Predicting distances using a linear model: the case of varietal distinctness

Differences between plant varieties are based on phenotypic observations, which are both space and time consuming. Moreover, the phenotypic data result from the combined effects of genotype and environment. On the contrary, molecular data are easier to obtain and give a direct access to the genotype. In order to save experimental trials and to concentrate efforts on the relevant comparisons between varieties, the relationship between phenotypic and genetic distances is studied. It appears that the classical genetic distances based on molecular data are not appropriate for predicting phenotypic distances. In the linear model framework, we define a new pseudo genetic distance, which is a prediction of the phenotypic one. The distribution of this distance given the pseudo genetic distance is established. Statistical properties of the predicted distance are derived when the parameters of the model are either given or estimated. We finally apply these results to distinguishing between 144 maize lines. This case study is very satisfactory because the use of anonymous molecular markers (RFLP) leads to saving 29% of the trials with an acceptable error risk. These results need to be confirmed on other varieties and species and would certainly be improved by using genes coding for phenotypic traits.     

The quincunx: history and mathematics

Received: December 30, 1999; revised version: July 19, 2000     

Modelling change in cognitive understanding with finite mixtures

Psychological theories often posit the existence of several different states. Individuals are viewed as belonging to one of the states at a given age, but with development pass to another state. A main problem in evaluating such theories is representing the transition from one state to another over age. A stochastic transition framework is proposed which should be useful in many different settings. The model is illustrated with data from a cognitive development task.     

Restricted minimax robust designs for misspecified regression models

The authors propose and explore new regression designs. Within a particular parametric class, these designs are minimax robust against bias caused by model misspecification while attaining reasonable levels of efficiency as well. The introduction of this restricted class of designs is motivated by a desire to avoid the mathematical and numerical intractability found in the unrestricted minimax theory. Robustness is provided against a family of model departures sufficiently broad that the minimax design measures are necessarily absolutely continuous. Examples of implementation involve approximate polynomial and second order multiple regression.     

The hybrid self and the ambivalence of boundaries

The paper outlines the main features of the contemporary discourse on hybrid subjectivity, a discourse which is internally differentiated along ‘organic’, ‘intentional’, and critical social theory lines. It then examines how these discourses can be applied to our understanding of hybrid cultures and identities. The article focuses on two central claims underlying the intentional approach: one, that cultural boundaries are theoretically and empirically problematic; and secondly, that a hybrid position provides the potential for an enlightened and critical world-view. In response, two contentions are articulated that will provide a more nuanced understanding of the hybrid self. Drawing on the work of Simmel and Park, the paper, in contrast to the intentional account, highlights the ambivalence of boundaries; secondly, a critical investigation of the enlightened hybrid consciousness is offered which suggests that this new form of consciousness underplays the role of prejudice and ambivalence. As a result of these discussions, the article demonstrates that the discourse on hybrid identity raises key theoretical issues either ignored or insufficiently addressed by existing scholarship.     

Data skeletons: simultaneous estimation of multiple quantiles for massive streaming datasets with applications to density estimation

We consider the problem of density estimation when the data is in the form of a continuous stream with no fixed length. In this setting, implementations of the usual methods of density estimation such as kernel density estimation are problematic. We propose a method of density estimation for massive datasets that is based upon taking the derivative of a smooth curve that has been fit through a set of quantile estimates. To achieve this, a low-storage, single-pass, sequential method is proposed for simultaneous estimation of multiple quantiles for massive datasets that form the basis of this method of density estimation. For comparison, we also consider a sequential kernel density estimator. The proposed methods are shown through simulation study to perform well and to have several distinct advantages over existing methods.     

Feature significance in generalized additive models

This paper develops inference for the significance of features such as peaks and valleys observed in additive modeling through an extension of the SiZer-type methodology of Chaudhuri and Marron (1999) and Godtliebsen et al. (2002, 2004) to the case where the outcome is discrete. We consider the problem of determining the significance of features such as peaks or valleys in observed covariate effects both for the case of additive modeling where the main predictor of interest is univariate as well as the problem of studying the significance of features such as peaks, inclines, ridges and valleys when the main predictor of interest is geographical location. We work with low rank radial spline smoothers to allow to the handling of sparse designs and large sample sizes. Reducing the problem to a Generalised Linear Mixed Model (GLMM) framework enables derivation of simulation-based critical value approximations and guards against the problem of multiple inferences over a range of predictor values. Such a reduction also allows for easy adjustment for confounders including those which have an unknown or complex effect on the outcome. A simulation study indicates that our method has satisfactory power. Finally, we illustrate our methodology on several data sets.     

Easy-to-construct confidence bands for comparing two simple linear regression lines

This paper shows how to construct confidence bands for the difference between two simple linear regression lines. These confidence bands provide directly the information on the magnitude of the difference between the regression lines over an interval of interest and, as a by-product, can be used as a formal test of the difference between the two regression lines. Various different shapes of confidence bands are illustrated, and particular attention is paid towards confidence bands whose construction only involves critical points from standard distributions so that they are consequently easy to construct.     

Double Sampling Ratio-product Estimator of a Finite Population Mean in Sample Surveys

It is well known that two-phase (or double) sampling is of significant use in practice when the population parameter(s) (say, population mean X¯) of the auxiliary variate x is not known. Keeping this in view, we have suggested a class of ratio-product estimators in two-phase sampling with its properties. The asymptotically optimum estimators (AOEs) in the class are identified in two different cases with their variances. Conditions for the proposed estimator to be more efficient than the two-phase sampling ratio, product and mean per unit estimator are investigated. Comparison with single phase sampling is also discussed. An empirical study is carried out to demonstrate the efficiency of the suggested estimator over conventional estimators.     

On-Line Scheduling of Two-Machine Open Shops Where Jobs Arrive Over Time

We investigate the problem of on-line scheduling two-machine open shops with the objective of minimizing the makespan.Jobs arrive independently over time, and the existence of a job is not known until its arrival. In the clairvoyant on-line model, the processing requirement of every job becomes fully known at the arrival of the job, while inthe non-clairvoyant on-line model, this processing requirement is notknown until the job is processed and completed.In both models, scheduling of a job is irrevocable.We study the two-machine open shop problem for both models in the preemptive and in the non-preemptive version. For each of the four variants, we provide an algorithm that is best possible with respect to the worst-case performance. In the clairvoyant on-line model, the best worst-case performance ratios are 5/4 (preemptive) and 3/2 (non-preemptive), and in the non-clairvoyant on-line model, they are 3/2 (preemptive and non-preemptive).