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.     

Consistent maximum likelihood estimation of a unimodal density using shape restrictions

It is well known that the unimodal maximum likelihood estimator of a density is consistent everywhere but at the mode. The authors review various ways to solve this problem and propose a new estimator that is concave over an interval containing the mode; this interval may be chosen by the user or through an algorithm. The authors show how to implement their solution and compare it to other approaches through simulations. They show that the new estimator is consistent everywhere and determine its rate of convergence in the Hellinger metric.     

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.     

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.     

A spatiotemporal auto-regressive moving average model for solar radiation

Summary.  To investigate the variability in energy output from a network of photovoltaic cells, solar radiation was recorded at 10 sites every 10 min in the Pentland Hills to the south of Edinburgh. We identify spatiotemporal auto-regressive moving average models as the most appropriate to address this problem. Although previously considered computationally prohibitive to work with, we show that by approximating using toroidal space and fitting by matching auto-correlations, calculations can be substantially reduced. We find that a first-order spatiotemporal auto-regressive (STAR(1)) process with a first-order neighbourhood structure and a Matern noise process provide an adequate fit to the data, and we demonstrate its use in simulating realizations of energy output.     

Predicting body fat using weight–height indices

While body fat is the most accurate measure of obesity, its measurement requires special equipment that can be costly and time consuming to operate. Attention has thus typically focused on the easier to calculate body mass index (BMI). However, the ability of BMI to accurately identify obesity has been increasingly questioned. This paper focuses attention on whether more general body mass indices are appropriate measures of body fat. Using a data set of body fat, height, and weight measurements, general models are estimated which nest a wide variety of weight–height indices as special cases. In the absence of a race and gender categorisation, the conventional BMI was found to be the appropriate index with which to predict body fat. When such a categorisation was made, however, the BMI was never selected as the appropriate index. In general, predicted female body fat was some 10 kg higher than that of a male of identical build and predicted % body fat was over 11 percentage points higher, but age effects were smaller for females. Considerable racial differences in predicted body fat were found for males, but such differences were less marked for females. The implications of this finding for interpreting recent research on the effect of obesity on health, society, and economic factors are considered.