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.     

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.     

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.     

Optimal scaling of Metropolis algorithms: Heading toward general target distributions

The authors provide an overview of optimal scaling results for the Metropolis algorithm with Gaussian proposal distribution. They address in more depth the case of high‐dimensional target distributions formed of independent, but not identically distributed components. They attempt to give an intuitive explanation as to why the well‐known optimal acceptance rate of 0.234 is not always suitable. They show how to find the asymptotically optimal acceptance rate when needed, and they explain why it is sometimes necessary to turn to inhomogeneous proposal distributions. Their results are illustrated with a simple example.     

A Bayesian Hierarchical Model for the Evaluation of a Website

Consider a website and the surfers visiting its pages. A typical issue of interest, for example while monitoring an advertising campaign, concerns whether a specific page has been designed successfully, i.e. is able to attract surfers or address them to other pages within the site. We assume that the surfing behaviour is fully described by the transition probabilities from one page to another, so that a clickstream (sequence of consecutively visited pages) can be viewed as a finite-state-space Markov chain. We then implement a variety of hierarchical prior distributions on the multivariate logits of the transition probabilities and define, for each page, a content effect and a link effect. The former measures the attractiveness of the page due to its contents, while the latter signals its ability to suggest further interesting links within the site. Moreover, we define an additional effect, representing overall page success, which incorporates both effects previously described. Using WinBUGS, we provide estimates and credible intervals for each of the above effects and rank pages accordingly.     

Glass ceilings or sticky floors? A model of high-income law graduates

Minorities and females are underrepresented in the top-income quintile of law school graduates. Employing a binary logistic regression model, I examine whether this is due to a“glass ceiling” (an invisible barrier erected by third parties) or a“sticky floor” (self-imposed limitations regarding employment). My major finding is that being female, a minority, or disabled did not significantly reduce one's probability of making the top-income quintile once hours of work, experience, and other factors are taken into account. My findings directly contradict the large body of glass-ceiling literature and support the sticky-floor model. I thank the Law School Admission Council for funding this research. Helpful comments and suggestions were received from Robert Nelson of Northwestern University and the American Bar Foundation, Steven Conroy of the University of West Florida, and R. Kim Craft and Douglas Bonzo of Southern Utah University. The views expressed here are solely those of the author and do not necessarily reflect those of the institutions or persons listed above.     

CORPORATE TAX INCIDENCE AND INEFFICIENCY WHEN CORPORATE AND NONCORPORATE GOODS ARE CLOSE SUBSTITUTES

An important deficiency in Harberger's [1962] model of corporate income taxation is its inability to consider both corporate and noncorporate production of the same good. Within-industry substitution has potentially major implications for both the excess burden and incidence of the corporate tax.
We analyze this within-industry substitution using a model in which each industry/sector contains corporate and noncorporate firms (with identical production functions) which produce goods that are close substitutes. The scope for considerable within-industry substitution of noncorporate for corporate capital leads to a very much larger excess burden than that in the Harberger model.