Median estimation through a regression transformation

The author considers the problem of constructing confidence intervals for the median of a future observation at certain values of exogenous variables, following a normalizing transformation. He shows that when this transformation is estimated, the usual interval obtained through an inverse transformation needs to be corrected, even when the sample size is large. He then gives a simple analytical solution to this problem and provides simulation results confirming the good small‐sample properties of the corrected interval. He also presents two concrete illustrations.     

Robust inference in generalized linear models for longitudinal data

The author develops a robust quasi‐likelihood method, which appears to be useful for down‐weighting any influential data points when estimating the model parameters. He illustrates the computational issues of the method in an example. He uses simulations to study the behaviour of the robust estimates when data are contaminated with outliers, and he compares these estimates to those obtained by the ordinary quasi‐likelihood method.     

Nonparametric adaptive likelihood weights

The weighted likelihood can be used to make inference about one population when data from similar populations are available. The author shows heuristically that the weighted likelihood can be seen as a special case of the entropy maximization principle. This leads him to propose the minimum averaged mean squared error (MAMSE) weights. He describes an algorithm for calculating these weights and shows its convergence using the Kuhn‐Tucker conditions. He explores the performance and properties of the weighted likelihood based on MAMSE weights through simulations.     

Accurate detection of excess over a standard based on a random sample

A known number N of packages each contain, in differing unknown amounts, both substances of no particular import and some substance of interest, the total weight of the latter substance for all N of the packages being an unknown quantity T. Based on the amounts of the substance of interest found in each of n (n ≦= N) randomly sampled packages one is to decide, with a very small probability of the error of wrongly deciding that T exceeds L, whether or not the quantity T exceeds a given amount L. An optimal way of doing this is presented in which the probability of the error of wrongly deciding that T exceeds L can be precisely bounded above as desired.     

Approximating bayesian inference by weighted likelihood

The author proposes to use weighted likelihood to approximate Bayesian inference when no external or prior information is available. He proposes a weighted likelihood estimator that minimizes the empirical Bayes risk under relative entropy loss. He discusses connections among the weighted likelihood, empirical Bayes and James‐Stein estimators. Both simulated and real data sets are used for illustration purposes.     

Prisoner escort in Scotland: Costs, projection and performance under scrutiny

David Eyre is a journalist. He says that he is a little ignorant when it comes to statistics, as he thinks many people in the media are. Which is pretty surprising when you consider the number of stories that are based on statistics—everything from crime surveys to NHS waiting lists. Here he and Sheila Bird describe how they sought to address this problem in the context of prisoner escort in Scotland.     

Skew Gaussian Process for Nonlinear Regression

In this article, we extend the Gaussian process for regression model by assuming a skew Gaussian process prior on the input function and a skew Gaussian white noise on the error term. Under these assumptions, the predictive density of the output function at a new fixed input is obtained in a closed form. Also, we study the Gaussian process predictor when the errors depart from the Gaussianity to the skew Gaussian white noise. The bias is derived in a closed form and is studied for some special cases. We conduct a simulation study to compare the empirical distribution function of the Gaussian process predictor under Gaussian white noise and skew Gaussian white noise.     

Deception and dishonesty with data: fraud in science

The scientific community was shaken last year when leading stem cell and cloning researcher Woo Suk Hwang was accused of making up his results. He is not alone; Newton, Sigmund Freud and Nobel prizewinners have all been accused of being less than honest with data. David Hand looks at fraud in science and finds it is hardly rare.     

The breakdown and influence properties of outlier rejection-plus-mean procedures

In a recent paper, Hampel (1985) studied the properties of rejection-plus-mean procedures as estimators of a location parameter. He reported that these procedures have low breakdown and high variance. In this article it is pointed out that these results are due to the outliers being rejected in a forwards-stepping manner, and when a more appropriate backwards-stepping approach is used, rejection-plus-mean procedures lead to estimators with high breakdown and high variance. In this article it is pointed out that these results are due to the outliers being rejected in a forwards-stepping manner, and when a more appropriate backwards-stepping approach is used, rejection-plus-mean procedures lead to estimator with high breakdown and redescending theoretical influence function.     

Generalized gamma parameter estimation and moment evaluation

The generalized gamma distribution includes the exponential distribution, the gamma distribution, and the Weibull distribution as special cases. It also includes the log-normal distribution in the limit as one of its parameters goes to infinity. Prentice (1974) developed an estimation method that is effective even when the underlying distribution is nearly log-normal. He reparameterized the density function so that it achieved the limiting case in a smooth fashion relative to the new parameters. He also gave formulas for the second partial derivatives of the log-density function to be used in the nearly log-normal case. His formulas included infinite summations, and he did not estimate the error in approximating these summations.

We derive approximations for the log-density function and moments of the generalized gamma distribution that are smooth in the nearly log-normal case and involve only finite summations. Absolute error bounds for these approximations are included. The approximation for the first moment is applied to the problem of estimating the parameters of a generalized gamma distribution under the constraint that the distribution have mean one. This enables the development of a correspondence between the parameters in a mean one generalized gamma distribution and certain parameters in acoustic scattering theory.     

Distribution‐free statistical intervals via ranked‐set sampling

The author shows how to construct distribution‐free statistical intervals from ranked‐set sampling. He considers the cases of confidence, tolerance, and prediction intervals. He shows how to compute their coverage probabilities and he compares their performance to that of intervals based on simple random sampling. He finds that the ranked‐set sampling‐based intervals are at least as good as their classical counterpart in most settings of interest, although the nature of the advantage depends on the type of interval considered.     

目光深远的统计学大师 ——张尧庭先生逝世五周年纪念

 张尧庭先生是一位目光深远的统计学大师。本文认为他生前提出的下述观点即“统计学的发展全靠数学与实际问题的推动”,“为反映整体的、动态的东西统计学必须要有新突破”,以及“促进数理统计和经济统计的学术交流”等,在今天仍然具有现实意义,可为我们现时的统计学教学与研究的深入发展提供有益参考。     

Some linear model techniques for analyzing small-circle spherical data

The author investigates least squares as a method for fitting small-circle models to a sample of unit vectors in R³. He highlights a local linear model underlying the estimation of the parameters of a circle. This model is used to construct an estimation algorithm and regression-type inference procedures for the parameters of a circle. It makes it possible to compare the fit of a small circle with that of a spherical ellipse. The limitations of the least-squares approach are emphasized: when the errors are bounded away from 0, the least-squares estimators are not consistent as the sample size goes to infinity. Two examples, concerned with the migration of elephant seals and with the classification of geological folds, are analyzed using the linear model techniques proposed in this work.     

Environmental stochasticity of gompertz model with time delay

We consider the environmental stochasticity of the Gompertz model with time delay when the parameters are assumed to be described by correlated Gaussian white noise processes. The delay kernel is assumed to be exponentially decaying and the Fokker-Planck equation is obtained in both the Stratonovich and Ito calculi. The exact expressions for the first and second order moments of the logarithm of population size are evaluated and the stability of the system in mean as well as In mean-square is discussed.     

CHARLES HENRY WICKENS: 1872–1939

An account of the life of the second Commonwealth Statistician, Charles Henry Wickens (1872–1939), has been given. After a primary school education in a Victorian country centre, Wickens became Associate of the Institute of Actuaries. Having joined the public service of Western Australia in 1897, he was appointed Compiler in the Commonwealth Bureau of Census and Statistics in 1906; he served as Commonwealth Statistician and Actuary, 1922 to 1932, giving outstanding service as government adviser and head of an important government department. He was a leader among theoretical and practical economists. His contributions to the study of Australian demography, especially life tables and vital statistics, were of the highest quality and permanent value. He made also scholarly contributions to actuarial theory and to the popularization of the work of the Bureau.     

Asymptotic properties of the complex valued non-linear regression model

The non-linear regression model, when the parameters are complex valued is considered here. Jennrich(1969) considered the non-linear regression model when the parameters are real valued. He first rigorously proved the existence of the least square estimator and showed its consistency properties and asymptotic normality. In this paper we generalise the idea for the com-plex parameters case. Large sample properties of the proposed estimator has been studied.     

关于我国民族统计几个基本理论问题的思考

我国实施西部大开发战略 ,在很大程度上是为了促进少数民族繁荣和推动民族自治地方社会经济的向前发展。这也是新世纪初期我国民族工作的首要任务。民族统计工作 ,作为民族工作的重要组成部分 ,肩负着为国家提供民族自治地方发展的数据信息、为提高少数民族人民生活水平献计献策、为党和政府制定正确的决策提供咨询意见的重任。新中国建立以来 ,我国政府一直进行着民族统计工作 ,改革开放以后 ,民族统计工作更是逐年得到加强。国家民委专门设立统计处 ,领导全国的民族统计工作 ,取得了很大的成绩 ,为国家民族工作做出了应有的贡献。但从目前…     

Defying symmetry

John Venn, Cambridge don, is best known for the "Venn diagram", which he introduced in the course of his lectures on logic and published in 1880. But he had other strings to his bow. He wrote The Logic of Chance, which greatly influenced the development of the frequentist viewpoint and included the first drawing of a random walk in the plane (accompanied by the realization that in the limit the figure was fractal, as we should now say). He gave the first British lecture course on Theory of Statistics, in the Moral Science Tripos in 1890, and among historians he is famous for that branch of local history which concentrates on colleges, universities and their members.     

An affine‐invariant multivariate sign test for cluster correlated data

The author presents a multivariate location model for cluster correlated observations. He proposes an affine‐invariant multivariate sign statistic for testing the value of the location parameter. His statistic is an adaptation of that proposed by Randles (2000). The author shows, under very mild conditions, that his test statistic is asymptotically distributed as a chi‐squared random variable under the null hypothesis. In particular, the test can be used for skewed populations. In the context of a general multivariate normal model, the author obtains values of his test's Pitman asymptotic efficiency relative to another test based on the overall average. He shows that there is an improvement in the relative performance of the new test as soon as intra‐cluster correlation is present Even in the univariate case, the new test can be very competitive for Gaussian data. Furthermore, the statistic is easy to compute, even for large dimensional data. The author shows through simulations that his test performs well compared to the average‐based test. He illustrates its use with real data.     

Modelling data observed irregularly over space and regularly in time

When the data has been collected regularly over time and irregularly over space, it is difficult to impose an explicit auto-regressive structure over the space as it is over time. We study a phenomenon on a number of fixed locations. On each location the process forms an auto-regressive time series. The second-order dependence over space is reflected by the covariance matrix of the noise process, which is ‘white’ in time but not over the space. We consider the asymptotic properties of our inference methods, when the number of recordings in time only tends to infinity.