A NOTE ON A SEQUENTIAL GROUP t-TEST

A sequential probability ratio test (SPET) of the mean of a normal distribution with unknown variance, based on an independent sequence of groups of observations, is investigated and its efficiency compared with that of the WAGE sequential t-test, which is based on an invariantly sufficient sequence of test statistics.     

A Reparameterisation Of A Bivariate Gamma Extension

Becker and Roux (1981) invebiiyated a bivariate gamma extension based on a piausible physica! model. This paper introduces a useful reparameterisation of this bivariate gamma extension. Based on he suggested reparameterisation, a procedure that may be utilised to test for bivariate independence is discussed for a special case of the gamma extension     

A Model For Developing A Recreation Strategy

A model for use in developing a recreation strategy is described. The model utilises the general concepts of category analysis in estimating demand for recreation. The procedure is illustrated by an analysis of the demand for active indoor sports and games in South Yorkshire. It is concluded that the methodology described might provide a useful instrument for regional recreational planning.     

A. S. A. Programs

Arranged for the 25th Session of the INTERNATIONAL STATISTICAL INSTITUTE     

A FINE-TUNED ESTIMATOR OF A GENERAL CONVERGENCE RATE

A general rate estimation method based on the in‐sample evolution of appropriately chosen diverging/converging statistics has recently been proposed by D.N. Politis [C. R. Acad. Sci. Paris, Ser. I, vol. 335, pp. 279–282, 2002] and T. McElroy & D.N. Politis [Ann. Statist., vol. 35, pp. 1827–1848, 2007]. In this paper, we show how a modification of the original estimators achieves a competitive rate of convergence. The modified estimators require the choice of a tuning parameter; an optimal such choice is generally a non‐trivial problem in practice. Some discussion to that effect is given, as well as a small simulation study in a heavy‐tailed setting.     

DECOMPOSITION OF A SEMI-MARKOV PROCESS UNDER A MARKOVIAN RULE

Consider a semi-Markov process {X(t), t>0} with transition epochs T₀ T₁, T₂…. Suppose that at each one of the epochs {T_n} one of R possible events, E₁, E₂,…, E_R can happen, where the occurrences of successive events form a Markov chain. for a fixed r, let the times the event E_r happens be U_o U₁, U₂,…. In this paper we are interested in the process {Y(t), t>0)} where Y(t)=X(U_k) if and only if U_k≤tk+1. It will be shown that {Y(t)} is a semi-Markov process, and its properties with respect to those of {X(t)} will be examined.     

A GROUP OF SPLIT-PLOT DESIGNS WITH A HETEROSCEDASTIC MODEL

For a group of split-plot designs it is assumed that the error variance is constant for a particular experiment but it varies from experiment to experiment. Assuming error variances to be known, estimators of the treatment parameters are obtained by weighted (generalised) least squares method and the corresponding analysis is given. For unknown error variances, an adjustment of the statistics using estimated weights is proposed for removing much of the resulting bias. The adjustment stems from a theorem due to Meier (1953).     

ELICITING A DIRECTED ACYCLIC GRAPH FOR A MULTIVARIATE TIME SERIES OF VEHICLE COUNTS IN A TRAFFIC NETWORK

The problem of modelling multivariate time series of vehicle counts in traffic networks is considered. It is proposed to use a model called the linear multiregression dynamic model (LMDM). The LMDM is a multivariate Bayesian dynamic model which uses any conditional independence and causal structure across the time series to break down the complex multivariate model into simpler univariate dynamic linear models. The conditional independence and causal structure in the time series can be represented by a directed acyclic graph (DAG). The DAG not only gives a useful pictorial representation of the multivariate structure, but it is also used to build the LMDM. Therefore, eliciting a DAG which gives a realistic representation of the series is a crucial part of the modelling process. A DAG is elicited for the multivariate time series of hourly vehicle counts at the junction of three major roads in the UK. A flow diagram is introduced to give a pictorial representation of the possible vehicle routes through the network. It is shown how this flow diagram, together with a map of the network, can suggest a DAG for the time series suitable for use with an LMDM.     

A LINEAR MODEL WITH ERRORS LACKING A VARIANCE II1

Numerical results are presented for estimates of the parameters in the linear model Y =βX +ε in which X is normally distributed and ε is symmetric stable. The study complements an earlier paper of the same title and the main concern is with numerical comparisons between four estimates of β; the least squares estimate, the minimum absolute deviations estimate, and two moment estimates of the form derived in Chambers and Heathcote (1975). The generation of fifty independent sets of observations (X_j, Y_j), j = 1,2, …, n for each of n = 100, 500 and selected combinations of parameter values provided the basis of the results. It is indicated that the moment estimators and the minimum absolute deviation estimator performed comparably, and are a significant improvement on the least squares estimator. The main conclusion is that one of the moment estimates, based on a two stage adaptive procedure and denoted by β¯_n(t_a) below, is generally the most useful of the four.     

A Modest Proposal: A New Standard for the Normal

The extensive research literature in many areas of behavioral, medical, and social sciences has led some reviewers to the use of quantitative methods for research synthesis. Typically, these analyses have involved estimating the effect magnitude from each of a series of studies and averaging the estimates to obtain a single index of effect magnitude. This article provides some statistical methods for estimating and testing linear models for effect magnitude and can be used for determining the effect of variations in experimental conditions. These methods can be used for synthesizing the results of studies where the index of effect magnitude is a correlation coefficient or standardized mean difference. A natural test for model specification is also given.     

A cautionary tale

Anthony Edwards wrote this cautionary tale for genetics students at Stanford University whom he was teaching in 1965. It has not previously been published. "Its appearance now is due to my having been asked whether a copy from the papers of the Nobel Laureate Joshua Lederberg might be put on the web by the US National Library of Medicine", he says. "Lederberg was Professor of Genetics at Stanford at the time and I must have given him a copy. More remarkably, he thought it worth keeping." It concerns what is known as Simpson's paradox.     

A rich opportunity

Certain sectors are well known for employing large numbers of statisticians, points out David Hand. These include the pharmaceutical sector, medical research and government. Less well known, however, is that the personal . Financial services sector also requires large numbers of numerate people, and that statisticians, with their understanding of risk and uncertainty and their ability to extract information from large quantities of data, are in particular demand.