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.     

Loss functions for estimation of extrema with an application to disease mapping

It is often of interest to find the maximum or near maxima among a set of vector‐valued parameters in a statistical model; in the case of disease mapping, for example, these correspond to relative‐risk “hotspots” where public‐health intervention may be needed. The general problem is one of estimating nonlinear functions of the ensemble of relative risks, but biased estimates result if posterior means are simply substituted into these nonlinear functions. The authors obtain better estimates of extrema from a new, weighted ranks squared error loss function. The derivation of these Bayes estimators assumes a hidden‐Markov random‐field model for relative risks, and their behaviour is illustrated with real and simulated data.     

An Empirical Examination of Quality Certification in a "Lemons Market"

This article examines the effect third-party certification has on a market characterized by adverse selection. Using an original data set from the market for young thoroughbreds, we show that certification alleviates problems of adverse selection by examining the effect certification has on breeder decisions to retain or sell horses and the effect these decisions have on observed prices. Data on the racetrack performance of the horses confirm the results.     

Profile of Some Patients Who Prematurely Terminate Analysis

This paper is concerned with cases in which patients who have been well established in treatment decide to end it prematurely. In examining the issue among my patients who left against my advice, I isolated in some of them a number of common traits, of which the existence of a long-standing idealizing transference was central. Four of these cases are presented, including two in which the resistance was successfully penetrated and two in which it was not and the patient left treatment. The definition of premature termination is seen in the context of that of a complete analysis.