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.     

Constrained allocation problems with single-peaked preferences: An axiomatic analysis

We introduce a new class of problems that contains two existing classes: allocation problems with single-peaked preferences and bankruptcy problems. On this class, we analyze the implications of well-known properties such as Pareto optimality, strategy-proofness, resource-monotonicity, no-envy, equal treatment of equals, and two new properties we introduce, hierarchical no-envy and independence of nonbinding constraints. Unlike earlier literature, we consider rules that allow free-disposability. We present characterizations of a rule we introduce on this domain. We relate this rule to well-known rules on the aforementioned subdomains. Based on this relation, we present a characterization of a well-known bankruptcy rule called the constrained equal awards rule. Received: 22 June 2000/Accepted: 21 March 2002 This paper is based on the first chapter of my Ph.D. thesis submitted to the University of Rochester. I wish to thank my advisor, William Thomson, for helpful comments and suggestions.     

Goodness‐of‐fit methods for matched case‐control studies

The authors propose graphical and numerical methods for checking the adequacy of the logistic regression model for matched case‐control data. Their approach is based on the cumulative sum of residuals over the covariate or linear predictor. Under the assumed model, the cumulative residual process converges weakly to a centered Gaussian limit whose distribution can be approximated via computer simulation. The observed cumulative residual pattern can then be compared both visually and analytically to a certain number of simulated realizations of the approximate limiting process under the null hypothesis. The proposed techniques allow one to check the functional form of each covariate, the logistic link function as well as the overall model adequacy. The authors assess the performance of the proposed methods through simulation studies and illustrate them using data from a cardiovascular study.     

The Effect of Learning Experiences and Context on Infant Imitation and Generalization

Over the first years of life, infants gradually develop the ability to retrieve their memories across cue and contextual changes. Whereas maturational factors drive some of these developments in memory ability, experiences occurring within the learning event may also impact infants' ability to retrieve memories in new situations. In 2 experiments we examined whether it was possible to facilitate 12‐month‐old infants' generalization of learning in the deferred imitation paradigm by varying experiences before or during the demonstration session, or during the retention interval. In Experiment 1, altering the length, timing, or variability of training had no impact on generalization; infants showed a low, but consistent level of memory retrieval. In Experiment 2, infants who experienced a unique context for encoding and retrieval exhibited generalization; infants who experienced the context prior to the demonstration session, or during the retention interval, did not. Specificity is a robust feature of infant memory and is not substantially altered by encoding experiences in an observational learning paradigm. Previous history with a learning environment can, however, impact the flexibility of memory retrieval.     

Spaces of Participation in Pre‐School: Arenas for Establishing Power Orders?

This article reports an ethnographic study of pre‐school children's social knowledge domains. Results show how the children's shared knowledge concerning social status and social differentiation in the group was strengthened and confirmed during a traditional teacher‐led ring game, where they were supposed to choose a friend. We suggest that from the perspective of the children, the game situation may be understood as, at the same time, a space of participation and an arena for establishing the power order. From the perspective of the teacher, pedagogical intentions may be challenged as they encounter and are mediated and interpreted by children's peer‐cultures.     

Three-level main-effects designs exploiting prior information about model uncertainty

To explore the projection efficiency of a design, Tsai, et al [2000. Projective three-level main effects designs robust to model uncertainty. Biometrika 87, 467–475] introduced the Q criterion to compare three-level main-effects designs for quantitative factors that allow the consideration of interactions in addition to main effects. In this paper, we extend their method and focus on the case in which experimenters have some prior knowledge, in advance of running the experiment, about the probabilities of effects being non-negligible. A criterion which incorporates experimenters’ prior beliefs about the importance of each effect is introduced to compare orthogonal, or nearly orthogonal, main effects designs with robustness to interactions as a secondary consideration. We show that this criterion, exploiting prior information about model uncertainty, can lead to more appropriate designs reflecting experimenters’ prior beliefs.     

Statistical consulting

The paper and the special issue focus on the activity of statistical consulting and its varieties. This includes academic consulting, consulting to and in industry as well as statistics in public media.