistical Methods & Applications - We extend a result of Dubins (Ann Probab 3:89–99, 1975) from bounded to unbounded random variables. Dubins showed that a finitely additive expectation...     

A unification of tail estimators

This work considers estimators of the tails of the cdf, quantile function and edf, which are generally applicable because they use only those observations in the sample which exceed a high threshold value. Three seemingly different approaches have been proposed by Hill (1975), Hall (1982), and Pickands (1975). Herein the tail behavior of the underlying probability model is expressed using the density-quantile function. This general tail behavior model is shown to be a common origin for the parametric models proposed by Hill, Hall, and Pickands' GPD model. Further, this tail behavior model motivates a representation for the quantile function of the exceedences which is used to obtain a parametric model for tail estimates using the exceedences which unifies the seemingly different tail estimators mentioned above.     

A Survey regarding the Reporting of Simulation Studies

Hoaglin and Andrews (1975) proposed standards for computational practice and the reporting of computation-based studies. They observed that “statisticians … often pay too little attention to their own principles of design.” To see if the design and reporting had improved, we surveyed five major statistical journals for 1975, 1978, and 1981 to ascertain whether reported simulation studies involved a specified design, justified the choice of the number of iterations, and specified the random number generator(s) used. Eighteen percent of the 1,198 papers surveyed included results based on simulation. We found that 9% of the papers including a simulation study justified the choice of the number of iterations and 44% at least partially specified the random number generator. Hoaglin and Andrews's observation appears still to be true.     

On the robustness of the optimum balanced 2m factorial designs of resolution v (given by Srivastava and Chopra) in the presence of outliers

In this paper we study the sensitivity of the optimum balanced resolution V plans for 2^m factorials, to outliers, using the measure suggested by Box and Drapper (1975). We observe that the designs are robust, i.e., have low sensitivity.     

On Efron's Parameterization

This paper discusses a curved exponential family of distributions which is defined by a differential equation with respect to the expectation parameters in the two–dimensional exponential family. The differential equation considered here is the same as the one given by Efron (1975) for the trinomial distribution. This equation is extended here to a general exponential family, and called Efron's parameterization in the two–dimensional exponential family. The solution of Efron's parameterization is obtained explicitly in an exponential family, although Kumagai & Inagaki (1996) showed that there exists no proper solution of Efron's equation for the trinomial distribution, in line with the counterexample given by Efron (1975 p. 1206). The paper gives some characterizations of Efron's parameterization with special reference to Fisher's circle model. The implications of these characterizations are the two–dimensional normal distribution and a spiral curve in the plane.     

Book reviews

Data Reduction, Analysing and Interpreting Statistical Data by A S C Ehrenberg. John Wiley & Sons, (1975) pp xvii + 391. Price cloth £9.00, paper £3.95.     

Demographic issues in the Krosno voivodship from 1975 to 1984

An analysis of population trends in Krosno voivodship, Poland, for the period 1975-1984 is presented. Topics covered include population growth, density, and rural-urban distribution; natural increase; and selected demographic indicators.     

Interpenetrating subsampling of unequal samples and the estimator with distinct units

In this article Pathak's (1964) results on estimation of mean and variance for k-equal subsamples and Rao's (1975) result on the expectation of the reciprocal of the number of distinct units obtained from two unequal subsamples , for interpenetrating subsampling scheme, have been extended to the case of k-unequal subsamples.     

An Interview with Jean Hirons,CONSER Coordinator

Abstract

Jean Hirons, Cooperative Online Serials (CONSER) Coordinator, retired June 30 from the Library of Congress after a career of over thirty years in libraries. Jean plans to begin a new career as a pastel painter. I spoke to Jean in May 2003 to get her views on CONSER's role in developing standards for cataloging electronic resources. Serials Review 2003; 29:233–236.     

Short-run price forecast performance of individual and composite models for 496 corn cash markets

Using daily prices from 496 corn cash markets for July 2006–February 2011, this study investigates short-run forecast performance of 31 individual and 10 composite models for each market at horizons of 5, 10, and 30 days. Over the performance evaluation period September 2010–February 2011, two composite models are optimal across horizons for different markets based on the mean-squared error. For around half of the markets at the horizon of 5 days and most of them at 10 and 30 days, the mean-squared error of a market's optimal model is significantly different from those of at least other 23 models evaluated for it. Root-mean-squared error reductions through switching from non-optimal models to the optimal are generally around 0.40%, 0.55%, and 0.87% at horizons of 5, 10, and 30 days.     

Properties of a class of binary ARMA models

We investigate a class of ARMA-type models for stationary binary time series developed in [M. Kanter, Autoregression for discrete processes mod 2, J. Appl. Probabil. 12 (1975), pp. 371–375, E. McKenzie, Extending the correlation structure of exponential autoregressive-moving-average processes, J. Appl. Prob. 18 (1981), pp. 181–189.], which we shall refer to as BinARMA models. This sparsely parameterized model family is even able to deal with negative autocorrelations, which occur in language modelling, for instance. While the autocorrelation structure of the BinAR(p) models has been studied before in [M. Kanter, Autoregression for discrete processes mod 2, J. Appl. Probabil. 12 (1975), pp. 371–375], we shall present new results on the autocorrelation structure of general BinARMA models. These results simplify in the BinMA(q) case, while the known results concerning BinAR(p) models are included as a special case. A real-data example indicates possible fields of application of these models.