Linear Estimators and Predictors Based on Generalized Order Statistics from Generalized Pareto Distributions

Prediction of record values by using quantile regression curves and distortion functions

The purpose of the paper is to provide a general method based on conditional quantile curves to predict record values from preceding records. The predictions are based on conditional median (or median regression) curves. Moreover, conditional quantiles curves are used to provide confidence bands for these predictions. The method is based on the recently introduced concept of multivariate distorted distributions that are used instead of copulas to represent the dependence structure. This concept allows us to compute the conditional quantile curves in a simple way. The theoretical findings are illustrated with a non-parametric model (standard uniform), two parametric models (exponential and Pareto), and a non-parametric procedure for the general case. A real data set and a simulated case study in reliability are analysed.

Eleven biosynthetic genes explain the majority of natural variation in carotenoid levels in maize grain

Vitamin A deficiency remains prevalent in parts of Asia, Latin America, and sub-Saharan Africa where maize (Zea mays) is a food staple. Extensive natural variation exists for carotenoids in maize grain. Here, to understand its genetic basis, we conducted a joint linkage and genome-wide association study of the US maize nested association mapping panel. Eleven of the 44 detected quantitative trait loci (QTL) were resolved to individual genes. Six of these were correlated expression and effect QTL (ceeQTL), showing strong correlations between RNA-seq expression abundances and QTL allelic effect estimates across six stages of grain development. These six ceeQTL also had the largest percentage of phenotypic variance explained, and in major part comprised the three to five loci capturing the bulk of genetic variation for each trait. Most of these ceeQTL had strongly correlated QTL allelic effect estimates across multiple traits. These findings provide an in-depth genome-level understanding of the genetic and molecular control of carotenoids in plants. In addition, these findings provide a roadmap to accelerate breeding for provitamin A and other priority carotenoid traits in maize grain that should be readily extendable to other cereals.

Maximum product of spacings prediction of future record values

A spacings-based prediction method for future upper record values is proposed as an alternative to maximum likelihood prediction. For an underlying family of distributions with continuous cumulative distribution functions, the general form of the predictor as a function of the estimator of the distributional parameters is established. A connection between this method and the maximum observed likelihood prediction procedure is shown. The maximum product of spacings predictor turns out to be useful to predict the next record value in contrast to likelihood-based procedures, which provide trivial predictors in this particular case. Moreover, examples are given for the exponential and the Pareto distributions, and a real data set is analyzed.

Maximum observed likelihood prediction of future record values

Point prediction of future upper record values is considered. For an underlying absolutely continuous distribution with strictly increasing cumulative distribution function, the general form of the predictor obtained by maximizing the observed predictive likelihood function is established. The results are illustrated for the exponential, extreme-value and power-function distributions, and the performance of the obtained predictors is compared to that of maximum likelihood predictors on the basis of the mean squared error and the Pitman’s measure of closeness criteria. For exponential and extreme-value distributions, it is shown that under slight restrictions, the maximum observed likelihood predictor outperforms the maximum likelihood predictor in terms of both performance criteria.

Use of crash surrogates and exceedance statistics to estimate road safety

The limited ability of existing safety models to properly reflect crash causality has its source in cross-sectional analysis applied to the estimation of the intrinsically complex safety factors with highly aggregated and frequently poor quality of data. The adequacy of the data may be improved thanks to the unprecedented progress in sensing technologies and the invention of the naturalistic driving method of data collection. Proposed in this paper is a new modeling paradigm that integrates several types of safety models. The primary improvement results from a more adequate representation of the crash occurrence process by incorporating crash precursor events into the modeling framework. A Pareto-based estimating method for the likelihood of a collision occurrence, given a precursor event, is explained and illustrated with the simple example of road departures.