Using quantile averages in matched observational studies

In two observational studies, one investigating the effects of minimum wage laws on employment and the other of the effects of exposures to lead, an estimated treatment effect's sensitivity to hidden bias is examined. The estimate uses the combined quantile averages that were introduced in 1981 by B. M. Brown as simple, efficient, robust estimates of location admitting both exact and approximate confidence intervals and significance tests. Closely related to Gastwirth's estimate and Tukey's trimean, the combined quantile average has asymptotic efficiency for normal data that is comparable with that of a 15% trimmed mean, and higher efficiency than the trimean, but it has resistance to extreme observations or breakdown comparable with that of the trimean and better than the 15% trimmed mean. Combined quantile averages provide consistent estimates of an additive treatment effect in a matched randomized experiment. Sensitivity analyses are discussed for combined quantile averages when used in a matched observational study in which treatments are not randomly assigned. In a sensitivity analysis in an observational study, subjects are assumed to differ with respect to an unobserved covariate that was not adequately controlled by the matching, so that treatments are assigned within pairs with probabilities that are unequal and unknown. The sensitivity analysis proposed here uses significance levels, point estimates and confidence intervals based on combined quantile averages and examines how these inferences change under a range of assumptions about biases due to an unobserved covariate. The procedures are applied in the studies of minimum wage laws and exposures to lead. The first example is also used to illustrate sensitivity analysis with an instrumental variable.     

Modelling Variability in the Branching Structure of Strawberry Inflorescences

The branching structure of inflorescences of the cultivated strawberry ( Fragaria × ananassa Duch.) is very variable. This paper demonstrates that some aspects of this variability are well described by a simple stochastic model of branching that has two adjustable parameters. The model is shown to provide a good fit to data from a set of almost 700 inflorescences of the cultivar Elsanta, collected over two successive years. For one parameter the maximum likelihood estimator is a moment estimator which is fully efficient even if the detailed branching structure of the inflorescences is not recorded. This parameter provides a convenient summary of branching vigour. The maximum likelihood estimator of the second parameter must be determined iteratively and can be quite inefficient unless the full branching structure is recorded. The model demonstrates that branching structure is affected by the order in which inflorescences emerge on the plant.     

Likelihood Factorizations for Mixed Discrete and Continuous Variables

Some general remarks are made about likelihood factorizations, distinguishing parameter-based factorizations and concentration-graph factorizations. Two parametric families of distributions for mixed discrete and continuous variables are discussed. Conditions on graphs are given for the circumstances under which their joint analysis can be split into separate analyses, each involving a reduced set of component variables and parameters. The result shows marked differences between the two families although both involve the same necessary condition on prime graphs. This condition is both necessary and sufficient for simplified estimation in Gaussian and for discrete log linear models.     

Weighted Approximations to Continuous Time Martingales with Applications

A weighted approximation to a sequence of continuous time martingales by a time transformed Wiener process is established. The basic tool of proof is the Skorohod imbedding for martingale difference sequences. As an application of the main result a useful weighted approximation to the randomly weighted uniform empirical process is derived. A number of other applications are also discussed.     

A methodological strategy for a one-number census in the UK

As a result of lessons learnt from the 1991 census, a research programme was set up to seek improvements in census methodology. Underenumeration has been placed top of the agenda in this programme, and every effort is being made to achieve as high a coverage as possible in the 2001 census. In recognition, however, that 100% coverage will never be achieved, the one-number census (ONC) project was established to measure the degree of underenumeration in the 2001 census and, if possible, to adjust fully the outputs from the census for that undercount. A key component of this adjustment process is a census coverage survey (CCS). This paper presents an overview of the ONC project, focusing on the design and analysis methodology for the CCS. It also presents results that allow the reader to evaluate the robustness of this methodology.     

Multivariate bandwidth selection for local linear regression

The existence and properties of optimal bandwidths for multivariate local linear regression are established, using either a scalar bandwidth for all regressors or a diagonal bandwidth vector that has a different bandwidth for each regressor. Both involve functionals of the derivatives of the unknown multivariate regression function. Estimating these functionals is difficult primarily because they contain multivariate derivatives. In this paper, an estimator of the multivariate second derivative is obtained via local cubic regression with most cross-terms left out. This estimator has the optimal rate of convergence but is simpler and uses much less computing time than the full local estimator. Using this as a pilot estimator, we obtain plug-in formulae for the optimal bandwidth, both scalar and diagonal, for multivariate local linear regression. As a simpler alternative, we also provide rule-of-thumb bandwidth selectors. All these bandwidths have satisfactory performance in our simulation study.     

SPC—a team effort for process improvement across four Area Control Centres

This paper describes an innovative application of statistical process control to the online remote control of the UK's gas transportation networks. The gas industry went through a number of changes in ownership, regulation, access to networks, organization and management culture in the 1990s. The application of SPC was motivated by these changes along with the desire to apply the best industrial statistics theory to practical problems. The work was initiated by a studentship, with the technology gradually being transferred to the industry. The combined efforts of control engineers and statisticians helped develop a novel SPC system. Having set up the control limits, a system was devised to automatically update and publish the control charts on a daily basis. The charts and an associated discussion forum are available to both managers and control engineers throughout the country at their desktop PCs. The paper describes methods of involving people to design first-class systems to achieve continual process improvement. It describes how the traditional benefits of SPC can be realized in a 'distal team working', and 'soft systems', context of four Area Control Centres, controlling a system delivering two thirds of the UK's energy needs.     

Boosting with Bayesian stumps

Boosting is a new, powerful method for classification. It is an iterative procedure which successively classifies a weighted version of the sample, and then reweights this sample dependent on how successful the classification was. In this paper we review some of the commonly used methods for performing boosting and show how they can be fit into a Bayesian setup at each iteration of the algorithm. We demonstrate how this formulation gives rise to a new splitting criterion when using a domain-partitioning classification method such as a decision tree. Further we can improve the predictive performance of simple decision trees, known as stumps, by using a posterior weighted average of them to classify at each step of the algorithm, rather than just a single stump. The main advantage of this approach is to reduce the number of boosting iterations required to produce a good classifier with only a minimal increase in the computational complexity of the algorithm.     

Recovering Information from Incremental Responses

Some yields analysed and reported in the literature have been adjusted by subtracting a control. It is found that full information can be recovered for estimable parameters and the error variance using these incremental responses, in comparison with unadjusted data. These findings are of practical importance, and they supplement materials usually found in a graduate course in linear inference. The issues are illustrated using a case study from the literature.     

SPC as a tool for creating a successful business measurement framework

Many companies are trying to get to the bottom of what their main objectives are and what their business should be doing. The new Six Sigma approach concentrates on clarifying business strategy and making sure that everything relates to company objectives. It is vital to clarify each part of the business in such a way that everyone can understand the causes of variation that can lead to improvements in processes and performance. This paper describes a situation where the full implementation of SPC methodology has made possible a visual and widely appreciated summary of the performance of one important aspect of the business. The major part of the work was identifying the core objectives and deciding how to encapsulate each of them in one or more suitable measurements. The next step was to review the practicalities of obtaining the measurements and their reliability and representativeness. Finally, the measurements were presented in chart form and the more traditional steps of SPC analysis were commenced. Data from fast changing business environments are prone to many different problems, such as the short previous span of typical data, strange distributions and other uncertainties. Issues surrounding these and the eventual extraction of a meaningful set of information will be discussed in the paper. The measurement framework has proved very useful and, from an initial circulation of a handful of people, it now forms an important part of an information process that provides responsible managers with valuable control information. The measurement framework is kept fresh and vital by constant review and modifications. Improved electronic data collection and dissemination of the report has proved very important.