New imperfect rankings models for ranked set sampling

Ranked set sampling is a sampling approach that leads to improved statistical inference in situations where the units to be sampled can be ranked relative to each other prior to formal measurement. This ranking may be done either by subjective judgment or according to an auxiliary variable, and it need not be completely accurate. In fact, results in the literature have shown that no matter how poor the quality of the ranking, procedures based on ranked set sampling tend to be at least as efficient as procedures based on simple random sampling. However, efforts to quantify the gains in efficiency for ranked set sampling procedures have been hampered by a shortage of available models for imperfect rankings. In this paper, we introduce a new class of models for imperfect rankings, and we provide a rigorous proof that essentially any reasonable model for imperfect rankings is a limit of models in this class. We then describe a specific, easily applied method for selecting an appropriate imperfect rankings model from the class.     

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.     

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.     

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.     

Estimating the distribution function using k-tuple ranked set samples

The basic assumption underlying the concept of ranked set sampling is that actual measurement of units is expensive, whereas ranking is cheap. This may not be true in reality in certain cases where ranking may be moderately expensive. In such situations, based on total cost considerations, k-tuple ranked set sampling is known to be a viable alternative, where one selects k units (instead of one) from each ranked set. In this article, we consider estimation of the distribution function based on k-tuple ranked set samples when the cost of selecting and ranking units is not ignorable. We investigate estimation both in the balanced and unbalanced data case. Properties of the estimation procedure in the presence of ranking error are also investigated. Results of simulation studies as well as an application to a real data set are presented to illustrate some of the theoretical findings.     

The Development of Affect Specificity in Infants' Use of Emotion Cues

This study examined the emergence of affect specificity in infancy. In this study, infants received verbal and facial signals of 2 different, negatively valenced emotions (fear and sadness) as well as neutral affect via a television monitor to determine if they could make qualitative distinctions among emotions of the same valence. Twenty 12‐ to 14‐month‐olds and 20 16‐ to 18‐month‐olds were examined. Results suggested that younger infants showed no evidence of referential specificity, as they responded similarly to both the target and distracter toys, and showed no evidence of affect specificity, showing no difference in play between affect conditions. Older infants, in contrast, showed evidence both of referential and affect specificity. With respect to affect specificity, 16‐ to 18‐month‐olds touched the target toy less in the fear condition than in the sad condition and showed a larger proportion of negative facial expressions in the sad condition versus the fear condition. These findings suggest a developmental emergence after 15 months of age for affect specificity in relating emotional messages to objects.